Daily Papers

In natural language processing, it has been observed recently that generalization could be greatly improved by finetuning a large-scale language model pretrained on a large unlabeled corpus. Despite its recent success and wide adoption, finetuning a large pretrained language model on a downstream task is prone to degenerate performance when there are only a small number of training instances available. In this paper, we introduce a new regularization technique, to which we refer as "mixout", motivated by dropout. Mixout stochastically mixes the parameters of two models. We show that our mixout technique regularizes learning to minimize the deviation from one of the two models and that the strength of regularization adapts along the optimization trajectory. We empirically evaluate the proposed mixout and its variants on finetuning a pretrained language model on downstream tasks. More specifically, we demonstrate that the stability of finetuning and the average accuracy greatly increase when we use the proposed approach to regularize finetuning of BERT on downstream tasks in GLUE.

Convolutional neural network training can suffer from diverse issues like exploding or vanishing gradients, scaling-based weight space symmetry and covariant-shift. In order to address these issues, researchers develop weight regularization methods and activation normalization methods. In this work we propose a weight soft-regularization method based on the Oblique manifold. The proposed method uses a loss function which pushes each weight vector to have a norm close to one, i.e. the weight matrix is smoothly steered toward the so-called Oblique manifold. We evaluate our method on the very popular CIFAR-10, CIFAR-100 and ImageNet 2012 datasets using two state-of-the-art architectures, namely the ResNet and wide-ResNet. Our method introduces negligible computational overhead and the results show that it is competitive to the state-of-the-art and in some cases superior to it. Additionally, the results are less sensitive to hyperparameter settings such as batch size and regularization factor.

Pruning is a model compression method that removes redundant parameters in deep neural networks (DNNs) while maintaining accuracy. Most available filter pruning methods require complex treatments such as iterative pruning, features statistics/ranking, or additional optimization designs in the training process. In this paper, we propose a simple and effective regularization strategy from a new perspective of evolution of features, which we call feature flow regularization (FFR), for improving structured sparsity and filter pruning in DNNs. Specifically, FFR imposes controls on the gradient and curvature of feature flow along the neural network, which implicitly increases the sparsity of the parameters. The principle behind FFR is that coherent and smooth evolution of features will lead to an efficient network that avoids redundant parameters. The high structured sparsity obtained from FFR enables us to prune filters effectively. Experiments with VGGNets, ResNets on CIFAR-10/100, and Tiny ImageNet datasets demonstrate that FFR can significantly improve both unstructured and structured sparsity. Our pruning results in terms of reduction of parameters and FLOPs are comparable to or even better than those of state-of-the-art pruning methods.

Effective regularization techniques are highly desired in deep learning for alleviating overfitting and improving generalization. This work proposes a new regularization scheme, based on the understanding that the flat local minima of the empirical risk cause the model to generalize better. This scheme is referred to as adversarial model perturbation (AMP), where instead of directly minimizing the empirical risk, an alternative "AMP loss" is minimized via SGD. Specifically, the AMP loss is obtained from the empirical risk by applying the "worst" norm-bounded perturbation on each point in the parameter space. Comparing with most existing regularization schemes, AMP has strong theoretical justifications, in that minimizing the AMP loss can be shown theoretically to favour flat local minima of the empirical risk. Extensive experiments on various modern deep architectures establish AMP as a new state of the art among regularization schemes. Our code is available at https://github.com/hiyouga/AMP-Regularizer.

Sparsely gated Mixture of Experts (MoE) models have been shown to be a compute-efficient method to scale model capacity for multilingual machine translation. However, for low-resource tasks, MoE models severely over-fit. We show effective regularization strategies, namely dropout techniques for MoE layers in EOM and FOM, Conditional MoE Routing and Curriculum Learning methods that prevent over-fitting and improve the performance of MoE models on low-resource tasks without adversely affecting high-resource tasks. On a massively multilingual machine translation benchmark, our strategies result in about +1 chrF++ improvement in very low resource language pairs. We perform an extensive analysis of the learned MoE routing to better understand the impact of our regularization methods and how we can improve them.

This paper introduces Least Volume-a simple yet effective regularization inspired by geometric intuition-that can reduce the necessary number of latent dimensions needed by an autoencoder without requiring any prior knowledge of the intrinsic dimensionality of the dataset. We show that the Lipschitz continuity of the decoder is the key to making it work, provide a proof that PCA is just a linear special case of it, and reveal that it has a similar PCA-like importance ordering effect when applied to nonlinear models. We demonstrate the intuition behind the regularization on some pedagogical toy problems, and its effectiveness on several benchmark problems, including MNIST, CIFAR-10 and CelebA.

Aligning language models with human preferences is crucial for reducing errors and biases in these models. Alignment techniques, such as reinforcement learning from human feedback (RLHF), are typically cast as optimizing a tradeoff between human preference rewards and a proximity regularization term that encourages staying close to the unaligned model. Selecting an appropriate level of regularization is critical: insufficient regularization can lead to reduced model capabilities due to reward hacking, whereas excessive regularization hinders alignment. Traditional methods for finding the optimal regularization level require retraining multiple models with varying regularization strengths. This process, however, is resource-intensive, especially for large models. To address this challenge, we propose decoding-time realignment (DeRa), a simple method to explore and evaluate different regularization strengths in aligned models without retraining. DeRa enables control over the degree of alignment, allowing users to smoothly transition between unaligned and aligned models. It also enhances the efficiency of hyperparameter tuning by enabling the identification of effective regularization strengths using a validation dataset.

The generalization capability of deep neural networks has been substantially improved by applying a wide spectrum of regularization methods, e.g., restricting function space, injecting randomness during training, augmenting data, etc. In this work, we propose a simple yet effective regularization method named progressive self-knowledge distillation (PS-KD), which progressively distills a model's own knowledge to soften hard targets (i.e., one-hot vectors) during training. Hence, it can be interpreted within a framework of knowledge distillation as a student becomes a teacher itself. Specifically, targets are adjusted adaptively by combining the ground-truth and past predictions from the model itself. We show that PS-KD provides an effect of hard example mining by rescaling gradients according to difficulty in classifying examples. The proposed method is applicable to any supervised learning tasks with hard targets and can be easily combined with existing regularization methods to further enhance the generalization performance. Furthermore, it is confirmed that PS-KD achieves not only better accuracy, but also provides high quality of confidence estimates in terms of calibration as well as ordinal ranking. Extensive experimental results on three different tasks, image classification, object detection, and machine translation, demonstrate that our method consistently improves the performance of the state-of-the-art baselines. The code is available at https://github.com/lgcnsai/PS-KD-Pytorch.

Current image tokenization methods require a large number of tokens to capture the information contained within images. Although the amount of information varies across images, most image tokenizers only support fixed-length tokenization, leading to inefficiency in token allocation. In this study, we introduce One-D-Piece, a discrete image tokenizer designed for variable-length tokenization, achieving quality-controllable mechanism. To enable variable compression rate, we introduce a simple but effective regularization mechanism named "Tail Token Drop" into discrete one-dimensional image tokenizers. This method encourages critical information to concentrate at the head of the token sequence, enabling support of variadic tokenization, while preserving state-of-the-art reconstruction quality. We evaluate our tokenizer across multiple reconstruction quality metrics and find that it delivers significantly better perceptual quality than existing quality-controllable compression methods, including JPEG and WebP, at smaller byte sizes. Furthermore, we assess our tokenizer on various downstream computer vision tasks, including image classification, object detection, semantic segmentation, and depth estimation, confirming its adaptability to numerous applications compared to other variable-rate methods. Our approach demonstrates the versatility of variable-length discrete image tokenization, establishing a new paradigm in both compression efficiency and reconstruction performance. Finally, we validate the effectiveness of tail token drop via detailed analysis of tokenizers.

Multiple Instance Learning (MIL) has demonstrated effectiveness in analyzing whole slide images (WSIs), yet it often encounters overfitting challenges in real-world applications, particularly in the form of attention over-concentration. While existing methods to alleviate this issue introduce complex modules or processing steps, such as multiple-stage training and teacher-student distillation, this paper proposes a simple yet effective regularization: Attention Entropy Maximization (AEM). Motivated by our investigation revealing a positive correlation between attention entropy and model performance, AEM incorporates a negative entropy loss for attention values into the standard MIL framework, penalizing overly concentrated attention and encouraging the model to consider a broader range of informative regions in WSIs, potentially improving its generalization capabilities. Compared to existing overfitting mitigation methods, our AEM approach offers advantages of simplicity, efficiency, and versatility. It requires no additional modules or processing steps, involves only one hyperparameter, and demonstrates compatibility with MIL frameworks and techniques. These advantages make AEM particularly attractive for practical applications. We evaluate AEM on three benchmark datasets, demonstrating consistent performance improvements over existing methods. Furthermore, AEM shows high versatility, integrating effectively with four feature extractors, two advanced MIL frameworks, three attention mechanisms, and Subsampling augmentation technique. The source code is available at https://github.com/dazhangyu123/AEM.

In the realms of computer vision and natural language processing, Large Vision-Language Models (LVLMs) have become indispensable tools, proficient in generating textual descriptions based on visual inputs. Despite their advancements, our investigation reveals a noteworthy bias in the generated content, where the output is primarily influenced by the underlying Large Language Models (LLMs) prior rather than the input image. Our empirical experiments underscore the persistence of this bias, as LVLMs often provide confident answers even in the absence of relevant images or given incongruent visual input. To rectify these biases and redirect the model's focus toward vision information, we introduce two simple, training-free strategies. Firstly, for tasks such as classification or multi-choice question-answering (QA), we propose a ``calibration'' step through affine transformation to adjust the output distribution. This ``Post-Hoc debias'' approach ensures uniform scores for each answer when the image is absent, serving as an effective regularization technique to alleviate the influence of LLM priors. For more intricate open-ended generation tasks, we extend this method to ``Debias sampling'', drawing inspirations from contrastive decoding methods. Furthermore, our investigation sheds light on the instability of LVLMs across various decoding configurations. Through systematic exploration of different settings, we significantly enhance performance, surpassing reported results and raising concerns about the fairness of existing evaluations. Comprehensive experiments substantiate the effectiveness of our proposed strategies in mitigating biases. These strategies not only prove beneficial in minimizing hallucinations but also contribute to the generation of more helpful and precise illustrations.

In the pursuit of reducing the number of trainable parameters in deep transformer networks, we employ Reinforcement Learning to dynamically select layers during training and tie them together. Every few iterations, the RL agent is asked whether to train each layer i independently or to copy the weights of a previous layer j<i. This facilitates weight sharing, reduces the number of trainable parameters, and also serves as an effective regularization technique. Experimental evaluations validate that our model modestly outperforms the baseline transformer model with regard to perplexity and drastically reduces the number of trainable parameters. In particular, the memory consumption during training is up to one order of magnitude less than the conventional training method.

Existing losses used in deep metric learning (DML) for image retrieval often lead to highly non-uniform intra-class and inter-class representation structures across test classes and data distributions. When combined with the common practice of using a fixed threshold to declare a match, this gives rise to significant performance variations in terms of false accept rate (FAR) and false reject rate (FRR) across test classes and data distributions. We define this issue in DML as threshold inconsistency. In real-world applications, such inconsistency often complicates the threshold selection process when deploying commercial image retrieval systems. To measure this inconsistency, we propose a novel variance-based metric called Operating-Point-Inconsistency-Score (OPIS) that quantifies the variance in the operating characteristics across classes. Using the OPIS metric, we find that achieving high accuracy levels in a DML model does not automatically guarantee threshold consistency. In fact, our investigation reveals a Pareto frontier in the high-accuracy regime, where existing methods to improve accuracy often lead to degradation in threshold consistency. To address this trade-off, we introduce the Threshold-Consistent Margin (TCM) loss, a simple yet effective regularization technique that promotes uniformity in representation structures across classes by selectively penalizing hard sample pairs. Extensive experiments demonstrate TCM's effectiveness in enhancing threshold consistency while preserving accuracy, simplifying the threshold selection process in practical DML settings.

Semi-supervised learning, i.e. jointly learning from labeled and unlabeled samples, is an active research topic due to its key role on relaxing human supervision. In the context of image classification, recent advances to learn from unlabeled samples are mainly focused on consistency regularization methods that encourage invariant predictions for different perturbations of unlabeled samples. We, conversely, propose to learn from unlabeled data by generating soft pseudo-labels using the network predictions. We show that a naive pseudo-labeling overfits to incorrect pseudo-labels due to the so-called confirmation bias and demonstrate that mixup augmentation and setting a minimum number of labeled samples per mini-batch are effective regularization techniques for reducing it. The proposed approach achieves state-of-the-art results in CIFAR-10/100, SVHN, and Mini-ImageNet despite being much simpler than other methods. These results demonstrate that pseudo-labeling alone can outperform consistency regularization methods, while the opposite was supposed in previous work. Source code is available at https://git.io/fjQsC.

Text-to-image generative models have recently attracted considerable interest, enabling the synthesis of high-quality images from textual prompts. However, these models often lack the capability to generate specific subjects from given reference images or to synthesize novel renditions under varying conditions. Methods like DreamBooth and Subject-driven Text-to-Image (SuTI) have made significant progress in this area. Yet, both approaches primarily focus on enhancing similarity to reference images and require expensive setups, often overlooking the need for efficient training and avoiding overfitting to the reference images. In this work, we present the lambda-Harmonic reward function, which provides a reliable reward signal and enables early stopping for faster training and effective regularization. By combining the Bradley-Terry preference model, the lambda-Harmonic reward function also provides preference labels for subject-driven generation tasks. We propose Reward Preference Optimization (RPO), which offers a simpler setup (requiring only 3% of the negative samples used by DreamBooth) and fewer gradient steps for fine-tuning. Unlike most existing methods, our approach does not require training a text encoder or optimizing text embeddings and achieves text-image alignment by fine-tuning only the U-Net component. Empirically, lambda-Harmonic proves to be a reliable approach for model selection in subject-driven generation tasks. Based on preference labels and early stopping validation from the lambda-Harmonic reward function, our algorithm achieves a state-of-the-art CLIP-I score of 0.833 and a CLIP-T score of 0.314 on DreamBench.

Modern convolutional networks are not shift-invariant, as small input shifts or translations can cause drastic changes in the output. Commonly used downsampling methods, such as max-pooling, strided-convolution, and average-pooling, ignore the sampling theorem. The well-known signal processing fix is anti-aliasing by low-pass filtering before downsampling. However, simply inserting this module into deep networks degrades performance; as a result, it is seldomly used today. We show that when integrated correctly, it is compatible with existing architectural components, such as max-pooling and strided-convolution. We observe increased accuracy in ImageNet classification, across several commonly-used architectures, such as ResNet, DenseNet, and MobileNet, indicating effective regularization. Furthermore, we observe better generalization, in terms of stability and robustness to input corruptions. Our results demonstrate that this classical signal processing technique has been undeservingly overlooked in modern deep networks. Code and anti-aliased versions of popular networks are available at https://richzhang.github.io/antialiased-cnns/ .

Subword segmentation is widely used to address the open vocabulary problem in machine translation. The dominant approach to subword segmentation is Byte Pair Encoding (BPE), which keeps the most frequent words intact while splitting the rare ones into multiple tokens. While multiple segmentations are possible even with the same vocabulary, BPE splits words into unique sequences; this may prevent a model from better learning the compositionality of words and being robust to segmentation errors. So far, the only way to overcome this BPE imperfection, its deterministic nature, was to create another subword segmentation algorithm (Kudo, 2018). In contrast, we show that BPE itself incorporates the ability to produce multiple segmentations of the same word. We introduce BPE-dropout - simple and effective subword regularization method based on and compatible with conventional BPE. It stochastically corrupts the segmentation procedure of BPE, which leads to producing multiple segmentations within the same fixed BPE framework. Using BPE-dropout during training and the standard BPE during inference improves translation quality up to 3 BLEU compared to BPE and up to 0.9 BLEU compared to the previous subword regularization.

Denoising Diffusion Probabilistic Models have shown an impressive generation quality, although their long sampling chain leads to high computational costs. In this paper, we observe that a long sampling chain also leads to an error accumulation phenomenon, which is similar to the exposure bias problem in autoregressive text generation. Specifically, we note that there is a discrepancy between training and testing, since the former is conditioned on the ground truth samples, while the latter is conditioned on the previously generated results. To alleviate this problem, we propose a very simple but effective training regularization, consisting in perturbing the ground truth samples to simulate the inference time prediction errors. We empirically show that, without affecting the recall and precision, the proposed input perturbation leads to a significant improvement in the sample quality while reducing both the training and the inference times. For instance, on CelebA 64times64, we achieve a new state-of-the-art FID score of 1.27, while saving 37.5% of the training time. The code is publicly available at https://github.com/forever208/DDPM-IP

Policy constraint methods to offline reinforcement learning (RL) typically utilize parameterization or regularization that constrains the policy to perform actions within the support set of the behavior policy. The elaborative designs of parameterization methods usually intrude into the policy networks, which may bring extra inference cost and cannot take full advantage of well-established online methods. Regularization methods reduce the divergence between the learned policy and the behavior policy, which may mismatch the inherent density-based definition of support set thereby failing to avoid the out-of-distribution actions effectively. This paper presents Supported Policy OpTimization (SPOT), which is directly derived from the theoretical formalization of the density-based support constraint. SPOT adopts a VAE-based density estimator to explicitly model the support set of behavior policy and presents a simple but effective density-based regularization term, which can be plugged non-intrusively into off-the-shelf off-policy RL algorithms. SPOT achieves the state-of-the-art performance on standard benchmarks for offline RL. Benefiting from the pluggable design, offline pretrained models from SPOT can also be applied to perform online fine-tuning seamlessly.

Topic models have been prevalent for decades with various applications. However, existing topic models commonly suffer from the notorious topic collapsing: discovered topics semantically collapse towards each other, leading to highly repetitive topics, insufficient topic discovery, and damaged model interpretability. In this paper, we propose a new neural topic model, Embedding Clustering Regularization Topic Model (ECRTM). Besides the existing reconstruction error, we propose a novel Embedding Clustering Regularization (ECR), which forces each topic embedding to be the center of a separately aggregated word embedding cluster in the semantic space. This enables each produced topic to contain distinct word semantics, which alleviates topic collapsing. Regularized by ECR, our ECRTM generates diverse and coherent topics together with high-quality topic distributions of documents. Extensive experiments on benchmark datasets demonstrate that ECRTM effectively addresses the topic collapsing issue and consistently surpasses state-of-the-art baselines in terms of topic quality, topic distributions of documents, and downstream classification tasks.

Subword units are an effective way to alleviate the open vocabulary problems in neural machine translation (NMT). While sentences are usually converted into unique subword sequences, subword segmentation is potentially ambiguous and multiple segmentations are possible even with the same vocabulary. The question addressed in this paper is whether it is possible to harness the segmentation ambiguity as a noise to improve the robustness of NMT. We present a simple regularization method, subword regularization, which trains the model with multiple subword segmentations probabilistically sampled during training. In addition, for better subword sampling, we propose a new subword segmentation algorithm based on a unigram language model. We experiment with multiple corpora and report consistent improvements especially on low resource and out-of-domain settings.

Parameter regularization or allocation methods are effective in overcoming catastrophic forgetting in lifelong learning. However, they solve all tasks in a sequence uniformly and ignore the differences in the learning difficulty of different tasks. So parameter regularization methods face significant forgetting when learning a new task very different from learned tasks, and parameter allocation methods face unnecessary parameter overhead when learning simple tasks. In this paper, we propose the Parameter Allocation & Regularization (PAR), which adaptively select an appropriate strategy for each task from parameter allocation and regularization based on its learning difficulty. A task is easy for a model that has learned tasks related to it and vice versa. We propose a divergence estimation method based on the Nearest-Prototype distance to measure the task relatedness using only features of the new task. Moreover, we propose a time-efficient relatedness-aware sampling-based architecture search strategy to reduce the parameter overhead for allocation. Experimental results on multiple benchmarks demonstrate that, compared with SOTAs, our method is scalable and significantly reduces the model's redundancy while improving the model's performance. Further qualitative analysis indicates that PAR obtains reasonable task-relatedness.

Regional dropout strategies have been proposed to enhance the performance of convolutional neural network classifiers. They have proved to be effective for guiding the model to attend on less discriminative parts of objects (e.g. leg as opposed to head of a person), thereby letting the network generalize better and have better object localization capabilities. On the other hand, current methods for regional dropout remove informative pixels on training images by overlaying a patch of either black pixels or random noise. Such removal is not desirable because it leads to information loss and inefficiency during training. We therefore propose the CutMix augmentation strategy: patches are cut and pasted among training images where the ground truth labels are also mixed proportionally to the area of the patches. By making efficient use of training pixels and retaining the regularization effect of regional dropout, CutMix consistently outperforms the state-of-the-art augmentation strategies on CIFAR and ImageNet classification tasks, as well as on the ImageNet weakly-supervised localization task. Moreover, unlike previous augmentation methods, our CutMix-trained ImageNet classifier, when used as a pretrained model, results in consistent performance gains in Pascal detection and MS-COCO image captioning benchmarks. We also show that CutMix improves the model robustness against input corruptions and its out-of-distribution detection performances. Source code and pretrained models are available at https://github.com/clovaai/CutMix-PyTorch .

Prompt tuning is a parameter-efficient method, which learns soft prompts and conditions frozen language models to perform specific downstream tasks. Though effective, prompt tuning under few-shot settings on the one hand heavily relies on a good initialization of soft prompts. On the other hand, it can easily overfit to few-shot training samples, thereby undermining generalizability. Existing works leverage pre-training or supervised meta-learning to initialize soft prompts but they fail to data-efficiently generalize to unseen downstream tasks. To address the above problems, this paper proposes a novel Self-sUpervised meta-Prompt learning framework with MEta-gradient Regularization for few-shot generalization (SUPMER). SUPMER leverages self-supervised meta-learning with a diverse set of well-designed meta-training tasks to learn a universal prompt initialization for efficient adaptation using only unlabeled data. Additionally, it jointly meta-learns a gradient regularization function to transform raw gradients into a domain-generalizable direction, thus alleviating the problem of overfitting. Extensive experiments show that SUPMER achieves better performance for different few-shot downstream tasks, and also exhibits a stronger domain generalization ability. The code for SUPMER will be available at https://github.com/beepkh/SUPMER.

Pruning methods have recently grown in popularity as an effective way to reduce the size and computational complexity of deep neural networks. Large numbers of parameters can be removed from trained models with little discernible loss in accuracy after a small number of continued training epochs. However, pruning too many parameters at once often causes an initial steep drop in accuracy which can undermine convergence quality. Iterative pruning approaches mitigate this by gradually removing a small number of parameters over multiple epochs. However, this can still lead to subnetworks that overfit local regions of the loss landscape. We introduce a novel and effective approach to tuning subnetworks through a regularization technique we call Stochastic Subnetwork Annealing. Instead of removing parameters in a discrete manner, we instead represent subnetworks with stochastic masks where each parameter has a probabilistic chance of being included or excluded on any given forward pass. We anneal these probabilities over time such that subnetwork structure slowly evolves as mask values become more deterministic, allowing for a smoother and more robust optimization of subnetworks at high levels of sparsity.

We propose a simple yet effective strategy to incorporate event knowledge extracted from event trigger annotations via posterior regularization to improve the event reasoning capability of mainstream question-answering (QA) models for event-centric QA. In particular, we define event-related knowledge constraints based on the event trigger annotations in the QA datasets, and subsequently use them to regularize the posterior answer output probabilities from the backbone pre-trained language models used in the QA setting. We explore two different posterior regularization strategies for extractive and generative QA separately. For extractive QA, the sentence-level event knowledge constraint is defined by assessing if a sentence contains an answer event or not, which is later used to modify the answer span extraction probability. For generative QA, the token-level event knowledge constraint is defined by comparing the generated token from the backbone language model with the answer event in order to introduce a reward or penalty term, which essentially adjusts the answer generative probability indirectly. We conduct experiments on two event-centric QA datasets, TORQUE and ESTER. The results show that our proposed approach can effectively inject event knowledge into existing pre-trained language models and achieves strong performance compared to existing QA models in answer evaluation. Code and models can be found: https://github.com/LuJunru/EventQAviaPR.

In this paper, we study the problem of learning image classification models in the presence of label noise. We revisit a simple compression regularization named Nested Dropout. We find that Nested Dropout, though originally proposed to perform fast information retrieval and adaptive data compression, can properly regularize a neural network to combat label noise. Moreover, owing to its simplicity, it can be easily combined with Co-teaching to further boost the performance. Our final model remains simple yet effective: it achieves comparable or even better performance than the state-of-the-art approaches on two real-world datasets with label noise which are Clothing1M and ANIMAL-10N. On Clothing1M, our approach obtains 74.9% accuracy which is slightly better than that of DivideMix. On ANIMAL-10N, we achieve 84.1% accuracy while the best public result by PLC is 83.4%. We hope that our simple approach can be served as a strong baseline for learning with label noise. Our implementation is available at https://github.com/yingyichen-cyy/Nested-Co-teaching.

The unsupervised task of Joint Alignment (JA) of images is beset by challenges such as high complexity, geometric distortions, and convergence to poor local or even global optima. Although Vision Transformers (ViT) have recently provided valuable features for JA, they fall short of fully addressing these issues. Consequently, researchers frequently depend on expensive models and numerous regularization terms, resulting in long training times and challenging hyperparameter tuning. We introduce the Spatial Joint Alignment Model (SpaceJAM), a novel approach that addresses the JA task with efficiency and simplicity. SpaceJAM leverages a compact architecture with only 16K trainable parameters and uniquely operates without the need for regularization or atlas maintenance. Evaluations on SPair-71K and CUB datasets demonstrate that SpaceJAM matches the alignment capabilities of existing methods while significantly reducing computational demands and achieving at least a 10x speedup. SpaceJAM sets a new standard for rapid and effective image alignment, making the process more accessible and efficient. Our code is available at: https://bgu-cs-vil.github.io/SpaceJAM/.

Pseudo-relevance feedback (PRF) has proven to be an effective query reformulation technique to improve retrieval accuracy. It aims to alleviate the mismatch of linguistic expressions between a query and its potential relevant documents. Existing PRF methods independently treat revised queries originating from the same query but using different numbers of feedback documents, resulting in severe query drift. Without comparing the effects of two different revisions from the same query, a PRF model may incorrectly focus on the additional irrelevant information increased in the more feedback, and thus reformulate a query that is less effective than the revision using the less feedback. Ideally, if a PRF model can distinguish between irrelevant and relevant information in the feedback, the more feedback documents there are, the better the revised query will be. To bridge this gap, we propose the Loss-over-Loss (LoL) framework to compare the reformulation losses between different revisions of the same query during training. Concretely, we revise an original query multiple times in parallel using different amounts of feedback and compute their reformulation losses. Then, we introduce an additional regularization loss on these reformulation losses to penalize revisions that use more feedback but gain larger losses. With such comparative regularization, the PRF model is expected to learn to suppress the extra increased irrelevant information by comparing the effects of different revised queries. Further, we present a differentiable query reformulation method to implement this framework. This method revises queries in the vector space and directly optimizes the retrieval performance of query vectors, applicable for both sparse and dense retrieval models. Empirical evaluation demonstrates the effectiveness and robustness of our method for two typical sparse and dense retrieval models.

The ability to learn different tasks sequentially is essential to the development of artificial intelligence. In general, neural networks lack this capability, the major obstacle being catastrophic forgetting. It occurs when the incrementally available information from non-stationary data distributions is continually acquired, disrupting what the model has already learned. Our approach remembers old tasks by projecting the representations of new tasks close to that of old tasks while keeping the decision boundaries unchanged. We employ the center loss as a regularization penalty that enforces new tasks' features to have the same class centers as old tasks and makes the features highly discriminative. This, in turn, leads to the least forgetting of already learned information. This method is easy to implement, requires minimal computational and memory overhead, and allows the neural network to maintain high performance across many sequentially encountered tasks. We also demonstrate that using the center loss in conjunction with the memory replay outperforms other replay-based strategies. Along with standard MNIST variants for continual learning, we apply our method to continual domain adaptation scenarios with the Digits and PACS datasets. We demonstrate that our approach is scalable, effective, and gives competitive performance compared to state-of-the-art continual learning methods.

We consider the problem of learning the best possible policy from a fixed dataset, known as offline Reinforcement Learning (RL). A common taxonomy of existing offline RL works is policy regularization, which typically constrains the learned policy by distribution or support of the behavior policy. However, distribution and support constraints are overly conservative since they both force the policy to choose similar actions as the behavior policy when considering particular states. It will limit the learned policy's performance, especially when the behavior policy is sub-optimal. In this paper, we find that regularizing the policy towards the nearest state-action pair can be more effective and thus propose Policy Regularization with Dataset Constraint (PRDC). When updating the policy in a given state, PRDC searches the entire dataset for the nearest state-action sample and then restricts the policy with the action of this sample. Unlike previous works, PRDC can guide the policy with proper behaviors from the dataset, allowing it to choose actions that do not appear in the dataset along with the given state. It is a softer constraint but still keeps enough conservatism from out-of-distribution actions. Empirical evidence and theoretical analysis show that PRDC can alleviate offline RL's fundamentally challenging value overestimation issue with a bounded performance gap. Moreover, on a set of locomotion and navigation tasks, PRDC achieves state-of-the-art performance compared with existing methods. Code is available at https://github.com/LAMDA-RL/PRDC

This paper presents a simple yet effective approach that improves continual test-time adaptation (TTA) in a memory-efficient manner. TTA may primarily be conducted on edge devices with limited memory, so reducing memory is crucial but has been overlooked in previous TTA studies. In addition, long-term adaptation often leads to catastrophic forgetting and error accumulation, which hinders applying TTA in real-world deployments. Our approach consists of two components to address these issues. First, we present lightweight meta networks that can adapt the frozen original networks to the target domain. This novel architecture minimizes memory consumption by decreasing the size of intermediate activations required for backpropagation. Second, our novel self-distilled regularization controls the output of the meta networks not to deviate significantly from the output of the frozen original networks, thereby preserving well-trained knowledge from the source domain. Without additional memory, this regularization prevents error accumulation and catastrophic forgetting, resulting in stable performance even in long-term test-time adaptation. We demonstrate that our simple yet effective strategy outperforms other state-of-the-art methods on various benchmarks for image classification and semantic segmentation tasks. Notably, our proposed method with ResNet-50 and WideResNet-40 takes 86% and 80% less memory than the recent state-of-the-art method, CoTTA.

Batch Normalization is a commonly used trick to improve the training of deep neural networks. These neural networks use L2 regularization, also called weight decay, ostensibly to prevent overfitting. However, we show that L2 regularization has no regularizing effect when combined with normalization. Instead, regularization has an influence on the scale of weights, and thereby on the effective learning rate. We investigate this dependence, both in theory, and experimentally. We show that popular optimization methods such as ADAM only partially eliminate the influence of normalization on the learning rate. This leads to a discussion on other ways to mitigate this issue.

Continual learning (CL) refers to the ability of an intelligent system to sequentially acquire and retain knowledge from a stream of data with as little computational overhead as possible. To this end; regularization, replay, architecture, and parameter isolation approaches were introduced to the literature. Parameter isolation using a sparse network which enables to allocate distinct parts of the neural network to different tasks and also allows to share of parameters between tasks if they are similar. Dynamic Sparse Training (DST) is a prominent way to find these sparse networks and isolate them for each task. This paper is the first empirical study investigating the effect of different DST components under the CL paradigm to fill a critical research gap and shed light on the optimal configuration of DST for CL if it exists. Therefore, we perform a comprehensive study in which we investigate various DST components to find the best topology per task on well-known CIFAR100 and miniImageNet benchmarks in a task-incremental CL setup since our primary focus is to evaluate the performance of various DST criteria, rather than the process of mask selection. We found that, at a low sparsity level, Erdos-Renyi Kernel (ERK) initialization utilizes the backbone more efficiently and allows to effectively learn increments of tasks. At a high sparsity level, however, uniform initialization demonstrates more reliable and robust performance. In terms of growth strategy; performance is dependent on the defined initialization strategy, and the extent of sparsity. Finally, adaptivity within DST components is a promising way for better continual learners.

The recent advent of diffusion models has led to significant progress in solving inverse problems, leveraging these models as effective generative priors. Nonetheless, challenges related to the ill-posed nature of such problems remain, often due to inherent ambiguities in measurements. Drawing inspiration from the human ability to resolve visual ambiguities through perceptual biases, here we introduce a novel latent diffusion inverse solver by incorporating regularization by texts (TReg). Specifically, TReg applies the textual description of the preconception of the solution during the reverse sampling phase, of which description isndynamically reinforced through null-text optimization for adaptive negation. Our comprehensive experimental results demonstrate that TReg successfully mitigates ambiguity in latent diffusion inverse solvers, enhancing their effectiveness and accuracy.

Deep neural networks often work well when they are over-parameterized and trained with a massive amount of noise and regularization, such as weight decay and dropout. Although dropout is widely used as a regularization technique for fully connected layers, it is often less effective for convolutional layers. This lack of success of dropout for convolutional layers is perhaps due to the fact that activation units in convolutional layers are spatially correlated so information can still flow through convolutional networks despite dropout. Thus a structured form of dropout is needed to regularize convolutional networks. In this paper, we introduce DropBlock, a form of structured dropout, where units in a contiguous region of a feature map are dropped together. We found that applying DropbBlock in skip connections in addition to the convolution layers increases the accuracy. Also, gradually increasing number of dropped units during training leads to better accuracy and more robust to hyperparameter choices. Extensive experiments show that DropBlock works better than dropout in regularizing convolutional networks. On ImageNet classification, ResNet-50 architecture with DropBlock achieves 78.13% accuracy, which is more than 1.6% improvement on the baseline. On COCO detection, DropBlock improves Average Precision of RetinaNet from 36.8% to 38.4%.

Transformers have gained increasing popularity in a wide range of applications, including Natural Language Processing (NLP), Computer Vision and Speech Recognition, because of their powerful representational capacity. However, harnessing this representational capacity effectively requires a large amount of data, strong regularization, or both, to mitigate overfitting. Recently, the power of the Transformer has been unlocked by self-supervised pretraining strategies based on masked autoencoders which rely on reconstructing masked inputs, directly, or contrastively from unmasked content. This pretraining strategy which has been used in BERT models in NLP, Wav2Vec models in Speech and, recently, in MAE models in Vision, forces the model to learn about relationships between the content in different parts of the input using autoencoding related objectives. In this paper, we propose a novel, but surprisingly simple alternative to content reconstruction~-- that of predicting locations from content, without providing positional information for it. Doing so requires the Transformer to understand the positional relationships between different parts of the input, from their content alone. This amounts to an efficient implementation where the pretext task is a classification problem among all possible positions for each input token. We experiment on both Vision and Speech benchmarks, where our approach brings improvements over strong supervised training baselines and is comparable to modern unsupervised/self-supervised pretraining methods. Our method also enables Transformers trained without position embeddings to outperform ones trained with full position information.

Large language models (LLMs) are increasingly deployed via public-facing interfaces to interact with millions of users, each with diverse preferences. Despite this, preference tuning of LLMs predominantly relies on reward models trained using binary judgments where annotators select the preferred choice out of pairs of model outputs. In this work, we argue that this reliance on binary choices does not capture the broader, aggregate preferences of the target user in real-world tasks. We propose a taxonomy that identifies two dimensions of subjectivity where different users disagree on the preferred output-namely, the Plurality of Responses to Prompts, where prompts allow for multiple correct answers, and the Indistinguishability of Responses, where candidate outputs are paraphrases of each other. We show that reward models correlate weakly with user preferences in these cases. As a first step to address this issue, we introduce a simple yet effective method that augments existing binary preference datasets with synthetic preference judgments to estimate potential user disagreement. Incorporating these via a margin term as a form of regularization during model training yields predictions that better align with the aggregate user preferences.

The visual models pretrained on large-scale benchmarks encode general knowledge and prove effective in building more powerful representations for downstream tasks. Most existing approaches follow the fine-tuning paradigm, either by initializing or regularizing the downstream model based on the pretrained one. The former fails to retain the knowledge in the successive fine-tuning phase, thereby prone to be over-fitting, and the latter imposes strong constraints to the weights or feature maps of the downstream model without considering semantic drift, often incurring insufficient optimization. To deal with these issues, we propose a novel fine-tuning framework, namely distribution regularization with semantic calibration (DR-Tune). It employs distribution regularization by enforcing the downstream task head to decrease its classification error on the pretrained feature distribution, which prevents it from over-fitting while enabling sufficient training of downstream encoders. Furthermore, to alleviate the interference by semantic drift, we develop the semantic calibration (SC) module to align the global shape and class centers of the pretrained and downstream feature distributions. Extensive experiments on widely used image classification datasets show that DR-Tune consistently improves the performance when combing with various backbones under different pretraining strategies. Code is available at: https://github.com/weeknan/DR-Tune.

Regularization is a set of techniques that are used to improve the generalization ability of deep neural networks. In this paper, we introduce weight compander (WC), a novel effective method to improve generalization by reparameterizing each weight in deep neural networks using a nonlinear function. It is a general, intuitive, cheap and easy to implement method, which can be combined with various other regularization techniques. Large weights in deep neural networks are a sign of a more complex network that is overfitted to the training data. Moreover, regularized networks tend to have a greater range of weights around zero with fewer weights centered at zero. We introduce a weight reparameterization function which is applied to each weight and implicitly reduces overfitting by restricting the magnitude of the weights while forcing them away from zero at the same time. This leads to a more democratic decision-making in the network. Firstly, individual weights cannot have too much influence in the prediction process due to the restriction of their magnitude. Secondly, more weights are used in the prediction process, since they are forced away from zero during the training. This promotes the extraction of more features from the input data and increases the level of weight redundancy, which makes the network less sensitive to statistical differences between training and test data. We extend our method to learn the hyperparameters of the introduced weight reparameterization function. This avoids hyperparameter search and gives the network the opportunity to align the weight reparameterization with the training progress. We show experimentally that using weight compander in addition to standard regularization methods improves the performance of neural networks.

The recent integration of deep learning and pairwise similarity annotation-based constrained clustering -- i.e., deep constrained clustering (DCC) -- has proven effective for incorporating weak supervision into massive data clustering: Less than 1% of pair similarity annotations can often substantially enhance the clustering accuracy. However, beyond empirical successes, there is a lack of understanding of DCC. In addition, many DCC paradigms are sensitive to annotation noise, but performance-guaranteed noisy DCC methods have been largely elusive. This work first takes a deep look into a recently emerged logistic loss function of DCC, and characterizes its theoretical properties. Our result shows that the logistic DCC loss ensures the identifiability of data membership under reasonable conditions, which may shed light on its effectiveness in practice. Building upon this understanding, a new loss function based on geometric factor analysis is proposed to fend against noisy annotations. It is shown that even under unknown annotation confusions, the data membership can still be provably identified under our proposed learning criterion. The proposed approach is tested over multiple datasets to validate our claims.

Building recommendation systems via federated learning (FL) is a new emerging challenge for advancing next-generation Internet service and privacy protection. Existing approaches train shared item embedding by FL while keeping the user embedding private on client side. However, item embedding identical for all clients cannot capture users' individual differences on perceiving the same item and thus leads to poor personalization. Moreover, dense item embedding in FL results in expensive communication cost and latency. To address these challenges, we propose Federated Recommendation with Additive Personalization (FedRAP), which learns a global view of items via FL and a personalized view locally on each user. FedRAP enforces sparsity of the global view to save FL's communication cost and encourages difference between the two views through regularization. We propose an effective curriculum to learn the local and global views progressively with increasing regularization weights. To produce recommendations for an user, FedRAP adds the two views together to obtain a personalized item embedding. FedRAP achieves the best performance in FL setting on multiple benchmarks. It outperforms recent federated recommendation methods and several ablation study baselines.

Recent prompt-based approaches allow pretrained language models to achieve strong performances on few-shot finetuning by reformulating downstream tasks as a language modeling problem. In this work, we demonstrate that, despite its advantages on low data regimes, finetuned prompt-based models for sentence pair classification tasks still suffer from a common pitfall of adopting inference heuristics based on lexical overlap, e.g., models incorrectly assuming a sentence pair is of the same meaning because they consist of the same set of words. Interestingly, we find that this particular inference heuristic is significantly less present in the zero-shot evaluation of the prompt-based model, indicating how finetuning can be destructive to useful knowledge learned during the pretraining. We then show that adding a regularization that preserves pretraining weights is effective in mitigating this destructive tendency of few-shot finetuning. Our evaluation on three datasets demonstrates promising improvements on the three corresponding challenge datasets used to diagnose the inference heuristics.

Combining offline and online reinforcement learning (RL) is crucial for efficient and safe learning. However, previous approaches treat offline and online learning as separate procedures, resulting in redundant designs and limited performance. We ask: Can we achieve straightforward yet effective offline and online learning without introducing extra conservatism or regularization? In this study, we propose Uni-o4, which utilizes an on-policy objective for both offline and online learning. Owning to the alignment of objectives in two phases, the RL agent can transfer between offline and online learning seamlessly. This property enhances the flexibility of the learning paradigm, allowing for arbitrary combinations of pretraining, fine-tuning, offline, and online learning. In the offline phase, specifically, Uni-o4 leverages diverse ensemble policies to address the mismatch issues between the estimated behavior policy and the offline dataset. Through a simple offline policy evaluation (OPE) approach, Uni-o4 can achieve multi-step policy improvement safely. We demonstrate that by employing the method above, the fusion of these two paradigms can yield superior offline initialization as well as stable and rapid online fine-tuning capabilities. Through real-world robot tasks, we highlight the benefits of this paradigm for rapid deployment in challenging, previously unseen real-world environments. Additionally, through comprehensive evaluations using numerous simulated benchmarks, we substantiate that our method achieves state-of-the-art performance in both offline and offline-to-online fine-tuning learning. Our website: https://lei-kun.github.io/uni-o4/ .

Since the control of the Lipschitz constant has a great impact on the training stability, generalization, and robustness of neural networks, the estimation of this value is nowadays a real scientific challenge. In this paper we introduce a precise, fast, and differentiable upper bound for the spectral norm of convolutional layers using circulant matrix theory and a new alternative to the Power iteration. Called the Gram iteration, our approach exhibits a superlinear convergence. First, we show through a comprehensive set of experiments that our approach outperforms other state-of-the-art methods in terms of precision, computational cost, and scalability. Then, it proves highly effective for the Lipschitz regularization of convolutional neural networks, with competitive results against concurrent approaches. Code is available at https://github.com/blaisedelattre/lip4conv.

Recently, the RGB images and point clouds fusion methods have been proposed to jointly estimate 2D optical flow and 3D scene flow. However, as both conventional RGB cameras and LiDAR sensors adopt a frame-based data acquisition mechanism, their performance is limited by the fixed low sampling rates, especially in highly-dynamic scenes. By contrast, the event camera can asynchronously capture the intensity changes with a very high temporal resolution, providing complementary dynamic information of the observed scenes. In this paper, we incorporate RGB images, Point clouds and Events for joint optical flow and scene flow estimation with our proposed multi-stage multimodal fusion model, RPEFlow. First, we present an attention fusion module with a cross-attention mechanism to implicitly explore the internal cross-modal correlation for 2D and 3D branches, respectively. Second, we introduce a mutual information regularization term to explicitly model the complementary information of three modalities for effective multimodal feature learning. We also contribute a new synthetic dataset to advocate further research. Experiments on both synthetic and real datasets show that our model outperforms the existing state-of-the-art by a wide margin. Code and dataset is available at https://npucvr.github.io/RPEFlow.

Self-correction is a highly desirable capability of large language models (LLMs), yet it has consistently been found to be largely ineffective in modern LLMs. Existing approaches for training self-correction either require multiple models or rely on a more capable model or other forms of supervision. To this end, we develop a multi-turn online reinforcement learning (RL) approach, SCoRe, that significantly improves an LLM's self-correction ability using entirely self-generated data. To build SCoRe, we first show that variants of supervised fine-tuning (SFT) on offline model-generated correction traces are insufficient for instilling self-correction behavior. In particular, we observe that training via SFT either suffers from a distribution mismatch between the training data and the model's own responses or implicitly prefers only a certain mode of correction behavior that is often not effective at test time. SCoRe addresses these challenges by training under the model's own distribution of self-generated correction traces and using appropriate regularization to steer the learning process into learning a self-correction strategy that is effective at test time as opposed to simply fitting high-reward responses for a given prompt. This regularization prescribes running a first phase of RL on a base model to generate a policy initialization that is less susceptible to collapse and then using a reward bonus to amplify self-correction during training. When applied to Gemini 1.0 Pro and 1.5 Flash models, we find that SCoRe achieves state-of-the-art self-correction performance, improving the base models' self-correction by 15.6% and 9.1% respectively on the MATH and HumanEval benchmarks.

The remarkable success of large language pretraining and the discovery of scaling laws signify a paradigm shift in machine learning. Notably, the primary objective has evolved from minimizing generalization error to reducing approximation error, and the most effective strategy has transitioned from regularization (in a broad sense) to scaling up models. This raises a critical question: Do the established principles that proved successful in the generalization-centric era remain valid in this new era of scaling? This paper examines several influential regularization-based principles that may no longer hold true in the scaling-centric, large language model (LLM) era. These principles include explicit L2 regularization and implicit regularization through small batch sizes and large learning rates. Additionally, we identify a new phenomenon termed ``scaling law crossover,'' where two scaling curves intersect at a certain scale, implying that methods effective at smaller scales may not generalize to larger ones. Together, these observations highlight two fundamental questions within this new paradigm: bullet Guiding Principles for Scaling: If regularization is no longer the primary guiding principle for model design, what new principles are emerging to guide scaling? bullet Model Comparison at Scale: How to reliably and effectively compare models at the scale where only a single experiment is feasible?

For the first time, we explore few-shot tuning of vision foundation models for class-incremental learning. Unlike existing few-shot class incremental learning (FSCIL) methods, which train an encoder on a base session to ensure forward compatibility for future continual learning, foundation models are generally trained on large unlabelled data without such considerations. This renders prior methods from traditional FSCIL incompatible for FSCIL with the foundation model. To this end, we propose Consistency-guided Asynchronous Contrastive Tuning (CoACT), a new approach to continually tune foundation models for new classes in few-shot settings. CoACT comprises three components: (i) asynchronous contrastive tuning, which learns new classes by including LoRA modules in the pre-trained encoder, while enforcing consistency between two asynchronous encoders; (ii) controlled fine-tuning, which facilitates effective tuning of a subset of the foundation model; and (iii) consistency-guided incremental tuning, which enforces additional regularization during later sessions to reduce forgetting of the learned classes. We perform an extensive study on 16 diverse datasets and demonstrate the effectiveness of CoACT, outperforming the best baseline method by 2.47% on average and with up to 12.52% on individual datasets. Additionally, CoACT shows reduced forgetting and robustness in low-shot experiments. As an added bonus, CoACT shows up to 13.5% improvement in standard FSCIL over the current SOTA on benchmark evaluations. We make our code publicly available at https://github.com/ShuvenduRoy/CoACT-FSCIL.

We introduce a novel class of sample-based explanations we term high-dimensional representers, that can be used to explain the predictions of a regularized high-dimensional model in terms of importance weights for each of the training samples. Our workhorse is a novel representer theorem for general regularized high-dimensional models, which decomposes the model prediction in terms of contributions from each of the training samples: with positive (negative) values corresponding to positive (negative) impact training samples to the model's prediction. We derive consequences for the canonical instances of ell_1 regularized sparse models, and nuclear norm regularized low-rank models. As a case study, we further investigate the application of low-rank models in the context of collaborative filtering, where we instantiate high-dimensional representers for specific popular classes of models. Finally, we study the empirical performance of our proposed methods on three real-world binary classification datasets and two recommender system datasets. We also showcase the utility of high-dimensional representers in explaining model recommendations.

Deep neural networks exploiting millions of parameters are nowadays the norm in deep learning applications. This is a potential issue because of the great amount of computational resources needed for training, and of the possible loss of generalization performance of overparametrized networks. We propose in this paper a method for learning sparse neural topologies via a regularization technique which identifies non relevant weights and selectively shrinks their norm, while performing a classic update for relevant ones. This technique, which is an improvement of classical weight decay, is based on the definition of a regularization term which can be added to any loss functional regardless of its form, resulting in a unified general framework exploitable in many different contexts. The actual elimination of parameters identified as irrelevant is handled by an iterative pruning algorithm. We tested the proposed technique on different image classification and Natural language generation tasks, obtaining results on par or better then competitors in terms of sparsity and metrics, while achieving strong models compression.

In neural Information Retrieval, ongoing research is directed towards improving the first retriever in ranking pipelines. Learning dense embeddings to conduct retrieval using efficient approximate nearest neighbors methods has proven to work well. Meanwhile, there has been a growing interest in learning sparse representations for documents and queries, that could inherit from the desirable properties of bag-of-words models such as the exact matching of terms and the efficiency of inverted indexes. In this work, we present a new first-stage ranker based on explicit sparsity regularization and a log-saturation effect on term weights, leading to highly sparse representations and competitive results with respect to state-of-the-art dense and sparse methods. Our approach is simple, trained end-to-end in a single stage. We also explore the trade-off between effectiveness and efficiency, by controlling the contribution of the sparsity regularization.

Loss of plasticity is a phenomenon where neural networks become more difficult to train during the course of learning. Continual learning algorithms seek to mitigate this effect by sustaining good predictive performance while maintaining network trainability. We develop new techniques for improving continual learning by first reconsidering how initialization can ensure trainability during early phases of learning. From this perspective, we derive new regularization strategies for continual learning that ensure beneficial initialization properties are better maintained throughout training. In particular, we investigate two new regularization techniques for continual learning: (i) Wasserstein regularization toward the initial weight distribution, which is less restrictive than regularizing toward initial weights; and (ii) regularizing weight matrix singular values, which directly ensures gradient diversity is maintained throughout training. We present an experimental analysis that shows these alternative regularizers can improve continual learning performance across a range of supervised learning tasks and model architectures. The alternative regularizers prove to be less sensitive to hyperparameters while demonstrating better training in individual tasks, sustaining trainability as new tasks arrive, and achieving better generalization performance.

When training large flexible models, practitioners often rely on grid search to select hyperparameters that control over-fitting. This grid search has several disadvantages: the search is computationally expensive, requires carving out a validation set that reduces the available data for training, and requires users to specify candidate values. In this paper, we propose an alternative: directly learning regularization hyperparameters on the full training set via the evidence lower bound ("ELBo") objective from variational methods. For deep neural networks with millions of parameters, we recommend a modified ELBo that upweights the influence of the data likelihood relative to the prior. Our proposed technique overcomes all three disadvantages of grid search. In a case study on transfer learning of image classifiers, we show how our method reduces the 88+ hour grid search of past work to under 3 hours while delivering comparable accuracy. We further demonstrate how our approach enables efficient yet accurate approximations of Gaussian processes with learnable length-scale kernels.

This paper offers a new perspective to ease the challenge of domain generalization, which involves maintaining robust results even in unseen environments. Our design focuses on the decision-making process in the final classifier layer. Specifically, we propose treating the element-wise contributions to the final results as the rationale for making a decision and representing the rationale for each sample as a matrix. For a well-generalized model, we suggest the rationale matrices for samples belonging to the same category should be similar, indicating the model relies on domain-invariant clues to make decisions, thereby ensuring robust results. To implement this idea, we introduce a rationale invariance loss as a simple regularization technique, requiring only a few lines of code. Our experiments demonstrate that the proposed approach achieves competitive results across various datasets, despite its simplicity. Code is available at https://github.com/liangchen527/RIDG.

Convolutional neural networks are capable of learning powerful representational spaces, which are necessary for tackling complex learning tasks. However, due to the model capacity required to capture such representations, they are often susceptible to overfitting and therefore require proper regularization in order to generalize well. In this paper, we show that the simple regularization technique of randomly masking out square regions of input during training, which we call cutout, can be used to improve the robustness and overall performance of convolutional neural networks. Not only is this method extremely easy to implement, but we also demonstrate that it can be used in conjunction with existing forms of data augmentation and other regularizers to further improve model performance. We evaluate this method by applying it to current state-of-the-art architectures on the CIFAR-10, CIFAR-100, and SVHN datasets, yielding new state-of-the-art results of 2.56%, 15.20%, and 1.30% test error respectively. Code is available at https://github.com/uoguelph-mlrg/Cutout

We propose a novel framework to perform classification via deep learning in the presence of noisy annotations. When trained on noisy labels, deep neural networks have been observed to first fit the training data with clean labels during an "early learning" phase, before eventually memorizing the examples with false labels. We prove that early learning and memorization are fundamental phenomena in high-dimensional classification tasks, even in simple linear models, and give a theoretical explanation in this setting. Motivated by these findings, we develop a new technique for noisy classification tasks, which exploits the progress of the early learning phase. In contrast with existing approaches, which use the model output during early learning to detect the examples with clean labels, and either ignore or attempt to correct the false labels, we take a different route and instead capitalize on early learning via regularization. There are two key elements to our approach. First, we leverage semi-supervised learning techniques to produce target probabilities based on the model outputs. Second, we design a regularization term that steers the model towards these targets, implicitly preventing memorization of the false labels. The resulting framework is shown to provide robustness to noisy annotations on several standard benchmarks and real-world datasets, where it achieves results comparable to the state of the art.

Although deep neural networks achieve tremendous success on various classification tasks, the generalization ability drops sheer when training datasets exhibit long-tailed distributions. One of the reasons is that the learned representations (i.e. features) from the imbalanced datasets are less effective than those from balanced datasets. Specifically, the learned representation under class-balanced distribution will present the Neural Collapse (NC) phenomena. NC indicates the features from the same category are close to each other and from different categories are maximally distant, showing an optimal linear separable state of classification. However, the pattern differs on imbalanced datasets and is partially responsible for the reduced performance of the model. In this work, we propose two explicit feature regularization terms to learn high-quality representation for class-imbalanced data. With the proposed regularization, NC phenomena will appear under the class-imbalanced distribution, and the generalization ability can be significantly improved. Our method is easily implemented, highly effective, and can be plugged into most existing methods. The extensive experimental results on widely-used benchmarks show the effectiveness of our method

Catastrophic overfitting (CO) in single-step adversarial training (AT) results in abrupt drops in the adversarial test accuracy (even down to 0%). For models trained with multi-step AT, it has been observed that the loss function behaves locally linearly with respect to the input, this is however lost in single-step AT. To address CO in single-step AT, several methods have been proposed to enforce local linearity of the loss via regularization. However, these regularization terms considerably slow down training due to Double Backpropagation. Instead, in this work, we introduce a regularization term, called ELLE, to mitigate CO effectively and efficiently in classical AT evaluations, as well as some more difficult regimes, e.g., large adversarial perturbations and long training schedules. Our regularization term can be theoretically linked to curvature of the loss function and is computationally cheaper than previous methods by avoiding Double Backpropagation. Our thorough experimental validation demonstrates that our work does not suffer from CO, even in challenging settings where previous works suffer from it. We also notice that adapting our regularization parameter during training (ELLE-A) greatly improves the performance, specially in large epsilon setups. Our implementation is available in https://github.com/LIONS-EPFL/ELLE .

It is widely believed that the implicit regularization of SGD is fundamental to the impressive generalization behavior we observe in neural networks. In this work, we demonstrate that non-stochastic full-batch training can achieve comparably strong performance to SGD on CIFAR-10 using modern architectures. To this end, we show that the implicit regularization of SGD can be completely replaced with explicit regularization even when comparing against a strong and well-researched baseline. Our observations indicate that the perceived difficulty of full-batch training may be the result of its optimization properties and the disproportionate time and effort spent by the ML community tuning optimizers and hyperparameters for small-batch training.

In this paper we study the effects of quantization in DNN training. We hypothesize that weight quantization is a form of regularization and the amount of regularization is correlated with the quantization level (precision). We confirm our hypothesis by providing analytical study and empirical results. By modeling weight quantization as a form of additive noise to weights, we explore how this noise propagates through the network at training time. We then show that the magnitude of this noise is correlated with the level of quantization. To confirm our analytical study, we performed an extensive list of experiments summarized in this paper in which we show that the regularization effects of quantization can be seen in various vision tasks and models, over various datasets. Based on our study, we propose that 8-bit quantization provides a reliable form of regularization in different vision tasks and models.

In the era of proliferation of large language and image generation models, the phenomenon of "model collapse" refers to the situation whereby as a model is trained recursively on data generated from previous generations of itself over time, its performance degrades until the model eventually becomes completely useless, i.e the model collapses. In this work, we study this phenomenon in the setting of high-dimensional regression and obtain analytic formulae which quantitatively outline this phenomenon in a broad range of regimes. In the special case of polynomial decaying spectral and source conditions, we obtain modified scaling laws which exhibit new crossover phenomena from fast to slow rates. We also propose a simple strategy based on adaptive regularization to mitigate model collapse. Our theoretical results are validated with experiments.

Adversarial training, which is to enhance robustness against adversarial attacks, has received much attention because it is easy to generate human-imperceptible perturbations of data to deceive a given deep neural network. In this paper, we propose a new adversarial training algorithm that is theoretically well motivated and empirically superior to other existing algorithms. A novel feature of the proposed algorithm is to apply more regularization to data vulnerable to adversarial attacks than other existing regularization algorithms do. Theoretically, we show that our algorithm can be understood as an algorithm of minimizing the regularized empirical risk motivated from a newly derived upper bound of the robust risk. Numerical experiments illustrate that our proposed algorithm improves the generalization (accuracy on examples) and robustness (accuracy on adversarial attacks) simultaneously to achieve the state-of-the-art performance.

Although deep learning has produced dazzling successes for applications of image, speech, and video processing in the past few years, most trainings are with suboptimal hyper-parameters, requiring unnecessarily long training times. Setting the hyper-parameters remains a black art that requires years of experience to acquire. This report proposes several efficient ways to set the hyper-parameters that significantly reduce training time and improves performance. Specifically, this report shows how to examine the training validation/test loss function for subtle clues of underfitting and overfitting and suggests guidelines for moving toward the optimal balance point. Then it discusses how to increase/decrease the learning rate/momentum to speed up training. Our experiments show that it is crucial to balance every manner of regularization for each dataset and architecture. Weight decay is used as a sample regularizer to show how its optimal value is tightly coupled with the learning rates and momentums. Files to help replicate the results reported here are available.

We develop a novel theoretical framework for understating OT schemes respecting a class structure. For this purpose, we propose a convex OT program with a sum-of-norms regularization term, which provably recovers the underlying class structure under geometric assumptions. Furthermore, we derive an accelerated proximal algorithm with a closed-form projection and proximal operator scheme, thereby affording a more scalable algorithm for computing optimal transport plans. We provide a novel argument for the uniqueness of the optimum even in the absence of strong convexity. Our experiments show that the new regularizer not only results in a better preservation of the class structure in the data but also yields additional robustness to the data geometry, compared to previous regularizers.

Over-parameterized deep networks trained using gradient-based optimizers are a popular choice for solving classification and ranking problems. Without appropriately tuned ell_2 regularization or weight decay, such networks have the tendency to make output scores (logits) and network weights large, causing training loss to become too small and the network to lose its adaptivity (ability to move around) in the parameter space. Although regularization is typically understood from an overfitting perspective, we highlight its role in making the network more adaptive and enabling it to escape more easily from weights that generalize poorly. To provide such a capability, we propose a method called Logit Attenuating Weight Normalization (LAWN), that can be stacked onto any gradient-based optimizer. LAWN controls the logits by constraining the weight norms of layers in the final homogeneous sub-network. Empirically, we show that the resulting LAWN variant of the optimizer makes a deep network more adaptive to finding minimas with superior generalization performance on large-scale image classification and recommender systems. While LAWN is particularly impressive in improving Adam, it greatly improves all optimizers when used with large batch sizes

Recent research has highlighted the importance of dataset size in scaling language models. However, large language models (LLMs) are notoriously token-hungry during pre-training, and high-quality text data on the web is approaching its scaling limit for LLMs. To further enhance LLMs, a straightforward approach is to repeat the pre-training data for additional epochs. In this study, we empirically investigate three key aspects under this approach. First, we explore the consequences of repeating pre-training data, revealing that the model is susceptible to overfitting, leading to multi-epoch degradation. Second, we examine the key factors contributing to multi-epoch degradation, finding that significant factors include dataset size, model parameters, and training objectives, while less influential factors consist of dataset quality and model FLOPs. Finally, we explore whether widely used regularization can alleviate multi-epoch degradation. Most regularization techniques do not yield significant improvements, except for dropout, which demonstrates remarkable effectiveness but requires careful tuning when scaling up the model size. Additionally, we discover that leveraging mixture-of-experts (MoE) enables cost-effective and efficient hyper-parameter tuning for computationally intensive dense LLMs with comparable trainable parameters, potentially impacting efficient LLM development on a broader scale.

It is impossible today to pretend that the practice of machine learning is compatible with the idea that training and testing data follow the same distribution. Several authors have recently used ensemble techniques to show how scenarios involving multiple data distributions are best served by representations that are both richer than those obtained by regularizing for the best in-distribution performance, and richer than those obtained under the influence of the implicit sparsity bias of common stochastic gradient procedures. This contribution investigates the use of very high dropout rates instead of ensembles to obtain such rich representations. Although training a deep network from scratch using such dropout rates is virtually impossible, fine-tuning a large pre-trained model under such conditions is not only possible but also achieves out-of-distribution performances that exceed those of both ensembles and weight averaging methods such as model soups. This result has practical significance because the importance of the fine-tuning scenario has considerably grown in recent years. This result also provides interesting insights on the nature of rich representations and on the intrinsically linear nature of fine-tuning a large network using a comparatively small dataset.

We consider the problem of accurate quantization for language models, where both the weights and activations are uniformly quantized to 4 bits per parameter, the lowest bitwidth format natively supported by GPU hardware. In this context, the key challenge is activation quantization: it is known that language models contain outlier channels whose values on average are orders of magnitude higher than than other channels, which prevents accurate low-bitwidth quantization with known techniques. We systematically study this phenomena and find that these outlier channels emerge early in training, and that they occur more frequently in layers with residual streams. We then propose a simple strategy which regularizes a layer's inputs via quantization-aware training (QAT) and its outputs via activation kurtosis regularization. We show that regularizing both the inputs and outputs is crucial for preventing a model's "migrating" the difficulty in input quantization to the weights, which makes post-training quantization (PTQ) of weights more difficult. When combined with weight PTQ, we show that our approach can obtain a W4A4 model that performs competitively to the standard-precision W16A16 baseline.

Deep learning has been wildly successful in practice and most state-of-the-art machine learning methods are based on neural networks. Lacking, however, is a rigorous mathematical theory that adequately explains the amazing performance of deep neural networks. In this article, we present a relatively new mathematical framework that provides the beginning of a deeper understanding of deep learning. This framework precisely characterizes the functional properties of neural networks that are trained to fit to data. The key mathematical tools which support this framework include transform-domain sparse regularization, the Radon transform of computed tomography, and approximation theory, which are all techniques deeply rooted in signal processing. This framework explains the effect of weight decay regularization in neural network training, the use of skip connections and low-rank weight matrices in network architectures, the role of sparsity in neural networks, and explains why neural networks can perform well in high-dimensional problems.

Despite their massive size, successful deep artificial neural networks can exhibit a remarkably small difference between training and test performance. Conventional wisdom attributes small generalization error either to properties of the model family, or to the regularization techniques used during training. Through extensive systematic experiments, we show how these traditional approaches fail to explain why large neural networks generalize well in practice. Specifically, our experiments establish that state-of-the-art convolutional networks for image classification trained with stochastic gradient methods easily fit a random labeling of the training data. This phenomenon is qualitatively unaffected by explicit regularization, and occurs even if we replace the true images by completely unstructured random noise. We corroborate these experimental findings with a theoretical construction showing that simple depth two neural networks already have perfect finite sample expressivity as soon as the number of parameters exceeds the number of data points as it usually does in practice. We interpret our experimental findings by comparison with traditional models.

This book develops an effective theory approach to understanding deep neural networks of practical relevance. Beginning from a first-principles component-level picture of networks, we explain how to determine an accurate description of the output of trained networks by solving layer-to-layer iteration equations and nonlinear learning dynamics. A main result is that the predictions of networks are described by nearly-Gaussian distributions, with the depth-to-width aspect ratio of the network controlling the deviations from the infinite-width Gaussian description. We explain how these effectively-deep networks learn nontrivial representations from training and more broadly analyze the mechanism of representation learning for nonlinear models. From a nearly-kernel-methods perspective, we find that the dependence of such models' predictions on the underlying learning algorithm can be expressed in a simple and universal way. To obtain these results, we develop the notion of representation group flow (RG flow) to characterize the propagation of signals through the network. By tuning networks to criticality, we give a practical solution to the exploding and vanishing gradient problem. We further explain how RG flow leads to near-universal behavior and lets us categorize networks built from different activation functions into universality classes. Altogether, we show that the depth-to-width ratio governs the effective model complexity of the ensemble of trained networks. By using information-theoretic techniques, we estimate the optimal aspect ratio at which we expect the network to be practically most useful and show how residual connections can be used to push this scale to arbitrary depths. With these tools, we can learn in detail about the inductive bias of architectures, hyperparameters, and optimizers.

Introduced by Hinton et al. in 2012, dropout has stood the test of time as a regularizer for preventing overfitting in neural networks. In this study, we demonstrate that dropout can also mitigate underfitting when used at the start of training. During the early phase, we find dropout reduces the directional variance of gradients across mini-batches and helps align the mini-batch gradients with the entire dataset's gradient. This helps counteract the stochasticity of SGD and limit the influence of individual batches on model training. Our findings lead us to a solution for improving performance in underfitting models - early dropout: dropout is applied only during the initial phases of training, and turned off afterwards. Models equipped with early dropout achieve lower final training loss compared to their counterparts without dropout. Additionally, we explore a symmetric technique for regularizing overfitting models - late dropout, where dropout is not used in the early iterations and is only activated later in training. Experiments on ImageNet and various vision tasks demonstrate that our methods consistently improve generalization accuracy. Our results encourage more research on understanding regularization in deep learning and our methods can be useful tools for future neural network training, especially in the era of large data. Code is available at https://github.com/facebookresearch/dropout.

Large scale recommender models find most relevant items from huge catalogs, and they play a critical role in modern search and recommendation systems. To model the input space with large-vocab categorical features, a typical recommender model learns a joint embedding space through neural networks for both queries and items from user feedback data. However, with millions to billions of items in the corpus, users tend to provide feedback for a very small set of them, causing a power-law distribution. This makes the feedback data for long-tail items extremely sparse. Inspired by the recent success in self-supervised representation learning research in both computer vision and natural language understanding, we propose a multi-task self-supervised learning (SSL) framework for large-scale item recommendations. The framework is designed to tackle the label sparsity problem by learning better latent relationship of item features. Specifically, SSL improves item representation learning as well as serving as additional regularization to improve generalization. Furthermore, we propose a novel data augmentation method that utilizes feature correlations within the proposed framework. We evaluate our framework using two real-world datasets with 500M and 1B training examples respectively. Our results demonstrate the effectiveness of SSL regularization and show its superior performance over the state-of-the-art regularization techniques. We also have already launched the proposed techniques to a web-scale commercial app-to-app recommendation system, with significant improvements top-tier business metrics demonstrated in A/B experiments on live traffic. Our online results also verify our hypothesis that our framework indeed improves model performance even more on slices that lack supervision.

We analyze continual learning on a sequence of separable linear classification tasks with binary labels. We show theoretically that learning with weak regularization reduces to solving a sequential max-margin problem, corresponding to a special case of the Projection Onto Convex Sets (POCS) framework. We then develop upper bounds on the forgetting and other quantities of interest under various settings with recurring tasks, including cyclic and random orderings of tasks. We discuss several practical implications to popular training practices like regularization scheduling and weighting. We point out several theoretical differences between our continual classification setting and a recently studied continual regression setting.

Sparse neural networks are a key factor in developing resource-efficient machine learning applications. We propose the novel and powerful sparse learning method Adaptive Regularized Training (ART) to compress dense into sparse networks. Instead of the commonly used binary mask during training to reduce the number of model weights, we inherently shrink weights close to zero in an iterative manner with increasing weight regularization. Our method compresses the pre-trained model knowledge into the weights of highest magnitude. Therefore, we introduce a novel regularization loss named HyperSparse that exploits the highest weights while conserving the ability of weight exploration. Extensive experiments on CIFAR and TinyImageNet show that our method leads to notable performance gains compared to other sparsification methods, especially in extremely high sparsity regimes up to 99.8 percent model sparsity. Additional investigations provide new insights into the patterns that are encoded in weights with high magnitudes.

Generative models such as denoising diffusion models are quickly advancing their ability to approximate highly complex data distributions. They are also increasingly leveraged in scientific machine learning, where samples from the implied data distribution are expected to adhere to specific governing equations. We present a framework that unifies generative modeling and partial differential equation fulfillment by introducing a first-principle-based loss term that enforces generated samples to fulfill the underlying physical constraints. Our approach reduces the residual error by up to two orders of magnitude compared to previous work in a fluid flow case study and outperforms task-specific frameworks in relevant metrics for structural topology optimization. We also present numerical evidence that our extended training objective acts as a natural regularization mechanism against overfitting. Our framework is simple to implement and versatile in its applicability for imposing equality and inequality constraints as well as auxiliary optimization objectives.

Prompt tuning and adapter tuning have shown great potential in transferring pre-trained vision-language models (VLMs) to various downstream tasks. In this work, we design a new type of tuning method, termed as regularized mask tuning, which masks the network parameters through a learnable selection. Inspired by neural pathways, we argue that the knowledge required by a downstream task already exists in the pre-trained weights but just gets concealed in the upstream pre-training stage. To bring the useful knowledge back into light, we first identify a set of parameters that are important to a given downstream task, then attach a binary mask to each parameter, and finally optimize these masks on the downstream data with the parameters frozen. When updating the mask, we introduce a novel gradient dropout strategy to regularize the parameter selection, in order to prevent the model from forgetting old knowledge and overfitting the downstream data. Experimental results on 11 datasets demonstrate the consistent superiority of our method over previous alternatives. It is noteworthy that we manage to deliver 18.73% performance improvement compared to the zero-shot CLIP via masking an average of only 2.56% parameters. Furthermore, our method is synergistic with most existing parameter-efficient tuning methods and can boost the performance on top of them. Project page can be found here (https://wuw2019.github.io/R-AMT/).

To leverage the copious amount of data from source tasks and overcome the scarcity of the target task samples, representation learning based on multi-task pretraining has become a standard approach in many applications. However, up until now, most existing works design a source task selection strategy from a purely empirical perspective. Recently, chen2022active gave the first active multi-task representation learning (A-MTRL) algorithm which adaptively samples from source tasks and can provably reduce the total sample complexity using the L2-regularized-target-source-relevance parameter nu^2. But their work is theoretically suboptimal in terms of total source sample complexity and is less practical in some real-world scenarios where sparse training source task selection is desired. In this paper, we address both issues. Specifically, we show the strict dominance of the L1-regularized-relevance-based (nu^1-based) strategy by giving a lower bound for the nu^2-based strategy. When nu^1 is unknown, we propose a practical algorithm that uses the LASSO program to estimate nu^1. Our algorithm successfully recovers the optimal result in the known case. In addition to our sample complexity results, we also characterize the potential of our nu^1-based strategy in sample-cost-sensitive settings. Finally, we provide experiments on real-world computer vision datasets to illustrate the effectiveness of our proposed method.

Gradient regularization (GR) is a method that penalizes the gradient norm of the training loss during training. While some studies have reported that GR can improve generalization performance, little attention has been paid to it from the algorithmic perspective, that is, the algorithms of GR that efficiently improve the performance. In this study, we first reveal that a specific finite-difference computation, composed of both gradient ascent and descent steps, reduces the computational cost of GR. Next, we show that the finite-difference computation also works better in the sense of generalization performance. We theoretically analyze a solvable model, a diagonal linear network, and clarify that GR has a desirable implicit bias to so-called rich regime and finite-difference computation strengthens this bias. Furthermore, finite-difference GR is closely related to some other algorithms based on iterative ascent and descent steps for exploring flat minima. In particular, we reveal that the flooding method can perform finite-difference GR in an implicit way. Thus, this work broadens our understanding of GR for both practice and theory.

In recent years, the development of diffusion models has led to significant progress in image and video generation tasks, with pre-trained models like the Stable Diffusion series playing a crucial role. Inspired by model pruning which lightens large pre-trained models by removing unimportant parameters, we propose a novel model fine-tuning method to make full use of these ineffective parameters and enable the pre-trained model with new task-specified capabilities. In this work, we first investigate the importance of parameters in pre-trained diffusion models, and discover that the smallest 10% to 20% of parameters by absolute values do not contribute to the generation process. Based on this observation, we propose a method termed SaRA that re-utilizes these temporarily ineffective parameters, equating to optimizing a sparse weight matrix to learn the task-specific knowledge. To mitigate overfitting, we propose a nuclear-norm-based low-rank sparse training scheme for efficient fine-tuning. Furthermore, we design a new progressive parameter adjustment strategy to make full use of the re-trained/finetuned parameters. Finally, we propose a novel unstructural backpropagation strategy, which significantly reduces memory costs during fine-tuning. Our method enhances the generative capabilities of pre-trained models in downstream applications and outperforms traditional fine-tuning methods like LoRA in maintaining model's generalization ability. We validate our approach through fine-tuning experiments on SD models, demonstrating significant improvements. SaRA also offers a practical advantage that requires only a single line of code modification for efficient implementation and is seamlessly compatible with existing methods.

We introduce an algorithm where the individual bits representing the weights of a neural network are learned. This method allows training weights with integer values on arbitrary bit-depths and naturally uncovers sparse networks, without additional constraints or regularization techniques. We show better results than the standard training technique with fully connected networks and similar performance as compared to standard training for convolutional and residual networks. By training bits in a selective manner we found that the biggest contribution to achieving high accuracy is given by the first three most significant bits, while the rest provide an intrinsic regularization. As a consequence more than 90\% of a network can be used to store arbitrary codes without affecting its accuracy. These codes may be random noise, binary files or even the weights of previously trained networks.

Stochastic Gradient Descent (SGD) stands as a cornerstone optimization algorithm with proven real-world empirical successes but relatively limited theoretical understanding. Recent research has illuminated a key factor contributing to its practical efficacy: the implicit regularization it instigates. Several studies have investigated the linear stability property of SGD in the vicinity of a stationary point as a predictive proxy for sharpness and generalization error in overparameterized neural networks (Wu et al., 2022; Jastrzebski et al., 2019; Cohen et al., 2021). In this paper, we delve deeper into the relationship between linear stability and sharpness. More specifically, we meticulously delineate the necessary and sufficient conditions for linear stability, contingent on hyperparameters of SGD and the sharpness at the optimum. Towards this end, we introduce a novel coherence measure of the loss Hessian that encapsulates pertinent geometric properties of the loss function that are relevant to the linear stability of SGD. It enables us to provide a simplified sufficient condition for identifying linear instability at an optimum. Notably, compared to previous works, our analysis relies on significantly milder assumptions and is applicable for a broader class of loss functions than known before, encompassing not only mean-squared error but also cross-entropy loss.

Although diffusion models (DMs) have shown promising performances in a number of tasks (e.g., speech synthesis and image generation), they might suffer from error propagation because of their sequential structure. However, this is not certain because some sequential models, such as Conditional Random Field (CRF), are free from this problem. To address this issue, we develop a theoretical framework to mathematically formulate error propagation in the architecture of DMs, The framework contains three elements, including modular error, cumulative error, and propagation equation. The modular and cumulative errors are related by the equation, which interprets that DMs are indeed affected by error propagation. Our theoretical study also suggests that the cumulative error is closely related to the generation quality of DMs. Based on this finding, we apply the cumulative error as a regularization term to reduce error propagation. Because the term is computationally intractable, we derive its upper bound and design a bootstrap algorithm to efficiently estimate the bound for optimization. We have conducted extensive experiments on multiple image datasets, showing that our proposed regularization reduces error propagation, significantly improves vanilla DMs, and outperforms previous baselines.

Design of reliable systems must guarantee stability against input perturbations. In machine learning, such guarantee entails preventing overfitting and ensuring robustness of models against corruption of input data. In order to maximize stability, we analyze and develop a computationally efficient implementation of Jacobian regularization that increases classification margins of neural networks. The stabilizing effect of the Jacobian regularizer leads to significant improvements in robustness, as measured against both random and adversarial input perturbations, without severely degrading generalization properties on clean data.

Representations learned via self-supervised learning (SSL) can be susceptible to dimensional collapse, where the learned representation subspace is of extremely low dimensionality and thus fails to represent the full data distribution and modalities. Dimensional collapse also known as the "underfilling" phenomenon is one of the major causes of degraded performance on downstream tasks. Previous work has investigated the dimensional collapse problem of SSL at a global level. In this paper, we demonstrate that representations can span over high dimensional space globally, but collapse locally. To address this, we propose a method called local dimensionality regularization (LDReg). Our formulation is based on the derivation of the Fisher-Rao metric to compare and optimize local distance distributions at an asymptotically small radius for each data point. By increasing the local intrinsic dimensionality, we demonstrate through a range of experiments that LDReg improves the representation quality of SSL. The results also show that LDReg can regularize dimensionality at both local and global levels.

Many recent datasets contain a variety of different data modalities, for instance, image, question, and answer data in visual question answering (VQA). When training deep net classifiers on those multi-modal datasets, the modalities get exploited at different scales, i.e., some modalities can more easily contribute to the classification results than others. This is suboptimal because the classifier is inherently biased towards a subset of the modalities. To alleviate this shortcoming, we propose a novel regularization term based on the functional entropy. Intuitively, this term encourages to balance the contribution of each modality to the classification result. However, regularization with the functional entropy is challenging. To address this, we develop a method based on the log-Sobolev inequality, which bounds the functional entropy with the functional-Fisher-information. Intuitively, this maximizes the amount of information that the modalities contribute. On the two challenging multi-modal datasets VQA-CPv2 and SocialIQ, we obtain state-of-the-art results while more uniformly exploiting the modalities. In addition, we demonstrate the efficacy of our method on Colored MNIST.

Two different approaches exist to handle missing values for prediction: either imputation, prior to fitting any predictive algorithms, or dedicated methods able to natively incorporate missing values. While imputation is widely (and easily) use, it is unfortunately biased when low-capacity predictors (such as linear models) are applied afterward. However, in practice, naive imputation exhibits good predictive performance. In this paper, we study the impact of imputation in a high-dimensional linear model with MCAR missing data. We prove that zero imputation performs an implicit regularization closely related to the ridge method, often used in high-dimensional problems. Leveraging on this connection, we establish that the imputation bias is controlled by a ridge bias, which vanishes in high dimension. As a predictor, we argue in favor of the averaged SGD strategy, applied to zero-imputed data. We establish an upper bound on its generalization error, highlighting that imputation is benign in the d sqrt n regime. Experiments illustrate our findings.

Robust generalization is a major challenge in deep learning, particularly when the number of trainable parameters is very large. In general, it is very difficult to know if the network has memorized a particular set of examples or understood the underlying rule (or both). Motivated by this challenge, we study an interpretable model where generalizing representations are understood analytically, and are easily distinguishable from the memorizing ones. Namely, we consider multi-layer perceptron (MLP) and Transformer architectures trained on modular arithmetic tasks, where (xi cdot 100%) of labels are corrupted (i.e. some results of the modular operations in the training set are incorrect). We show that (i) it is possible for the network to memorize the corrupted labels and achieve 100% generalization at the same time; (ii) the memorizing neurons can be identified and pruned, lowering the accuracy on corrupted data and improving the accuracy on uncorrupted data; (iii) regularization methods such as weight decay, dropout and BatchNorm force the network to ignore the corrupted data during optimization, and achieve 100% accuracy on the uncorrupted dataset; and (iv) the effect of these regularization methods is (``mechanistically'') interpretable: weight decay and dropout force all the neurons to learn generalizing representations, while BatchNorm de-amplifies the output of memorizing neurons and amplifies the output of the generalizing ones. Finally, we show that in the presence of regularization, the training dynamics involves two consecutive stages: first, the network undergoes grokking dynamics reaching high train and test accuracy; second, it unlearns the memorizing representations, where the train accuracy suddenly jumps from 100% to 100 (1-xi)%.

Hyperparameter optimization can be formulated as a bilevel optimization problem, where the optimal parameters on the training set depend on the hyperparameters. We aim to adapt regularization hyperparameters for neural networks by fitting compact approximations to the best-response function, which maps hyperparameters to optimal weights and biases. We show how to construct scalable best-response approximations for neural networks by modeling the best-response as a single network whose hidden units are gated conditionally on the regularizer. We justify this approximation by showing the exact best-response for a shallow linear network with L2-regularized Jacobian can be represented by a similar gating mechanism. We fit this model using a gradient-based hyperparameter optimization algorithm which alternates between approximating the best-response around the current hyperparameters and optimizing the hyperparameters using the approximate best-response function. Unlike other gradient-based approaches, we do not require differentiating the training loss with respect to the hyperparameters, allowing us to tune discrete hyperparameters, data augmentation hyperparameters, and dropout probabilities. Because the hyperparameters are adapted online, our approach discovers hyperparameter schedules that can outperform fixed hyperparameter values. Empirically, our approach outperforms competing hyperparameter optimization methods on large-scale deep learning problems. We call our networks, which update their own hyperparameters online during training, Self-Tuning Networks (STNs).

There is a constant need for high-performing and computationally efficient neural network models for image super-resolution: computationally efficient models can be used via low-capacity devices and reduce carbon footprints. One way to obtain such models is to compress models, e.g. quantization. Another way is a neural architecture search that automatically discovers new, more efficient solutions. We propose a novel quantization-aware procedure, the QuantNAS that combines pros of these two approaches. To make QuantNAS work, the procedure looks for quantization-friendly super-resolution models. The approach utilizes entropy regularization, quantization noise, and Adaptive Deviation for Quantization (ADQ) module to enhance the search procedure. The entropy regularization technique prioritizes a single operation within each block of the search space. Adding quantization noise to parameters and activations approximates model degradation after quantization, resulting in a more quantization-friendly architectures. ADQ helps to alleviate problems caused by Batch Norm blocks in super-resolution models. Our experimental results show that the proposed approximations are better for search procedure than direct model quantization. QuantNAS discovers architectures with better PSNR/BitOps trade-off than uniform or mixed precision quantization of fixed architectures. We showcase the effectiveness of our method through its application to two search spaces inspired by the state-of-the-art SR models and RFDN. Thus, anyone can design a proper search space based on an existing architecture and apply our method to obtain better quality and efficiency. The proposed procedure is 30\% faster than direct weight quantization and is more stable.

Smoothness and low dimensional structures play central roles in improving generalization and stability in learning and statistics. This work combines techniques from semi-infinite constrained learning and manifold regularization to learn representations that are globally smooth on a manifold. To do so, it shows that under typical conditions the problem of learning a Lipschitz continuous function on a manifold is equivalent to a dynamically weighted manifold regularization problem. This observation leads to a practical algorithm based on a weighted Laplacian penalty whose weights are adapted using stochastic gradient techniques. It is shown that under mild conditions, this method estimates the Lipschitz constant of the solution, learning a globally smooth solution as a byproduct. Experiments on real world data illustrate the advantages of the proposed method relative to existing alternatives.

Low-Rank Adaptation (LoRA) is a widely-used parameter-efficient finetuning method for large language models. LoRA saves memory by training only low rank perturbations to selected weight matrices. In this work, we compare the performance of LoRA and full finetuning on two target domains, programming and mathematics. We consider both the instruction finetuning (approx100K prompt-response pairs) and continued pretraining (approx10B unstructured tokens) data regimes. Our results show that, in most settings, LoRA substantially underperforms full finetuning. Nevertheless, LoRA exhibits a desirable form of regularization: it better maintains the base model's performance on tasks outside the target domain. We show that LoRA provides stronger regularization compared to common techniques such as weight decay and dropout; it also helps maintain more diverse generations. We show that full finetuning learns perturbations with a rank that is 10-100X greater than typical LoRA configurations, possibly explaining some of the reported gaps. We conclude by proposing best practices for finetuning with LoRA.

Sparse Autoencoders (SAEs) have shown promise in improving the interpretability of neural network activations, but can learn features that are not features of the input, limiting their effectiveness. We propose Mutual Feature Regularization (MFR), a regularization technique for improving feature learning by encouraging SAEs trained in parallel to learn similar features. We motivate MFR by showing that features learned by multiple SAEs are more likely to correlate with features of the input. By training on synthetic data with known features of the input, we show that MFR can help SAEs learn those features, as we can directly compare the features learned by the SAE with the input features for the synthetic data. We then scale MFR to SAEs that are trained to denoise electroencephalography (EEG) data and SAEs that are trained to reconstruct GPT-2 Small activations. We show that MFR can improve the reconstruction loss of SAEs by up to 21.21\% on GPT-2 Small, and 6.67\% on EEG data. Our results suggest that the similarity between features learned by different SAEs can be leveraged to improve SAE training, thereby enhancing performance and the usefulness of SAEs for model interpretability.

Random masks define surprisingly effective sparse neural network models, as has been shown empirically. The resulting sparse networks can often compete with dense architectures and state-of-the-art lottery ticket pruning algorithms, even though they do not rely on computationally expensive prune-train iterations and can be drawn initially without significant computational overhead. We offer a theoretical explanation of how random masks can approximate arbitrary target networks if they are wider by a logarithmic factor in the inverse sparsity 1 / log(1/sparsity). This overparameterization factor is necessary at least for 3-layer random networks, which elucidates the observed degrading performance of random networks at higher sparsity. At moderate to high sparsity levels, however, our results imply that sparser networks are contained within random source networks so that any dense-to-sparse training scheme can be turned into a computationally more efficient sparse-to-sparse one by constraining the search to a fixed random mask. We demonstrate the feasibility of this approach in experiments for different pruning methods and propose particularly effective choices of initial layer-wise sparsity ratios of the random source network. As a special case, we show theoretically and experimentally that random source networks also contain strong lottery tickets.

PixelCNNs are a recently proposed class of powerful generative models with tractable likelihood. Here we discuss our implementation of PixelCNNs which we make available at https://github.com/openai/pixel-cnn. Our implementation contains a number of modifications to the original model that both simplify its structure and improve its performance. 1) We use a discretized logistic mixture likelihood on the pixels, rather than a 256-way softmax, which we find to speed up training. 2) We condition on whole pixels, rather than R/G/B sub-pixels, simplifying the model structure. 3) We use downsampling to efficiently capture structure at multiple resolutions. 4) We introduce additional short-cut connections to further speed up optimization. 5) We regularize the model using dropout. Finally, we present state-of-the-art log likelihood results on CIFAR-10 to demonstrate the usefulness of these modifications.

Proximal operators are ubiquitous in inverse problems, commonly appearing as part of algorithmic strategies to regularize problems that are otherwise ill-posed. Modern deep learning models have been brought to bear for these tasks too, as in the framework of plug-and-play or deep unrolling, where they loosely resemble proximal operators. Yet, something essential is lost in employing these purely data-driven approaches: there is no guarantee that a general deep network represents the proximal operator of any function, nor is there any characterization of the function for which the network might provide some approximate proximal. This not only makes guaranteeing convergence of iterative schemes challenging but, more fundamentally, complicates the analysis of what has been learned by these networks about their training data. Herein we provide a framework to develop learned proximal networks (LPN), prove that they provide exact proximal operators for a data-driven nonconvex regularizer, and show how a new training strategy, dubbed proximal matching, provably promotes the recovery of the log-prior of the true data distribution. Such LPN provide general, unsupervised, expressive proximal operators that can be used for general inverse problems with convergence guarantees. We illustrate our results in a series of cases of increasing complexity, demonstrating that these models not only result in state-of-the-art performance, but provide a window into the resulting priors learned from data.

We show that deep neural networks (DNNs) can efficiently learn any composition of functions with bounded F_{1}-norm, which allows DNNs to break the curse of dimensionality in ways that shallow networks cannot. More specifically, we derive a generalization bound that combines a covering number argument for compositionality, and the F_{1}-norm (or the related Barron norm) for large width adaptivity. We show that the global minimizer of the regularized loss of DNNs can fit for example the composition of two functions f^{*}=hcirc g from a small number of observations, assuming g is smooth/regular and reduces the dimensionality (e.g. g could be the modulo map of the symmetries of f^{*}), so that h can be learned in spite of its low regularity. The measures of regularity we consider is the Sobolev norm with different levels of differentiability, which is well adapted to the F_{1} norm. We compute scaling laws empirically and observe phase transitions depending on whether g or h is harder to learn, as predicted by our theory.

Deep learning classifiers face significant challenges when dealing with heterogeneous multi-modal and multi-organ biomedical datasets. The low-level feature distinguishability limited to imaging-modality hinders the classifiers' ability to learn high-level semantic relationships, resulting in sub-optimal performance. To address this issue, image augmentation strategies are employed as regularization techniques. While additive noise input during network training is a well-established augmentation as regularization method, modern pipelines often favor more robust techniques such as dropout and weight decay. This preference stems from the observation that combining these established techniques with noise input can adversely affect model performance. In this study, we propose a novel pretraining pipeline that learns to generate conditional noise mask specifically tailored to improve performance on multi-modal and multi-organ datasets. As a reinforcement learning algorithm, our approach employs a dual-component system comprising a very light-weight policy network that learns to sample conditional noise using a differentiable beta distribution as well as a classifier network. The policy network is trained using the reinforce algorithm to generate image-specific noise masks that regularize the classifier during pretraining. A key aspect is that the policy network's role is limited to obtaining an intermediate (or heated) model before fine-tuning. During inference, the policy network is omitted, allowing direct comparison between the baseline and noise-regularized models. We conducted experiments and related analyses on RadImageNet datasets. Results demonstrate that fine-tuning the intermediate models consistently outperforms conventional training algorithms on both classification and generalization to unseen concept tasks.

We present EGN, a stochastic second-order optimization algorithm that combines the generalized Gauss-Newton (GN) Hessian approximation with low-rank linear algebra to compute the descent direction. Leveraging the Duncan-Guttman matrix identity, the parameter update is obtained by factorizing a matrix which has the size of the mini-batch. This is particularly advantageous for large-scale machine learning problems where the dimension of the neural network parameter vector is several orders of magnitude larger than the batch size. Additionally, we show how improvements such as line search, adaptive regularization, and momentum can be seamlessly added to EGN to further accelerate the algorithm. Moreover, under mild assumptions, we prove that our algorithm converges to an epsilon-stationary point at a linear rate. Finally, our numerical experiments demonstrate that EGN consistently exceeds, or at most matches the generalization performance of well-tuned SGD, Adam, and SGN optimizers across various supervised and reinforcement learning tasks.

In this paper, we propose to use the general L^2-based Sobolev norms, i.e., H^s norms where sin R, to measure the data discrepancy due to noise in image processing tasks that are formulated as optimization problems. As opposed to a popular trend of developing regularization methods, we emphasize that an implicit regularization effect can be achieved through the class of Sobolev norms as the data-fitting term. Specifically, we analyze that the implicit regularization comes from the weights that the H^s norm imposes on different frequency contents of an underlying image. We further analyze the underlying noise assumption of using the Sobolev norm as the data-fitting term from a Bayesian perspective, build the connections with the Sobolev gradient-based methods and discuss the preconditioning effects on the convergence rate of the gradient descent algorithm, leading to a better understanding of functional spaces/metrics and the optimization process involved in image processing. Numerical results in full waveform inversion, image denoising and deblurring demonstrate the implicit regularization effects.

We investigate methods for combining multiple self-supervised tasks--i.e., supervised tasks where data can be collected without manual labeling--in order to train a single visual representation. First, we provide an apples-to-apples comparison of four different self-supervised tasks using the very deep ResNet-101 architecture. We then combine tasks to jointly train a network. We also explore lasso regularization to encourage the network to factorize the information in its representation, and methods for "harmonizing" network inputs in order to learn a more unified representation. We evaluate all methods on ImageNet classification, PASCAL VOC detection, and NYU depth prediction. Our results show that deeper networks work better, and that combining tasks--even via a naive multi-head architecture--always improves performance. Our best joint network nearly matches the PASCAL performance of a model pre-trained on ImageNet classification, and matches the ImageNet network on NYU depth prediction.

Vision Transformer models trained on large-scale datasets, although effective, often exhibit artifacts in the patch token they extract. While such defects can be alleviated by re-training the entire model with additional classification tokens, the underlying reasons for the presence of these tokens remain unclear. In this paper, we conduct a thorough investigation of this phenomenon, combining theoretical analysis with empirical observations. Our findings reveal that these artifacts originate from the pre-trained network itself, specifically stemming from the leading left singular vector of the network's weights. Furthermore, to mitigate these defects, we propose a novel fine-tuning smooth regularization that rectifies structural deficiencies using only a small dataset, thereby avoiding the need for complete re-training. We validate our method on various downstream tasks, including unsupervised segmentation, classification, supervised segmentation, and depth estimation, demonstrating its effectiveness in improving model performance. Codes and checkpoints are available at https://github.com/haoqiwang/sinder.

Accurate probabilistic predictions are essential for optimal decision making. While neural network miscalibration has been studied primarily in classification, we investigate this in the less-explored domain of regression. We conduct the largest empirical study to date to assess the probabilistic calibration of neural networks. We also analyze the performance of recalibration, conformal, and regularization methods to enhance probabilistic calibration. Additionally, we introduce novel differentiable recalibration and regularization methods, uncovering new insights into their effectiveness. Our findings reveal that regularization methods offer a favorable tradeoff between calibration and sharpness. Post-hoc methods exhibit superior probabilistic calibration, which we attribute to the finite-sample coverage guarantee of conformal prediction. Furthermore, we demonstrate that quantile recalibration can be considered as a specific case of conformal prediction. Our study is fully reproducible and implemented in a common code base for fair comparisons.

Harmful fine-tuning issue qi2023fine poses serious safety concerns for Large language models' fine-tuning-as-a-service. While existing defenses huang2024vaccine,rosati2024representation have been proposed to mitigate the issue, their performances are still far away from satisfactory, and the root cause of the problem has not been fully recovered. For the first time in the literature, we in this paper show that harmful perturbation over the model weights should be the root cause of alignment-broken of harmful fine-tuning. In order to attenuate the negative impact of harmful perturbation, we propose an alignment-stage solution, dubbed Booster. Technically, along with the original alignment loss, we append a loss regularizer in the alignment stage's optimization. The regularizer ensures that the model's harmful loss reduction before/after simulated harmful perturbation is attenuated, thereby mitigating the subsequent fine-tuning risk. Empirical results show that Booster can effectively reduce the harmful score of the fine-tuned models while maintaining the performance of downstream tasks. Our code is available at https://github.com/git-disl/Booster.

There are two widely known issues with properly training Recurrent Neural Networks, the vanishing and the exploding gradient problems detailed in Bengio et al. (1994). In this paper we attempt to improve the understanding of the underlying issues by exploring these problems from an analytical, a geometric and a dynamical systems perspective. Our analysis is used to justify a simple yet effective solution. We propose a gradient norm clipping strategy to deal with exploding gradients and a soft constraint for the vanishing gradients problem. We validate empirically our hypothesis and proposed solutions in the experimental section.

We provide a new efficient version of the backpropagation algorithm, specialized to the case where the weights of the neural network being trained are sparse. Our algorithm is general, as it applies to arbitrary (unstructured) sparsity and common layer types (e.g., convolutional or linear). We provide a fast vectorized implementation on commodity CPUs, and show that it can yield speedups in end-to-end runtime experiments, both in transfer learning using already-sparsified networks, and in training sparse networks from scratch. Thus, our results provide the first support for sparse training on commodity hardware.

We explore the impact of parameter sparsity on the scaling behavior of Transformers trained on massive datasets (i.e., "foundation models"), in both vision and language domains. In this setting, we identify the first scaling law describing the relationship between weight sparsity, number of non-zero parameters, and amount of training data, which we validate empirically across model and data scales; on ViT/JFT-4B and T5/C4. These results allow us to characterize the "optimal sparsity", the sparsity level which yields the best performance for a given effective model size and training budget. For a fixed number of non-zero parameters, we identify that the optimal sparsity increases with the amount of data used for training. We also extend our study to different sparsity structures (such as the hardware-friendly n:m pattern) and strategies (such as starting from a pretrained dense model). Our findings shed light on the power and limitations of weight sparsity across various parameter and computational settings, offering both theoretical understanding and practical implications for leveraging sparsity towards computational efficiency improvements.

Learning compact discrete representations of data is a key task on its own or for facilitating subsequent processing of data. In this paper we present a model that produces Discrete InfoMax Codes (DIMCO); we learn a probabilistic encoder that yields k-way d-dimensional codes associated with input data. Our model's learning objective is to maximize the mutual information between codes and labels with a regularization, which enforces entries of a codeword to be as independent as possible. We show that the infomax principle also justifies previous loss functions (e.g., cross-entropy) as its special cases. Our analysis also shows that using shorter codes, as DIMCO does, reduces overfitting in the context of few-shot classification. Through experiments in various domains, we observe this implicit meta-regularization effect of DIMCO. Furthermore, we show that the codes learned by DIMCO are efficient in terms of both memory and retrieval time compared to previous methods.

Despite recent progress in generative image modeling, successfully generating high-resolution, diverse samples from complex datasets such as ImageNet remains an elusive goal. To this end, we train Generative Adversarial Networks at the largest scale yet attempted, and study the instabilities specific to such scale. We find that applying orthogonal regularization to the generator renders it amenable to a simple "truncation trick," allowing fine control over the trade-off between sample fidelity and variety by reducing the variance of the Generator's input. Our modifications lead to models which set the new state of the art in class-conditional image synthesis. When trained on ImageNet at 128x128 resolution, our models (BigGANs) achieve an Inception Score (IS) of 166.5 and Frechet Inception Distance (FID) of 7.4, improving over the previous best IS of 52.52 and FID of 18.6.

Pre-training foundation models on large-scale datasets demonstrates exceptional performance. However, recent research questions this traditional notion, exploring whether an increase in pre-training data always leads to enhanced model performance. To address this issue, data-effective learning approaches have been introduced. However, current methods in this area lack a clear standard for sample selection. Our experiments reveal that by maximizing V-information, sample selection can be framed as an optimization problem, enabling effective improvement in model performance even with fewer samples. Under this guidance, we develop an optimal data-effective learning method (OptiDEL) to maximize V-information. The OptiDEL method generates hard samples to achieve or even exceed the performance of models trained on the full dataset while using substantially less data. We compare the OptiDEL method with state-of-the-art approaches finding that OptiDEL consistently outperforms existing approaches across different datasets, with foundation models trained on only 5% of the pre-training data surpassing the performance of those trained on the full dataset.

Owing to the growing concerns about privacy and regulatory compliance, it is desirable to regulate the output of generative models. To that end, the objective of this work is to prevent the generation of outputs containing undesired features from a pre-trained Generative Adversarial Network (GAN) where the underlying training data set is inaccessible. Our approach is inspired by the observation that the parameter space of GANs exhibits meaningful directions that can be leveraged to suppress specific undesired features. However, such directions usually result in the degradation of the quality of generated samples. Our proposed two-stage method, known as 'Adapt-then-Unlearn,' excels at unlearning such undesirable features while also maintaining the quality of generated samples. In the initial stage, we adapt a pre-trained GAN on a set of negative samples (containing undesired features) provided by the user. Subsequently, we train the original pre-trained GAN using positive samples, along with a repulsion regularizer. This regularizer encourages the learned model parameters to move away from the parameters of the adapted model (first stage) while not degrading the generation quality. We provide theoretical insights into the proposed method. To the best of our knowledge, our approach stands as the first method addressing unlearning within the realm of high-fidelity GANs (such as StyleGAN). We validate the effectiveness of our method through comprehensive experiments, encompassing both class-level unlearning on the MNIST and AFHQ dataset and feature-level unlearning tasks on the CelebA-HQ dataset. Our code and implementation is available at: https://github.com/atriguha/Adapt_Unlearn.

We propose UnMixMatch, a semi-supervised learning framework which can learn effective representations from unconstrained unlabelled data in order to scale up performance. Most existing semi-supervised methods rely on the assumption that labelled and unlabelled samples are drawn from the same distribution, which limits the potential for improvement through the use of free-living unlabeled data. Consequently, the generalizability and scalability of semi-supervised learning are often hindered by this assumption. Our method aims to overcome these constraints and effectively utilize unconstrained unlabelled data in semi-supervised learning. UnMixMatch consists of three main components: a supervised learner with hard augmentations that provides strong regularization, a contrastive consistency regularizer to learn underlying representations from the unlabelled data, and a self-supervised loss to enhance the representations that are learnt from the unlabelled data. We perform extensive experiments on 4 commonly used datasets and demonstrate superior performance over existing semi-supervised methods with a performance boost of 4.79%. Extensive ablation and sensitivity studies show the effectiveness and impact of each of the proposed components of our method.

Cosine-similarity is the cosine of the angle between two vectors, or equivalently the dot product between their normalizations. A popular application is to quantify semantic similarity between high-dimensional objects by applying cosine-similarity to a learned low-dimensional feature embedding. This can work better but sometimes also worse than the unnormalized dot-product between embedded vectors in practice. To gain insight into this empirical observation, we study embeddings derived from regularized linear models, where closed-form solutions facilitate analytical insights. We derive analytically how cosine-similarity can yield arbitrary and therefore meaningless `similarities.' For some linear models the similarities are not even unique, while for others they are implicitly controlled by the regularization. We discuss implications beyond linear models: a combination of different regularizations are employed when learning deep models; these have implicit and unintended effects when taking cosine-similarities of the resulting embeddings, rendering results opaque and possibly arbitrary. Based on these insights, we caution against blindly using cosine-similarity and outline alternatives.

We showcase important features of the dynamics of the Stochastic Gradient Descent (SGD) in the training of neural networks. We present empirical observations that commonly used large step sizes (i) lead the iterates to jump from one side of a valley to the other causing loss stabilization, and (ii) this stabilization induces a hidden stochastic dynamics orthogonal to the bouncing directions that biases it implicitly toward sparse predictors. Furthermore, we show empirically that the longer large step sizes keep SGD high in the loss landscape valleys, the better the implicit regularization can operate and find sparse representations. Notably, no explicit regularization is used so that the regularization effect comes solely from the SGD training dynamics influenced by the step size schedule. Therefore, these observations unveil how, through the step size schedules, both gradient and noise drive together the SGD dynamics through the loss landscape of neural networks. We justify these findings theoretically through the study of simple neural network models as well as qualitative arguments inspired from stochastic processes. Finally, this analysis allows us to shed a new light on some common practice and observed phenomena when training neural networks. The code of our experiments is available at https://github.com/tml-epfl/sgd-sparse-features.

Deep neural networks have been shown to suffer from a surprising weakness: their classification outputs can be changed by small, non-random perturbations of their inputs. This adversarial example phenomenon has been explained as originating from deep networks being "too linear" (Goodfellow et al., 2014). We show here that the linear explanation of adversarial examples presents a number of limitations: the formal argument is not convincing, linear classifiers do not always suffer from the phenomenon, and when they do their adversarial examples are different from the ones affecting deep networks. We propose a new perspective on the phenomenon. We argue that adversarial examples exist when the classification boundary lies close to the submanifold of sampled data, and present a mathematical analysis of this new perspective in the linear case. We define the notion of adversarial strength and show that it can be reduced to the deviation angle between the classifier considered and the nearest centroid classifier. Then, we show that the adversarial strength can be made arbitrarily high independently of the classification performance due to a mechanism that we call boundary tilting. This result leads us to defining a new taxonomy of adversarial examples. Finally, we show that the adversarial strength observed in practice is directly dependent on the level of regularisation used and the strongest adversarial examples, symptomatic of overfitting, can be avoided by using a proper level of regularisation.

This paper introduces EfficientNetV2, a new family of convolutional networks that have faster training speed and better parameter efficiency than previous models. To develop this family of models, we use a combination of training-aware neural architecture search and scaling, to jointly optimize training speed and parameter efficiency. The models were searched from the search space enriched with new ops such as Fused-MBConv. Our experiments show that EfficientNetV2 models train much faster than state-of-the-art models while being up to 6.8x smaller. Our training can be further sped up by progressively increasing the image size during training, but it often causes a drop in accuracy. To compensate for this accuracy drop, we propose to adaptively adjust regularization (e.g., dropout and data augmentation) as well, such that we can achieve both fast training and good accuracy. With progressive learning, our EfficientNetV2 significantly outperforms previous models on ImageNet and CIFAR/Cars/Flowers datasets. By pretraining on the same ImageNet21k, our EfficientNetV2 achieves 87.3% top-1 accuracy on ImageNet ILSVRC2012, outperforming the recent ViT by 2.0% accuracy while training 5x-11x faster using the same computing resources. Code will be available at https://github.com/google/automl/tree/master/efficientnetv2.

Bayesian inference usually requires running potentially costly inference procedures separately for every new observation. In contrast, the idea of amortized Bayesian inference is to initially invest computational cost in training an inference network on simulated data, which can subsequently be used to rapidly perform inference (i.e., to return estimates of posterior distributions) for new observations. This approach has been applied to many real-world models in the sciences and engineering, but it is unclear how robust the approach is to adversarial perturbations in the observed data. Here, we study the adversarial robustness of amortized Bayesian inference, focusing on simulation-based estimation of multi-dimensional posterior distributions. We show that almost unrecognizable, targeted perturbations of the observations can lead to drastic changes in the predicted posterior and highly unrealistic posterior predictive samples, across several benchmark tasks and a real-world example from neuroscience. We propose a computationally efficient regularization scheme based on penalizing the Fisher information of the conditional density estimator, and show how it improves the adversarial robustness of amortized Bayesian inference.

We investigate statistical properties of a likelihood approach to nonparametric estimation of a singular distribution using deep generative models. More specifically, a deep generative model is used to model high-dimensional data that are assumed to concentrate around some low-dimensional structure. Estimating the distribution supported on this low-dimensional structure, such as a low-dimensional manifold, is challenging due to its singularity with respect to the Lebesgue measure in the ambient space. In the considered model, a usual likelihood approach can fail to estimate the target distribution consistently due to the singularity. We prove that a novel and effective solution exists by perturbing the data with an instance noise, which leads to consistent estimation of the underlying distribution with desirable convergence rates. We also characterize the class of distributions that can be efficiently estimated via deep generative models. This class is sufficiently general to contain various structured distributions such as product distributions, classically smooth distributions and distributions supported on a low-dimensional manifold. Our analysis provides some insights on how deep generative models can avoid the curse of dimensionality for nonparametric distribution estimation. We conduct a thorough simulation study and real data analysis to empirically demonstrate that the proposed data perturbation technique improves the estimation performance significantly.

This manuscript considers the problem of learning a random Gaussian network function using a fully connected network with frozen intermediate layers and trainable readout layer. This problem can be seen as a natural generalization of the widely studied random features model to deeper architectures. First, we prove Gaussian universality of the test error in a ridge regression setting where the learner and target networks share the same intermediate layers, and provide a sharp asymptotic formula for it. Establishing this result requires proving a deterministic equivalent for traces of the deep random features sample covariance matrices which can be of independent interest. Second, we conjecture the asymptotic Gaussian universality of the test error in the more general setting of arbitrary convex losses and generic learner/target architectures. We provide extensive numerical evidence for this conjecture, which requires the derivation of closed-form expressions for the layer-wise post-activation population covariances. In light of our results, we investigate the interplay between architecture design and implicit regularization.

It is widely believed that a neural network can fit a training set containing at least as many samples as it has parameters, underpinning notions of overparameterized and underparameterized models. In practice, however, we only find solutions accessible via our training procedure, including the optimizer and regularizers, limiting flexibility. Moreover, the exact parameterization of the function class, built into an architecture, shapes its loss surface and impacts the minima we find. In this work, we examine the ability of neural networks to fit data in practice. Our findings indicate that: (1) standard optimizers find minima where the model can only fit training sets with significantly fewer samples than it has parameters; (2) convolutional networks are more parameter-efficient than MLPs and ViTs, even on randomly labeled data; (3) while stochastic training is thought to have a regularizing effect, SGD actually finds minima that fit more training data than full-batch gradient descent; (4) the difference in capacity to fit correctly labeled and incorrectly labeled samples can be predictive of generalization; (5) ReLU activation functions result in finding minima that fit more data despite being designed to avoid vanishing and exploding gradients in deep architectures.

In deep learning, often the training process finds an interpolator (a solution with 0 training loss), but the test loss is still low. This phenomenon, known as benign overfitting, is a major mystery that received a lot of recent attention. One common mechanism for benign overfitting is implicit regularization, where the training process leads to additional properties for the interpolator, often characterized by minimizing certain norms. However, even for a simple sparse linear regression problem y = beta^{*top} x +xi with sparse beta^*, neither minimum ell_1 or ell_2 norm interpolator gives the optimal test loss. In this work, we give a different parametrization of the model which leads to a new implicit regularization effect that combines the benefit of ell_1 and ell_2 interpolators. We show that training our new model via gradient descent leads to an interpolator with near-optimal test loss. Our result is based on careful analysis of the training dynamics and provides another example of implicit regularization effect that goes beyond norm minimization.

Deep neural networks include millions of learnable parameters, making their deployment over resource-constrained devices problematic. SeReNe (Sensitivity-based Regularization of Neurons) is a method for learning sparse topologies with a structure, exploiting neural sensitivity as a regularizer. We define the sensitivity of a neuron as the variation of the network output with respect to the variation of the activity of the neuron. The lower the sensitivity of a neuron, the less the network output is perturbed if the neuron output changes. By including the neuron sensitivity in the cost function as a regularization term, we areable to prune neurons with low sensitivity. As entire neurons are pruned rather then single parameters, practical network footprint reduction becomes possible. Our experimental results on multiple network architectures and datasets yield competitive compression ratios with respect to state-of-the-art references.

We identify and formalize a fundamental gradient descent phenomenon resulting in a learning proclivity in over-parameterized neural networks. Gradient Starvation arises when cross-entropy loss is minimized by capturing only a subset of features relevant for the task, despite the presence of other predictive features that fail to be discovered. This work provides a theoretical explanation for the emergence of such feature imbalance in neural networks. Using tools from Dynamical Systems theory, we identify simple properties of learning dynamics during gradient descent that lead to this imbalance, and prove that such a situation can be expected given certain statistical structure in training data. Based on our proposed formalism, we develop guarantees for a novel regularization method aimed at decoupling feature learning dynamics, improving accuracy and robustness in cases hindered by gradient starvation. We illustrate our findings with simple and real-world out-of-distribution (OOD) generalization experiments.

While diffusion models excel at generating high-quality images, prior work reports a significant performance gap between diffusion and autoregressive (AR) methods in language modeling. In this work, we show that simple masked discrete diffusion is more performant than previously thought. We apply an effective training recipe that improves the performance of masked diffusion models and derive a simplified, Rao-Blackwellized objective that results in additional improvements. Our objective has a simple form -- it is a mixture of classical masked language modeling losses -- and can be used to train encoder-only language models that admit efficient samplers, including ones that can generate arbitrary lengths of text semi-autoregressively like a traditional language model. On language modeling benchmarks, a range of masked diffusion models trained with modern engineering practices achieves a new state-of-the-art among diffusion models, and approaches AR perplexity. We release our code at: https://github.com/kuleshov-group/mdlm

Diffusion models have demonstrated compelling generation quality by optimizing the variational lower bound through a simple denoising score matching loss. In this paper, we provide theoretical evidence that the prevailing practice of using a constant loss weight strategy in diffusion models leads to biased estimation during the training phase. Simply optimizing the denoising network to predict Gaussian noise with constant weighting may hinder precise estimations of original images. To address the issue, we propose an elegant and effective weighting strategy grounded in the theoretically unbiased principle. Moreover, we conduct a comprehensive and systematic exploration to dissect the inherent bias problem deriving from constant weighting loss from the perspectives of its existence, impact and reasons. These analyses are expected to advance our understanding and demystify the inner workings of diffusion models. Through empirical evaluation, we demonstrate that our proposed debiased estimation method significantly enhances sample quality without the reliance on complex techniques, and exhibits improved efficiency compared to the baseline method both in training and sampling processes.

Practitioners prune neural networks for efficiency gains and generalization improvements, but few scrutinize the factors determining the prunability of a neural network the maximum fraction of weights that pruning can remove without compromising the model's test accuracy. In this work, we study the properties of input data that may contribute to the prunability of a neural network. For high dimensional input data such as images, text, and audio, the manifold hypothesis suggests that these high dimensional inputs approximately lie on or near a significantly lower dimensional manifold. Prior work demonstrates that the underlying low dimensional structure of the input data may affect the sample efficiency of learning. In this paper, we investigate whether the low dimensional structure of the input data affects the prunability of a neural network.

Label smoothing regularization (LSR) has a great success in training deep neural networks by stochastic algorithms such as stochastic gradient descent and its variants. However, the theoretical understanding of its power from the view of optimization is still rare. This study opens the door to a deep understanding of LSR by initiating the analysis. In this paper, we analyze the convergence behaviors of stochastic gradient descent with label smoothing regularization for solving non-convex problems and show that an appropriate LSR can help to speed up the convergence by reducing the variance. More interestingly, we proposed a simple yet effective strategy, namely Two-Stage LAbel smoothing algorithm (TSLA), that uses LSR in the early training epochs and drops it off in the later training epochs. We observe from the improved convergence result of TSLA that it benefits from LSR in the first stage and essentially converges faster in the second stage. To the best of our knowledge, this is the first work for understanding the power of LSR via establishing convergence complexity of stochastic methods with LSR in non-convex optimization. We empirically demonstrate the effectiveness of the proposed method in comparison with baselines on training ResNet models over benchmark data sets.

In this paper, we study the implicit regularization of stochastic gradient descent (SGD) through the lens of {\em dynamical stability} (Wu et al., 2018). We start by revising existing stability analyses of SGD, showing how the Frobenius norm and trace of Hessian relate to different notions of stability. Notably, if a global minimum is linearly stable for SGD, then the trace of Hessian must be less than or equal to 2/eta, where eta denotes the learning rate. By contrast, for gradient descent (GD), the stability imposes a similar constraint but only on the largest eigenvalue of Hessian. We then turn to analyze the generalization properties of these stable minima, focusing specifically on two-layer ReLU networks and diagonal linear networks. Notably, we establish the {\em equivalence} between these metrics of sharpness and certain parameter norms for the two models, which allows us to show that the stable minima of SGD provably generalize well. By contrast, the stability-induced regularization of GD is provably too weak to ensure satisfactory generalization. This discrepancy provides an explanation of why SGD often generalizes better than GD. Note that the learning rate (LR) plays a pivotal role in the strength of stability-induced regularization. As the LR increases, the regularization effect becomes more pronounced, elucidating why SGD with a larger LR consistently demonstrates superior generalization capabilities. Additionally, numerical experiments are provided to support our theoretical findings.

Deep neural network is difficult to train and this predicament becomes worse as the depth increases. The essence of this problem exists in the magnitude of backpropagated errors that will result in gradient vanishing or exploding phenomenon. We show that a variant of regularizer which utilizes orthonormality among different filter banks can alleviate this problem. Moreover, we design a backward error modulation mechanism based on the quasi-isometry assumption between two consecutive parametric layers. Equipped with these two ingredients, we propose several novel optimization solutions that can be utilized for training a specific-structured (repetitively triple modules of Conv-BNReLU) extremely deep convolutional neural network (CNN) WITHOUT any shortcuts/ identity mappings from scratch. Experiments show that our proposed solutions can achieve distinct improvements for a 44-layer and a 110-layer plain networks on both the CIFAR-10 and ImageNet datasets. Moreover, we can successfully train plain CNNs to match the performance of the residual counterparts. Besides, we propose new principles for designing network structure from the insights evoked by orthonormality. Combined with residual structure, we achieve comparative performance on the ImageNet dataset.

Optimal Transport is a useful metric to compare probability distributions and to compute a pairing given a ground cost. Its entropic regularization variant (eOT) is crucial to have fast algorithms and reflect fuzzy/noisy matchings. This work focuses on Inverse Optimal Transport (iOT), the problem of inferring the ground cost from samples drawn from a coupling that solves an eOT problem. It is a relevant problem that can be used to infer unobserved/missing links, and to obtain meaningful information about the structure of the ground cost yielding the pairing. On one side, iOT benefits from convexity, but on the other side, being ill-posed, it requires regularization to handle the sampling noise. This work presents an in-depth theoretical study of the l1 regularization to model for instance Euclidean costs with sparse interactions between features. Specifically, we derive a sufficient condition for the robust recovery of the sparsity of the ground cost that can be seen as a far reaching generalization of the Lasso's celebrated Irrepresentability Condition. To provide additional insight into this condition, we work out in detail the Gaussian case. We show that as the entropic penalty varies, the iOT problem interpolates between a graphical Lasso and a classical Lasso, thereby establishing a connection between iOT and graph estimation, an important problem in ML.

The ability to control for the kinds of information encoded in neural representation has a variety of use cases, especially in light of the challenge of interpreting these models. We present Iterative Null-space Projection (INLP), a novel method for removing information from neural representations. Our method is based on repeated training of linear classifiers that predict a certain property we aim to remove, followed by projection of the representations on their null-space. By doing so, the classifiers become oblivious to that target property, making it hard to linearly separate the data according to it. While applicable for multiple uses, we evaluate our method on bias and fairness use-cases, and show that our method is able to mitigate bias in word embeddings, as well as to increase fairness in a setting of multi-class classification.

Democratization of machine learning requires architectures that automatically adapt to new problems. Neural Differential Equations (NDEs) have emerged as a popular modeling framework by removing the need for ML practitioners to choose the number of layers in a recurrent model. While we can control the computational cost by choosing the number of layers in standard architectures, in NDEs the number of neural network evaluations for a forward pass can depend on the number of steps of the adaptive ODE solver. But, can we force the NDE to learn the version with the least steps while not increasing the training cost? Current strategies to overcome slow prediction require high order automatic differentiation, leading to significantly higher training time. We describe a novel regularization method that uses the internal cost heuristics of adaptive differential equation solvers combined with discrete adjoint sensitivities to guide the training process towards learning NDEs that are easier to solve. This approach opens up the blackbox numerical analysis behind the differential equation solver's algorithm and directly uses its local error estimates and stiffness heuristics as cheap and accurate cost estimates. We incorporate our method without any change in the underlying NDE framework and show that our method extends beyond Ordinary Differential Equations to accommodate Neural Stochastic Differential Equations. We demonstrate how our approach can halve the prediction time and, unlike other methods which can increase the training time by an order of magnitude, we demonstrate similar reduction in training times. Together this showcases how the knowledge embedded within state-of-the-art equation solvers can be used to enhance machine learning.

Supervised learning can be viewed as distilling relevant information from input data into feature representations. This process becomes difficult when supervision is noisy as the distilled information might not be relevant. In fact, recent research shows that networks can easily overfit all labels including those that are corrupted, and hence can hardly generalize to clean datasets. In this paper, we focus on the problem of learning with noisy labels and introduce compression inductive bias to network architectures to alleviate this over-fitting problem. More precisely, we revisit one classical regularization named Dropout and its variant Nested Dropout. Dropout can serve as a compression constraint for its feature dropping mechanism, while Nested Dropout further learns ordered feature representations w.r.t. feature importance. Moreover, the trained models with compression regularization are further combined with Co-teaching for performance boost. Theoretically, we conduct bias-variance decomposition of the objective function under compression regularization. We analyze it for both single model and Co-teaching. This decomposition provides three insights: (i) it shows that over-fitting is indeed an issue for learning with noisy labels; (ii) through an information bottleneck formulation, it explains why the proposed feature compression helps in combating label noise; (iii) it gives explanations on the performance boost brought by incorporating compression regularization into Co-teaching. Experiments show that our simple approach can have comparable or even better performance than the state-of-the-art methods on benchmarks with real-world label noise including Clothing1M and ANIMAL-10N. Our implementation is available at https://yingyichen-cyy.github.io/CompressFeatNoisyLabels/.

The presence of distribution shifts poses a significant challenge for deploying modern machine learning models in real-world applications. This work focuses on the target shift problem in a regression setting (Zhang et al., 2013; Nguyen et al., 2016). More specifically, the target variable y (also known as the response variable), which is continuous, has different marginal distributions in the training source and testing domain, while the conditional distribution of features x given y remains the same. While most literature focuses on classification tasks with finite target space, the regression problem has an infinite dimensional target space, which makes many of the existing methods inapplicable. In this work, we show that the continuous target shift problem can be addressed by estimating the importance weight function from an ill-posed integral equation. We propose a nonparametric regularized approach named ReTaSA to solve the ill-posed integral equation and provide theoretical justification for the estimated importance weight function. The effectiveness of the proposed method has been demonstrated with extensive numerical studies on synthetic and real-world datasets.

We derive a simple and model-independent formula for the change in the generalization gap due to a gradient descent update. We then compare the change in the test error for stochastic gradient descent to the change in test error from an equivalent number of gradient descent updates and show explicitly that stochastic gradient descent acts to regularize generalization error by decorrelating nearby updates. These calculations depends on the details of the model only through the mean and covariance of the gradient distribution, which may be readily measured for particular models of interest. We discuss further improvements to these calculations and comment on possible implications for stochastic optimization.

The Vision Transformer architecture is a deep learning model inspired by the success of the Transformer model in Natural Language Processing. However, the self-attention mechanism, large number of parameters, and the requirement for a substantial amount of training data still make Vision Transformers computationally burdensome. In this research, we investigate the possibility of applying Sparse Regularization to Vision Transformers and the impact of Pruning, either after Sparse Regularization or without it, on the trade-off between performance and efficiency. To accomplish this, we apply Sparse Regularization and Pruning methods to the Vision Transformer architecture for image classification tasks on the CIFAR-10, CIFAR-100, and ImageNet-100 datasets. The training process for the Vision Transformer model consists of two parts: pre-training and fine-tuning. Pre-training utilizes ImageNet21K data, followed by fine-tuning for 20 epochs. The results show that when testing with CIFAR-100 and ImageNet-100 data, models with Sparse Regularization can increase accuracy by 0.12%. Furthermore, applying pruning to models with Sparse Regularization yields even better results. Specifically, it increases the average accuracy by 0.568% on CIFAR-10 data, 1.764% on CIFAR-100, and 0.256% on ImageNet-100 data compared to pruning models without Sparse Regularization. Code can be accesed here: https://github.com/yogiprsty/Sparse-ViT

Neural retrievers based on dense representations combined with Approximate Nearest Neighbors search have recently received a lot of attention, owing their success to distillation and/or better sampling of examples for training -- while still relying on the same backbone architecture. In the meantime, sparse representation learning fueled by traditional inverted indexing techniques has seen a growing interest, inheriting from desirable IR priors such as explicit lexical matching. While some architectural variants have been proposed, a lesser effort has been put in the training of such models. In this work, we build on SPLADE -- a sparse expansion-based retriever -- and show to which extent it is able to benefit from the same training improvements as dense models, by studying the effect of distillation, hard-negative mining as well as the Pre-trained Language Model initialization. We furthermore study the link between effectiveness and efficiency, on in-domain and zero-shot settings, leading to state-of-the-art results in both scenarios for sufficiently expressive models.

N:M Structured sparsity has garnered significant interest as a result of relatively modest overhead and improved efficiency. Additionally, this form of sparsity holds considerable appeal for reducing the memory footprint owing to their modest representation overhead. There have been efforts to develop training recipes for N:M structured sparsity, they primarily focus on low-sparsity regions (sim50\%). Nonetheless, performance of models trained using these approaches tends to decline when confronted with high-sparsity regions (>80\%). In this work, we study the effectiveness of existing sparse training recipes at high-sparsity regions and argue that these methods fail to sustain the model quality on par with low-sparsity regions. We demonstrate that the significant factor contributing to this disparity is the presence of elevated levels of induced noise in the gradient magnitudes. To mitigate this undesirable effect, we employ decay mechanisms to progressively restrict the flow of gradients towards pruned elements. Our approach improves the model quality by up to 2% and 5% in vision and language models at high sparsity regime, respectively. We also evaluate the trade-off between model accuracy and training compute cost in terms of FLOPs. At iso-training FLOPs, our method yields better performance compared to conventional sparse training recipes, exhibiting an accuracy improvement of up to 2%. The source code is available at https://github.com/abhibambhaniya/progressive_gradient_flow_nm_sparsity.

Recently, diffusion models have made remarkable progress in text-to-image (T2I) generation, synthesizing images with high fidelity and diverse contents. Despite this advancement, latent space smoothness within diffusion models remains largely unexplored. Smooth latent spaces ensure that a perturbation on an input latent corresponds to a steady change in the output image. This property proves beneficial in downstream tasks, including image interpolation, inversion, and editing. In this work, we expose the non-smoothness of diffusion latent spaces by observing noticeable visual fluctuations resulting from minor latent variations. To tackle this issue, we propose Smooth Diffusion, a new category of diffusion models that can be simultaneously high-performing and smooth. Specifically, we introduce Step-wise Variation Regularization to enforce the proportion between the variations of an arbitrary input latent and that of the output image is a constant at any diffusion training step. In addition, we devise an interpolation standard deviation (ISTD) metric to effectively assess the latent space smoothness of a diffusion model. Extensive quantitative and qualitative experiments demonstrate that Smooth Diffusion stands out as a more desirable solution not only in T2I generation but also across various downstream tasks. Smooth Diffusion is implemented as a plug-and-play Smooth-LoRA to work with various community models. Code is available at https://github.com/SHI-Labs/Smooth-Diffusion.

We address the problem of network calibration adjusting miscalibrated confidences of deep neural networks. Many approaches to network calibration adopt a regularization-based method that exploits a regularization term to smooth the miscalibrated confidences. Although these approaches have shown the effectiveness on calibrating the networks, there is still a lack of understanding on the underlying principles of regularization in terms of network calibration. We present in this paper an in-depth analysis of existing regularization-based methods, providing a better understanding on how they affect to network calibration. Specifically, we have observed that 1) the regularization-based methods can be interpreted as variants of label smoothing, and 2) they do not always behave desirably. Based on the analysis, we introduce a novel loss function, dubbed ACLS, that unifies the merits of existing regularization methods, while avoiding the limitations. We show extensive experimental results for image classification and semantic segmentation on standard benchmarks, including CIFAR10, Tiny-ImageNet, ImageNet, and PASCAL VOC, demonstrating the effectiveness of our loss function.

Training deep neural networks for classification often includes minimizing the training loss beyond the zero training error point. In this phase of training, a "neural collapse" behavior has been observed: the variability of features (outputs of the penultimate layer) of within-class samples decreases and the mean features of different classes approach a certain tight frame structure. Recent works analyze this behavior via idealized unconstrained features models where all the minimizers exhibit exact collapse. However, with practical networks and datasets, the features typically do not reach exact collapse, e.g., because deep layers cannot arbitrarily modify intermediate features that are far from being collapsed. In this paper, we propose a richer model that can capture this phenomenon by forcing the features to stay in the vicinity of a predefined features matrix (e.g., intermediate features). We explore the model in the small vicinity case via perturbation analysis and establish results that cannot be obtained by the previously studied models. For example, we prove reduction in the within-class variability of the optimized features compared to the predefined input features (via analyzing gradient flow on the "central-path" with minimal assumptions), analyze the minimizers in the near-collapse regime, and provide insights on the effect of regularization hyperparameters on the closeness to collapse. We support our theory with experiments in practical deep learning settings.

While neural networks are used for classification tasks across domains, a long-standing open problem in machine learning is determining whether neural networks trained using standard procedures are optimal for classification, i.e., whether such models minimize the probability of misclassification for arbitrary data distributions. In this work, we identify and construct an explicit set of neural network classifiers that achieve optimality. Since effective neural networks in practice are typically both wide and deep, we analyze infinitely wide networks that are also infinitely deep. In particular, using the recent connection between infinitely wide neural networks and Neural Tangent Kernels, we provide explicit activation functions that can be used to construct networks that achieve optimality. Interestingly, these activation functions are simple and easy to implement, yet differ from commonly used activations such as ReLU or sigmoid. More generally, we create a taxonomy of infinitely wide and deep networks and show that these models implement one of three well-known classifiers depending on the activation function used: (1) 1-nearest neighbor (model predictions are given by the label of the nearest training example); (2) majority vote (model predictions are given by the label of the class with greatest representation in the training set); or (3) singular kernel classifiers (a set of classifiers containing those that achieve optimality). Our results highlight the benefit of using deep networks for classification tasks, in contrast to regression tasks, where excessive depth is harmful.

Recently, flat minima are proven to be effective for improving generalization and sharpness-aware minimization (SAM) achieves state-of-the-art performance. Yet the current definition of flatness discussed in SAM and its follow-ups are limited to the zeroth-order flatness (i.e., the worst-case loss within a perturbation radius). We show that the zeroth-order flatness can be insufficient to discriminate minima with low generalization error from those with high generalization error both when there is a single minimum or multiple minima within the given perturbation radius. Thus we present first-order flatness, a stronger measure of flatness focusing on the maximal gradient norm within a perturbation radius which bounds both the maximal eigenvalue of Hessian at local minima and the regularization function of SAM. We also present a novel training procedure named Gradient norm Aware Minimization (GAM) to seek minima with uniformly small curvature across all directions. Experimental results show that GAM improves the generalization of models trained with current optimizers such as SGD and AdamW on various datasets and networks. Furthermore, we show that GAM can help SAM find flatter minima and achieve better generalization.

We study the problem of learning a single neuron with respect to the L_2^2-loss in the presence of adversarial label noise. We give an efficient algorithm that, for a broad family of activations including ReLUs, approximates the optimal L_2^2-error within a constant factor. Our algorithm applies under much milder distributional assumptions compared to prior work. The key ingredient enabling our results is a novel connection to local error bounds from optimization theory.

Deep neural networks are highly performant, but might base their decision on spurious or background features that co-occur with certain classes, which can hurt generalization. To mitigate this issue, the usage of 'model guidance' has gained popularity recently: for this, models are guided to be "right for the right reasons" by regularizing the models' explanations to highlight the right features. Experimental validation of these approaches has thus far however been limited to relatively simple and / or synthetic datasets. To gain a better understanding of which model-guiding approaches actually transfer to more challenging real-world datasets, in this work we conduct an in-depth evaluation across various loss functions, attribution methods, models, and 'guidance depths' on the PASCAL VOC 2007 and MS COCO 2014 datasets, and show that model guidance can sometimes even improve model performance. In this context, we further propose a novel energy loss, show its effectiveness in directing the model to focus on object features. We also show that these gains can be achieved even with a small fraction (e.g. 1%) of bounding box annotations, highlighting the cost effectiveness of this approach. Lastly, we show that this approach can also improve generalization under distribution shifts. Code will be made available.

In this paper we propose to study generalization of neural networks on small algorithmically generated datasets. In this setting, questions about data efficiency, memorization, generalization, and speed of learning can be studied in great detail. In some situations we show that neural networks learn through a process of "grokking" a pattern in the data, improving generalization performance from random chance level to perfect generalization, and that this improvement in generalization can happen well past the point of overfitting. We also study generalization as a function of dataset size and find that smaller datasets require increasing amounts of optimization for generalization. We argue that these datasets provide a fertile ground for studying a poorly understood aspect of deep learning: generalization of overparametrized neural networks beyond memorization of the finite training dataset.

Convolutional Neural Networks have been shown to be vulnerable to adversarial examples, which are known to locate in subspaces close to where normal data lies but are not naturally occurring and of low probability. In this work, we investigate the potential effect defense techniques have on the geometry of the likelihood landscape - likelihood of the input images under the trained model. We first propose a way to visualize the likelihood landscape leveraging an energy-based model interpretation of discriminative classifiers. Then we introduce a measure to quantify the flatness of the likelihood landscape. We observe that a subset of adversarial defense techniques results in a similar effect of flattening the likelihood landscape. We further explore directly regularizing towards a flat landscape for adversarial robustness.

Imposing orthogonality on the layers of neural networks is known to facilitate the learning by limiting the exploding/vanishing of the gradient; decorrelate the features; improve the robustness. This paper studies the theoretical properties of orthogonal convolutional layers.We establish necessary and sufficient conditions on the layer architecture guaranteeing the existence of an orthogonal convolutional transform. The conditions prove that orthogonal convolutional transforms exist for almost all architectures used in practice for 'circular' padding.We also exhibit limitations with 'valid' boundary conditions and 'same' boundary conditions with zero-padding.Recently, a regularization term imposing the orthogonality of convolutional layers has been proposed, and impressive empirical results have been obtained in different applications (Wang et al. 2020).The second motivation of the present paper is to specify the theory behind this.We make the link between this regularization term and orthogonality measures. In doing so, we show that this regularization strategy is stable with respect to numerical and optimization errors and that, in the presence of small errors and when the size of the signal/image is large, the convolutional layers remain close to isometric.The theoretical results are confirmed with experiments and the landscape of the regularization term is studied. Experiments on real data sets show that when orthogonality is used to enforce robustness, the parameter multiplying the regularization termcan be used to tune a tradeoff between accuracy and orthogonality, for the benefit of both accuracy and robustness.Altogether, the study guarantees that the regularization proposed in Wang et al. (2020) is an efficient, flexible and stable numerical strategy to learn orthogonal convolutional layers.

Since the introduction of deep learning, a wide scope of representation properties, such as decorrelation, whitening, disentanglement, rank, isotropy, and mutual information, have been studied to improve the quality of representation. However, manipulating such properties can be challenging in terms of implementational effectiveness and general applicability. To address these limitations, we propose to regularize von Neumann entropy~(VNE) of representation. First, we demonstrate that the mathematical formulation of VNE is superior in effectively manipulating the eigenvalues of the representation autocorrelation matrix. Then, we demonstrate that it is widely applicable in improving state-of-the-art algorithms or popular benchmark algorithms by investigating domain-generalization, meta-learning, self-supervised learning, and generative models. In addition, we formally establish theoretical connections with rank, disentanglement, and isotropy of representation. Finally, we provide discussions on the dimension control of VNE and the relationship with Shannon entropy. Code is available at: https://github.com/jaeill/CVPR23-VNE.

We introduce a design strategy for neural network macro-architecture based on self-similarity. Repeated application of a simple expansion rule generates deep networks whose structural layouts are precisely truncated fractals. These networks contain interacting subpaths of different lengths, but do not include any pass-through or residual connections; every internal signal is transformed by a filter and nonlinearity before being seen by subsequent layers. In experiments, fractal networks match the excellent performance of standard residual networks on both CIFAR and ImageNet classification tasks, thereby demonstrating that residual representations may not be fundamental to the success of extremely deep convolutional neural networks. Rather, the key may be the ability to transition, during training, from effectively shallow to deep. We note similarities with student-teacher behavior and develop drop-path, a natural extension of dropout, to regularize co-adaptation of subpaths in fractal architectures. Such regularization allows extraction of high-performance fixed-depth subnetworks. Additionally, fractal networks exhibit an anytime property: shallow subnetworks provide a quick answer, while deeper subnetworks, with higher latency, provide a more accurate answer.

Diffusion inversion is the problem of taking an image and a text prompt that describes it and finding a noise latent that would generate the image. Most current inversion techniques operate by approximately solving an implicit equation and may converge slowly or yield poor reconstructed images. Here, we formulate the problem as finding the roots of an implicit equation and design a method to solve it efficiently. Our solution is based on Newton-Raphson (NR), a well-known technique in numerical analysis. A naive application of NR may be computationally infeasible and tends to converge to incorrect solutions. We describe an efficient regularized formulation that converges quickly to a solution that provides high-quality reconstructions. We also identify a source of inconsistency stemming from prompt conditioning during the inversion process, which significantly degrades the inversion quality. To address this, we introduce a prompt-aware adjustment of the encoding, effectively correcting this issue. Our solution, Regularized Newton-Raphson Inversion, inverts an image within 0.5 sec for latent consistency models, opening the door for interactive image editing. We further demonstrate improved results in image interpolation and generation of rare objects.

Parameter-efficient fine-tuning methods, represented by LoRA, play an essential role in adapting large-scale pre-trained models to downstream tasks. However, fine-tuning LoRA-series models also faces the risk of overfitting on the training dataset, and yet there's still a lack of theoretical guidance and practical mechanism to control overfitting on LoRA-based PEFT methods. In this paper, we propose a LoRA Dropout mechanism for the LoRA-based methods by introducing random noises to the learnable low-rank matrices and increasing parameter sparsity. We then demonstrate the theoretical mechanism of our LoRA Dropout mechanism from the perspective of sparsity regularization by providing a generalization error bound under this framework. Theoretical results show that appropriate sparsity would help tighten the gap between empirical and generalization risks and thereby control overfitting. Furthermore, based on the LoRA Dropout framework, we introduce a test-time ensemble strategy and provide theoretical evidence demonstrating that the ensemble method can further compress the error bound, and lead to better performance during inference time. Extensive experiments on various NLP tasks provide practical validations of the effectiveness of our LoRA Dropout framework in improving model accuracy and calibration.

The Invariant Risk Minimization (IRM) principle was first proposed by Arjovsky et al. [2019] to address the domain generalization problem by leveraging data heterogeneity from differing experimental conditions. Specifically, IRM seeks to find a data representation under which an optimal classifier remains invariant across all domains. Despite the conceptual appeal of IRM, the effectiveness of the originally proposed invariance penalty has recently been brought into question. In particular, there exists counterexamples for which that invariance penalty can be arbitrarily small for non-invariant data representations. We propose an alternative invariance penalty by revisiting the Gramian matrix of the data representation. We discuss the role of its eigenvalues in the relationship between the risk and the invariance penalty, and demonstrate that it is ill-conditioned for said counterexamples. The proposed approach is guaranteed to recover an invariant representation for linear settings under mild non-degeneracy conditions. Its effectiveness is substantiated by experiments on DomainBed and InvarianceUnitTest, two extensive test beds for domain generalization.

In disentangled representation learning, a model is asked to tease apart a dataset's underlying sources of variation and represent them independently of one another. Since the model is provided with no ground truth information about these sources, inductive biases take a paramount role in enabling disentanglement. In this work, we construct an inductive bias towards encoding to and decoding from an organized latent space. Concretely, we do this by (i) quantizing the latent space into discrete code vectors with a separate learnable scalar codebook per dimension and (ii) applying strong model regularization via an unusually high weight decay. Intuitively, the latent space design forces the encoder to combinatorially construct codes from a small number of distinct scalar values, which in turn enables the decoder to assign a consistent meaning to each value. Regularization then serves to drive the model towards this parsimonious strategy. We demonstrate the broad applicability of this approach by adding it to both basic data-reconstructing (vanilla autoencoder) and latent-reconstructing (InfoGAN) generative models. For reliable evaluation, we also propose InfoMEC, a new set of metrics for disentanglement that is cohesively grounded in information theory and fixes well-established shortcomings in previous metrics. Together with regularization, latent quantization dramatically improves the modularity and explicitness of learned representations on a representative suite of benchmark datasets. In particular, our quantized-latent autoencoder (QLAE) consistently outperforms strong methods from prior work in these key disentanglement properties without compromising data reconstruction.

In representation learning, uniformity refers to the uniform feature distribution in the latent space (i.e., unit hypersphere). Previous work has shown that improving uniformity contributes to the learning of under-represented classes. However, most of the previous work focused on classification; the representation space of imbalanced regression remains unexplored. Classification-based methods are not suitable for regression tasks because they cluster features into distinct groups without considering the continuous and ordered nature essential for regression. In a geometric aspect, we uniquely focus on ensuring uniformity in the latent space for imbalanced regression through two key losses: enveloping and homogeneity. The enveloping loss encourages the induced trace to uniformly occupy the surface of a hypersphere, while the homogeneity loss ensures smoothness, with representations evenly spaced at consistent intervals. Our method integrates these geometric principles into the data representations via a Surrogate-driven Representation Learning (SRL) framework. Experiments with real-world regression and operator learning tasks highlight the importance of uniformity in imbalanced regression and validate the efficacy of our geometry-based loss functions.

Convolutional neural networks show remarkable results in classification but struggle with learning new things on the fly. We present a novel rehearsal-free approach, where a deep neural network is continually learning new unseen object categories without saving any data of prior sequences. Our approach is called RECALL, as the network recalls categories by calculating logits for old categories before training new ones. These are then used during training to avoid changing the old categories. For each new sequence, a new head is added to accommodate the new categories. To mitigate forgetting, we present a regularization strategy where we replace the classification with a regression. Moreover, for the known categories, we propose a Mahalanobis loss that includes the variances to account for the changing densities between known and unknown categories. Finally, we present a novel dataset for continual learning, especially suited for object recognition on a mobile robot (HOWS-CL-25), including 150,795 synthetic images of 25 household object categories. Our approach RECALL outperforms the current state of the art on CORe50 and iCIFAR-100 and reaches the best performance on HOWS-CL-25.

Despite apparent human-level performances of deep neural networks (DNN), they behave fundamentally differently from humans. They easily change predictions when small corruptions such as blur and noise are applied on the input (lack of robustness), and they often produce confident predictions on out-of-distribution samples (improper uncertainty measure). While a number of researches have aimed to address those issues, proposed solutions are typically expensive and complicated (e.g. Bayesian inference and adversarial training). Meanwhile, many simple and cheap regularization methods have been developed to enhance the generalization of classifiers. Such regularization methods have largely been overlooked as baselines for addressing the robustness and uncertainty issues, as they are not specifically designed for that. In this paper, we provide extensive empirical evaluations on the robustness and uncertainty estimates of image classifiers (CIFAR-100 and ImageNet) trained with state-of-the-art regularization methods. Furthermore, experimental results show that certain regularization methods can serve as strong baseline methods for robustness and uncertainty estimation of DNNs.

This paper presents a comprehensive study on the role of Classifier-Free Guidance (CFG) in text-conditioned diffusion models from the perspective of inference efficiency. In particular, we relax the default choice of applying CFG in all diffusion steps and instead search for efficient guidance policies. We formulate the discovery of such policies in the differentiable Neural Architecture Search framework. Our findings suggest that the denoising steps proposed by CFG become increasingly aligned with simple conditional steps, which renders the extra neural network evaluation of CFG redundant, especially in the second half of the denoising process. Building upon this insight, we propose "Adaptive Guidance" (AG), an efficient variant of CFG, that adaptively omits network evaluations when the denoising process displays convergence. Our experiments demonstrate that AG preserves CFG's image quality while reducing computation by 25%. Thus, AG constitutes a plug-and-play alternative to Guidance Distillation, achieving 50% of the speed-ups of the latter while being training-free and retaining the capacity to handle negative prompts. Finally, we uncover further redundancies of CFG in the first half of the diffusion process, showing that entire neural function evaluations can be replaced by simple affine transformations of past score estimates. This method, termed LinearAG, offers even cheaper inference at the cost of deviating from the baseline model. Our findings provide insights into the efficiency of the conditional denoising process that contribute to more practical and swift deployment of text-conditioned diffusion models.

Self-supervision is often used for pre-training to foster performance on a downstream task by constructing meaningful representations of samples. Self-supervised learning (SSL) generally involves generating different views of the same sample and thus requires data augmentations that are challenging to construct for tabular data. This constitutes one of the main challenges of self-supervision for structured data. In the present work, we propose a novel augmentation-free SSL method for tabular data. Our approach, T-JEPA, relies on a Joint Embedding Predictive Architecture (JEPA) and is akin to mask reconstruction in the latent space. It involves predicting the latent representation of one subset of features from the latent representation of a different subset within the same sample, thereby learning rich representations without augmentations. We use our method as a pre-training technique and train several deep classifiers on the obtained representation. Our experimental results demonstrate a substantial improvement in both classification and regression tasks, outperforming models trained directly on samples in their original data space. Moreover, T-JEPA enables some methods to consistently outperform or match the performance of traditional methods likes Gradient Boosted Decision Trees. To understand why, we extensively characterize the obtained representations and show that T-JEPA effectively identifies relevant features for downstream tasks without access to the labels. Additionally, we introduce regularization tokens, a novel regularization method critical for training of JEPA-based models on structured data.

Regularized optimal transport (OT) is now increasingly used as a loss or as a matching layer in neural networks. Entropy-regularized OT can be computed using the Sinkhorn algorithm but it leads to fully-dense transportation plans, meaning that all sources are (fractionally) matched with all targets. To address this issue, several works have investigated quadratic regularization instead. This regularization preserves sparsity and leads to unconstrained and smooth (semi) dual objectives, that can be solved with off-the-shelf gradient methods. Unfortunately, quadratic regularization does not give direct control over the cardinality (number of nonzeros) of the transportation plan. We propose in this paper a new approach for OT with explicit cardinality constraints on the transportation plan. Our work is motivated by an application to sparse mixture of experts, where OT can be used to match input tokens such as image patches with expert models such as neural networks. Cardinality constraints ensure that at most k tokens are matched with an expert, which is crucial for computational performance reasons. Despite the nonconvexity of cardinality constraints, we show that the corresponding (semi) dual problems are tractable and can be solved with first-order gradient methods. Our method can be thought as a middle ground between unregularized OT (recovered in the limit case k=1) and quadratically-regularized OT (recovered when k is large enough). The smoothness of the objectives increases as k increases, giving rise to a trade-off between convergence speed and sparsity of the optimal plan.

Mixture of experts (MoE) has a well-principled finite mixture model construction for prediction, allowing the gating network (mixture weights) to learn from the predictors (explanatory variables) together with the experts' network (mixture component densities). We investigate the estimation properties of MoEs in a high-dimensional setting, where the number of predictors is much larger than the sample size, for which the literature lacks computational and especially theoretical results. We consider the class of finite MoE models with softmax gating functions and Gaussian regression experts, and focus on the theoretical properties of their l_1-regularized estimation via the Lasso. We provide a lower bound on the regularization parameter of the Lasso penalty that ensures an l_1-oracle inequality is satisfied by the Lasso estimator according to the Kullback--Leibler loss. We further state an l_1-ball oracle inequality for the l_1-penalized maximum likelihood estimator from the model selection.

Dropout is a widely utilized regularization technique in the training of neural networks, nevertheless, its underlying mechanism and its impact on achieving good generalization abilities remain poorly understood. In this work, we derive the stochastic modified equations for analyzing the dynamics of dropout, where its discrete iteration process is approximated by a class of stochastic differential equations. In order to investigate the underlying mechanism by which dropout facilitates the identification of flatter minima, we study the noise structure of the derived stochastic modified equation for dropout. By drawing upon the structural resemblance between the Hessian and covariance through several intuitive approximations, we empirically demonstrate the universal presence of the inverse variance-flatness relation and the Hessian-variance relation, throughout the training process of dropout. These theoretical and empirical findings make a substantial contribution to our understanding of the inherent tendency of dropout to locate flatter minima.

Deep neural networks trained on large supervised datasets have led to impressive results in image classification and other tasks. However, well-annotated datasets can be time-consuming and expensive to collect, lending increased interest to larger but noisy datasets that are more easily obtained. In this paper, we show that deep neural networks are capable of generalizing from training data for which true labels are massively outnumbered by incorrect labels. We demonstrate remarkably high test performance after training on corrupted data from MNIST, CIFAR, and ImageNet. For example, on MNIST we obtain test accuracy above 90 percent even after each clean training example has been diluted with 100 randomly-labeled examples. Such behavior holds across multiple patterns of label noise, even when erroneous labels are biased towards confusing classes. We show that training in this regime requires a significant but manageable increase in dataset size that is related to the factor by which correct labels have been diluted. Finally, we provide an analysis of our results that shows how increasing noise decreases the effective batch size.

Recent self-supervised methods for image representation learning are based on maximizing the agreement between embedding vectors from different views of the same image. A trivial solution is obtained when the encoder outputs constant vectors. This collapse problem is often avoided through implicit biases in the learning architecture, that often lack a clear justification or interpretation. In this paper, we introduce VICReg (Variance-Invariance-Covariance Regularization), a method that explicitly avoids the collapse problem with a simple regularization term on the variance of the embeddings along each dimension individually. VICReg combines the variance term with a decorrelation mechanism based on redundancy reduction and covariance regularization, and achieves results on par with the state of the art on several downstream tasks. In addition, we show that incorporating our new variance term into other methods helps stabilize the training and leads to performance improvements.

Continual learning is a setting where machine learning models learn novel concepts from continuously shifting training data, while simultaneously avoiding degradation of knowledge on previously seen classes which may disappear from the training data for extended periods of time (a phenomenon known as the catastrophic forgetting problem). Current approaches for continual learning of a single expanding task (aka class-incremental continual learning) require extensive rehearsal of previously seen data to avoid this degradation of knowledge. Unfortunately, rehearsal comes at a cost to memory, and it may also violate data-privacy. Instead, we explore combining knowledge distillation and parameter regularization in new ways to achieve strong continual learning performance without rehearsal. Specifically, we take a deep dive into common continual learning techniques: prediction distillation, feature distillation, L2 parameter regularization, and EWC parameter regularization. We first disprove the common assumption that parameter regularization techniques fail for rehearsal-free continual learning of a single, expanding task. Next, we explore how to leverage knowledge from a pre-trained model in rehearsal-free continual learning and find that vanilla L2 parameter regularization outperforms EWC parameter regularization and feature distillation. Finally, we explore the recently popular ImageNet-R benchmark, and show that L2 parameter regularization implemented in self-attention blocks of a ViT transformer outperforms recent popular prompting for continual learning methods.

Overparameterized neural networks can be highly accurate on average on an i.i.d. test set yet consistently fail on atypical groups of the data (e.g., by learning spurious correlations that hold on average but not in such groups). Distributionally robust optimization (DRO) allows us to learn models that instead minimize the worst-case training loss over a set of pre-defined groups. However, we find that naively applying group DRO to overparameterized neural networks fails: these models can perfectly fit the training data, and any model with vanishing average training loss also already has vanishing worst-case training loss. Instead, the poor worst-case performance arises from poor generalization on some groups. By coupling group DRO models with increased regularization---a stronger-than-typical L2 penalty or early stopping---we achieve substantially higher worst-group accuracies, with 10-40 percentage point improvements on a natural language inference task and two image tasks, while maintaining high average accuracies. Our results suggest that regularization is important for worst-group generalization in the overparameterized regime, even if it is not needed for average generalization. Finally, we introduce a stochastic optimization algorithm, with convergence guarantees, to efficiently train group DRO models.

Large language models (LLMs) have demonstrated remarkable proficiency across various natural language processing (NLP) tasks. However, adapting LLMs to downstream applications requires computationally intensive and memory-demanding fine-tuning procedures. To alleviate these burdens, parameter-efficient fine-tuning (PEFT) techniques have emerged as a promising approach to tailor LLMs with minimal computational overhead. While PEFT methods offer substantial advantages, they do not fully address the pervasive issue of bias propagation from pre-training data. This work introduces Bias-Alleviating Low-Rank Adaptation (BA-LoRA), a novel PEFT method designed to counteract bias inheritance. BA-LoRA incorporates three distinct regularization terms: (1) a consistency regularizer, (2) a diversity regularizer, and (3) a singular value decomposition regularizer. These regularizers aim to enhance the models' consistency, diversity, and generalization capabilities during fine-tuning. We conduct extensive experiments on natural language understanding (NLU) and natural language generation (NLG) tasks using prominent LLMs such as LLaMA, Mistral, and Gemma. The results demonstrate that BA-LoRA outperforms LoRA and its state-of-the-art variants. Moreover, our method effectively mitigates the adverse effects of pre-training bias, leading to more reliable and robust model outputs. The code is available at https://github.com/cyp-jlu-ai/BA-LoRA.

In this paper, we introduce a novel theoretical framework for multi-task regression, applying random matrix theory to provide precise performance estimations, under high-dimensional, non-Gaussian data distributions. We formulate a multi-task optimization problem as a regularization technique to enable single-task models to leverage multi-task learning information. We derive a closed-form solution for multi-task optimization in the context of linear models. Our analysis provides valuable insights by linking the multi-task learning performance to various model statistics such as raw data covariances, signal-generating hyperplanes, noise levels, as well as the size and number of datasets. We finally propose a consistent estimation of training and testing errors, thereby offering a robust foundation for hyperparameter optimization in multi-task regression scenarios. Experimental validations on both synthetic and real-world datasets in regression and multivariate time series forecasting demonstrate improvements on univariate models, incorporating our method into the training loss and thus leveraging multivariate information.

We study the SAM (Sharpness-Aware Minimization) optimizer which has recently attracted a lot of interest due to its increased performance over more classical variants of stochastic gradient descent. Our main contribution is the derivation of continuous-time models (in the form of SDEs) for SAM and two of its variants, both for the full-batch and mini-batch settings. We demonstrate that these SDEs are rigorous approximations of the real discrete-time algorithms (in a weak sense, scaling linearly with the learning rate). Using these models, we then offer an explanation of why SAM prefers flat minima over sharp ones~--~by showing that it minimizes an implicitly regularized loss with a Hessian-dependent noise structure. Finally, we prove that SAM is attracted to saddle points under some realistic conditions. Our theoretical results are supported by detailed experiments.

We propose the Wasserstein Auto-Encoder (WAE)---a new algorithm for building a generative model of the data distribution. WAE minimizes a penalized form of the Wasserstein distance between the model distribution and the target distribution, which leads to a different regularizer than the one used by the Variational Auto-Encoder (VAE). This regularizer encourages the encoded training distribution to match the prior. We compare our algorithm with several other techniques and show that it is a generalization of adversarial auto-encoders (AAE). Our experiments show that WAE shares many of the properties of VAEs (stable training, encoder-decoder architecture, nice latent manifold structure) while generating samples of better quality, as measured by the FID score.

In this paper, we derive a novel bound on the generalization error of Magnitude-Based pruning of overparameterized neural networks. Our work builds on the bounds in Arora et al. [2018] where the error depends on one, the approximation induced by pruning, and two, the number of parameters in the pruned model, and improves upon standard norm-based generalization bounds. The pruned estimates obtained using our new Magnitude-Based compression algorithm are close to the unpruned functions with high probability, which improves the first criteria. Using Sparse Matrix Sketching, the space of the pruned matrices can be efficiently represented in the space of dense matrices of much smaller dimensions, thereby lowering the second criterion. This leads to stronger generalization bound than many state-of-the-art methods, thereby breaking new ground in the algorithm development for pruning and bounding generalization error of overparameterized models. Beyond this, we extend our results to obtain generalization bound for Iterative Pruning [Frankle and Carbin, 2018]. We empirically verify the success of this new method on ReLU-activated Feed Forward Networks on the MNIST and CIFAR10 datasets.

We develop a fast, tractable technique called Net-Trim for simplifying a trained neural network. The method is a convex post-processing module, which prunes (sparsifies) a trained network layer by layer, while preserving the internal responses. We present a comprehensive analysis of Net-Trim from both the algorithmic and sample complexity standpoints, centered on a fast, scalable convex optimization program. Our analysis includes consistency results between the initial and retrained models before and after Net-Trim application and guarantees on the number of training samples needed to discover a network that can be expressed using a certain number of nonzero terms. Specifically, if there is a set of weights that uses at most s terms that can re-create the layer outputs from the layer inputs, we can find these weights from O(slog N/s) samples, where N is the input size. These theoretical results are similar to those for sparse regression using the Lasso, and our analysis uses some of the same recently-developed tools (namely recent results on the concentration of measure and convex analysis). Finally, we propose an algorithmic framework based on the alternating direction method of multipliers (ADMM), which allows a fast and simple implementation of Net-Trim for network pruning and compression.

Recent work shows that path gradient estimators for normalizing flows have lower variance compared to standard estimators for variational inference, resulting in improved training. However, they are often prohibitively more expensive from a computational point of view and cannot be applied to maximum likelihood training in a scalable manner, which severely hinders their widespread adoption. In this work, we overcome these crucial limitations. Specifically, we propose a fast path gradient estimator which improves computational efficiency significantly and works for all normalizing flow architectures of practical relevance. We then show that this estimator can also be applied to maximum likelihood training for which it has a regularizing effect as it can take the form of a given target energy function into account. We empirically establish its superior performance and reduced variance for several natural sciences applications.

We can better understand deep neural networks by identifying which features each of their neurons have learned to detect. To do so, researchers have created Deep Visualization techniques including activation maximization, which synthetically generates inputs (e.g. images) that maximally activate each neuron. A limitation of current techniques is that they assume each neuron detects only one type of feature, but we know that neurons can be multifaceted, in that they fire in response to many different types of features: for example, a grocery store class neuron must activate either for rows of produce or for a storefront. Previous activation maximization techniques constructed images without regard for the multiple different facets of a neuron, creating inappropriate mixes of colors, parts of objects, scales, orientations, etc. Here, we introduce an algorithm that explicitly uncovers the multiple facets of each neuron by producing a synthetic visualization of each of the types of images that activate a neuron. We also introduce regularization methods that produce state-of-the-art results in terms of the interpretability of images obtained by activation maximization. By separately synthesizing each type of image a neuron fires in response to, the visualizations have more appropriate colors and coherent global structure. Multifaceted feature visualization thus provides a clearer and more comprehensive description of the role of each neuron.

Recently, it has been observed that when representations are learnt in a way that encourages sparsity, improved performance is obtained on classification tasks. These methods involve combinations of activation functions, sampling steps and different kinds of penalties. To investigate the effectiveness of sparsity by itself, we propose the k-sparse autoencoder, which is an autoencoder with linear activation function, where in hidden layers only the k highest activities are kept. When applied to the MNIST and NORB datasets, we find that this method achieves better classification results than denoising autoencoders, networks trained with dropout, and RBMs. k-sparse autoencoders are simple to train and the encoding stage is very fast, making them well-suited to large problem sizes, where conventional sparse coding algorithms cannot be applied.

Sparsity in the structure of Neural Networks can lead to less energy consumption, less memory usage, faster computation times on convenient hardware, and automated machine learning. If sparsity gives rise to certain kinds of structure, it can explain automatically obtained features during learning. We provide insights into experiments in which we show how sparsity can be achieved through prior initialization, pruning, and during learning, and answer questions on the relationship between the structure of Neural Networks and their performance. This includes the first work of inducing priors from network theory into Recurrent Neural Networks and an architectural performance prediction during a Neural Architecture Search. Within our experiments, we show how magnitude class blinded pruning achieves 97.5% on MNIST with 80% compression and re-training, which is 0.5 points more than without compression, that magnitude class uniform pruning is significantly inferior to it and how a genetic search enhanced with performance prediction achieves 82.4% on CIFAR10. Further, performance prediction for Recurrent Networks learning the Reber grammar shows an R^2 of up to 0.81 given only structural information.

The emergence of Kolmogorov-Arnold Networks (KANs) has sparked significant interest and debate within the scientific community. This paper explores the application of KANs in the domain of computer vision (CV). We examine the convolutional version of KANs, considering various nonlinearity options beyond splines, such as Wavelet transforms and a range of polynomials. We propose a parameter-efficient design for Kolmogorov-Arnold convolutional layers and a parameter-efficient finetuning algorithm for pre-trained KAN models, as well as KAN convolutional versions of self-attention and focal modulation layers. We provide empirical evaluations conducted on MNIST, CIFAR10, CIFAR100, Tiny ImageNet, ImageNet1k, and HAM10000 datasets for image classification tasks. Additionally, we explore segmentation tasks, proposing U-Net-like architectures with KAN convolutions, and achieving state-of-the-art results on BUSI, GlaS, and CVC datasets. We summarized all of our findings in a preliminary design guide of KAN convolutional models for computer vision tasks. Furthermore, we investigate regularization techniques for KANs. All experimental code and implementations of convolutional layers and models, pre-trained on ImageNet1k weights are available on GitHub via this https://github.com/IvanDrokin/torch-conv-kan

Recent domain generalization (DG) approaches typically use the hypothesis learned on source domains for inference on the unseen target domain. However, such a hypothesis can be arbitrarily far from the optimal one for the target domain, induced by a gap termed ``adaptivity gap''. Without exploiting the domain information from the unseen test samples, adaptivity gap estimation and minimization are intractable, which hinders us to robustify a model to any unknown distribution. In this paper, we first establish a generalization bound that explicitly considers the adaptivity gap. Our bound motivates two strategies to reduce the gap: the first one is ensembling multiple classifiers to enrich the hypothesis space, then we propose effective gap estimation methods for guiding the selection of a better hypothesis for the target. The other method is minimizing the gap directly by adapting model parameters using online target samples. We thus propose Domain-specific Risk Minimization (DRM). During training, DRM models the distributions of different source domains separately; for inference, DRM performs online model steering using the source hypothesis for each arriving target sample. Extensive experiments demonstrate the effectiveness of the proposed DRM for domain generalization with the following advantages: 1) it significantly outperforms competitive baselines on different distributional shift settings; 2) it achieves either comparable or superior accuracies on all source domains compared to vanilla empirical risk minimization; 3) it remains simple and efficient during training, and 4) it is complementary to invariant learning approaches.

We consider the problem of linear estimation, and establish an extension of the Gauss-Markov theorem, in which the bias operator is allowed to be non-zero but bounded with respect to a matrix norm of Schatten type. We derive simple and explicit formulas for the optimal estimator in the cases of Nuclear and Spectral norms (with the Frobenius case recovering ridge regression). Additionally, we analytically derive the generalization error in multiple random matrix ensembles, and compare with Ridge regression. Finally, we conduct an extensive simulation study, in which we show that the cross-validated Nuclear and Spectral regressors can outperform Ridge in several circumstances.

Nonlinear sufficient dimension reductionlibing_generalSDR, which constructs nonlinear low-dimensional representations to summarize essential features of high-dimensional data, is an important branch of representation learning. However, most existing methods are not applicable when the response variables are complex non-Euclidean random objects, which are frequently encountered in many recent statistical applications. In this paper, we introduce a new statistical dependence measure termed Fr\'echet Cumulative Covariance (FCCov) and develop a novel nonlinear SDR framework based on FCCov. Our approach is not only applicable to complex non-Euclidean data, but also exhibits robustness against outliers. We further incorporate Feedforward Neural Networks (FNNs) and Convolutional Neural Networks (CNNs) to estimate nonlinear sufficient directions in the sample level. Theoretically, we prove that our method with squared Frobenius norm regularization achieves unbiasedness at the sigma-field level. Furthermore, we establish non-asymptotic convergence rates for our estimators based on FNNs and ResNet-type CNNs, which match the minimax rate of nonparametric regression up to logarithmic factors. Intensive simulation studies verify the performance of our methods in both Euclidean and non-Euclidean settings. We apply our method to facial expression recognition datasets and the results underscore more realistic and broader applicability of our proposal.

A key challenge of modern machine learning systems is to achieve Out-of-Distribution (OOD) generalization -- generalizing to target data whose distribution differs from that of source data. Despite its significant importance, the fundamental question of ``what are the most effective algorithms for OOD generalization'' remains open even under the standard setting of covariate shift. This paper addresses this fundamental question by proving that, surprisingly, classical Maximum Likelihood Estimation (MLE) purely using source data (without any modification) achieves the minimax optimality for covariate shift under the well-specified setting. That is, no algorithm performs better than MLE in this setting (up to a constant factor), justifying MLE is all you need. Our result holds for a very rich class of parametric models, and does not require any boundedness condition on the density ratio. We illustrate the wide applicability of our framework by instantiating it to three concrete examples -- linear regression, logistic regression, and phase retrieval. This paper further complement the study by proving that, under the misspecified setting, MLE is no longer the optimal choice, whereas Maximum Weighted Likelihood Estimator (MWLE) emerges as minimax optimal in certain scenarios.

We present an efficient method of utilizing pretrained language models, where we learn selective binary masks for pretrained weights in lieu of modifying them through finetuning. Extensive evaluations of masking BERT and RoBERTa on a series of NLP tasks show that our masking scheme yields performance comparable to finetuning, yet has a much smaller memory footprint when several tasks need to be inferred simultaneously. Through intrinsic evaluations, we show that representations computed by masked language models encode information necessary for solving downstream tasks. Analyzing the loss landscape, we show that masking and finetuning produce models that reside in minima that can be connected by a line segment with nearly constant test accuracy. This confirms that masking can be utilized as an efficient alternative to finetuning.

For an explanation of a deep learning model to be effective, it must provide both insight into a model and suggest a corresponding action in order to achieve some objective. Too often, the litany of proposed explainable deep learning methods stop at the first step, providing practitioners with insight into a model, but no way to act on it. In this paper, we propose contextual decomposition explanation penalization (CDEP), a method which enables practitioners to leverage existing explanation methods in order to increase the predictive accuracy of deep learning models. In particular, when shown that a model has incorrectly assigned importance to some features, CDEP enables practitioners to correct these errors by directly regularizing the provided explanations. Using explanations provided by contextual decomposition (CD) (Murdoch et al., 2018), we demonstrate the ability of our method to increase performance on an array of toy and real datasets.

Small sample sizes are common in many disciplines, which necessitates pooling roughly similar datasets across multiple institutions to study weak but relevant associations between images and disease outcomes. Such data often manifest shift/imbalance in covariates (i.e., secondary non-imaging data). Controlling for such nuisance variables is common within standard statistical analysis, but the ideas do not directly apply to overparameterized models. Consequently, recent work has shown how strategies from invariant representation learning provides a meaningful starting point, but the current repertoire of methods is limited to accounting for shifts/imbalances in just a couple of covariates at a time. In this paper, we show how viewing this problem from the perspective of Category theory provides a simple and effective solution that completely avoids elaborate multi-stage training pipelines that would otherwise be needed. We show the effectiveness of this approach via extensive experiments on real datasets. Further, we discuss how this style of formulation offers a unified perspective on at least 5+ distinct problem settings, from self-supervised learning to matching problems in 3D reconstruction.

Existing techniques for model inversion typically rely on hard-to-tune regularizers, such as total variation or feature regularization, which must be individually calibrated for each network in order to produce adequate images. In this work, we introduce Plug-In Inversion, which relies on a simple set of augmentations and does not require excessive hyper-parameter tuning. Under our proposed augmentation-based scheme, the same set of augmentation hyper-parameters can be used for inverting a wide range of image classification models, regardless of input dimensions or the architecture. We illustrate the practicality of our approach by inverting Vision Transformers (ViTs) and Multi-Layer Perceptrons (MLPs) trained on the ImageNet dataset, tasks which to the best of our knowledge have not been successfully accomplished by any previous works.

State-of-the-art methods for conditional average treatment effect (CATE) estimation make widespread use of representation learning. Here, the idea is to reduce the variance of the low-sample CATE estimation by a (potentially constrained) low-dimensional representation. However, low-dimensional representations can lose information about the observed confounders and thus lead to bias, because of which the validity of representation learning for CATE estimation is typically violated. In this paper, we propose a new, representation-agnostic framework for estimating bounds on the representation-induced confounding bias that comes from dimensionality reduction (or other constraints on the representations) in CATE estimation. First, we establish theoretically under which conditions CATEs are non-identifiable given low-dimensional (constrained) representations. Second, as our remedy, we propose to perform partial identification of CATEs or, equivalently, aim at estimating of lower and upper bounds of the representation-induced confounding bias. We demonstrate the effectiveness of our bounds in a series of experiments. In sum, our framework is of direct relevance in practice where the validity of CATE estimation is of importance.

Off-policy learning (OPL) aims at finding improved policies from logged bandit data, often by minimizing the inverse propensity scoring (IPS) estimator of the risk. In this work, we investigate a smooth regularization for IPS, for which we derive a two-sided PAC-Bayes generalization bound. The bound is tractable, scalable, interpretable and provides learning certificates. In particular, it is also valid for standard IPS without making the assumption that the importance weights are bounded. We demonstrate the relevance of our approach and its favorable performance through a set of learning tasks. Since our bound holds for standard IPS, we are able to provide insight into when regularizing IPS is useful. Namely, we identify cases where regularization might not be needed. This goes against the belief that, in practice, clipped IPS often enjoys favorable performance than standard IPS in OPL.

Grokking, the sudden generalization that occurs after prolonged overfitting, is a surprising phenomenon challenging our understanding of deep learning. Although significant progress has been made in understanding grokking, the reasons behind the delayed generalization and its dependence on regularization remain unclear. In this work, we argue that without regularization, grokking tasks push models to the edge of numerical stability, introducing floating point errors in the Softmax function, which we refer to as Softmax Collapse (SC). We demonstrate that SC prevents grokking and that mitigating SC enables grokking without regularization. Investigating the root cause of SC, we find that beyond the point of overfitting, the gradients strongly align with what we call the na\"ive loss minimization (NLM) direction. This component of the gradient does not alter the model's predictions but decreases the loss by scaling the logits, typically by scaling the weights along their current direction. We show that this scaling of the logits explains the delay in generalization characteristic of grokking and eventually leads to SC, halting further learning. To validate our hypotheses, we introduce two key contributions that address the challenges in grokking tasks: StableMax, a new activation function that prevents SC and enables grokking without regularization, and perpGrad, a training algorithm that promotes quick generalization in grokking tasks by preventing NLM altogether. These contributions provide new insights into grokking, elucidating its delayed generalization, reliance on regularization, and the effectiveness of existing grokking-inducing methods. Code for this paper is available at https://github.com/LucasPrietoAl/grokking-at-the-edge-of-numerical-stability.

We introduce Feasible Learning (FL), a sample-centric learning paradigm where models are trained by solving a feasibility problem that bounds the loss for each training sample. In contrast to the ubiquitous Empirical Risk Minimization (ERM) framework, which optimizes for average performance, FL demands satisfactory performance on every individual data point. Since any model that meets the prescribed performance threshold is a valid FL solution, the choice of optimization algorithm and its dynamics play a crucial role in shaping the properties of the resulting solutions. In particular, we study a primal-dual approach which dynamically re-weights the importance of each sample during training. To address the challenge of setting a meaningful threshold in practice, we introduce a relaxation of FL that incorporates slack variables of minimal norm. Our empirical analysis, spanning image classification, age regression, and preference optimization in large language models, demonstrates that models trained via FL can learn from data while displaying improved tail behavior compared to ERM, with only a marginal impact on average performance.

Masked image modeling (MIM) has attracted much research attention due to its promising potential for learning scalable visual representations. In typical approaches, models usually focus on predicting specific contents of masked patches, and their performances are highly related to pre-defined mask strategies. Intuitively, this procedure can be considered as training a student (the model) on solving given problems (predict masked patches). However, we argue that the model should not only focus on solving given problems, but also stand in the shoes of a teacher to produce a more challenging problem by itself. To this end, we propose Hard Patches Mining (HPM), a brand-new framework for MIM pre-training. We observe that the reconstruction loss can naturally be the metric of the difficulty of the pre-training task. Therefore, we introduce an auxiliary loss predictor, predicting patch-wise losses first and deciding where to mask next. It adopts a relative relationship learning strategy to prevent overfitting to exact reconstruction loss values. Experiments under various settings demonstrate the effectiveness of HPM in constructing masked images. Furthermore, we empirically find that solely introducing the loss prediction objective leads to powerful representations, verifying the efficacy of the ability to be aware of where is hard to reconstruct.

This paper investigates the distinctions between gradient methods applied to non-differentiable functions (NGDMs) and classical gradient descents (GDs) designed for differentiable functions. First, we demonstrate significant differences in the convergence properties of NGDMs compared to GDs, challenging the applicability of the extensive neural network convergence literature based on L-smoothness to non-smooth neural networks. Next, we demonstrate the paradoxical nature of NGDM solutions for L_{1}-regularized problems, showing that increasing the regularization penalty leads to an increase in the L_{1} norm of optimal solutions in NGDMs. Consequently, we show that widely adopted L_{1} penalization-based techniques for network pruning do not yield expected results. Finally, we explore the Edge of Stability phenomenon, indicating its inapplicability even to Lipschitz continuous convex differentiable functions, leaving its relevance to non-convex non-differentiable neural networks inconclusive. Our analysis exposes misguided interpretations of NGDMs in widely referenced papers and texts due to an overreliance on strong smoothness assumptions, emphasizing the necessity for a nuanced understanding of foundational assumptions in the analysis of these systems.

In our era of enormous neural networks, empirical progress has been driven by the philosophy that more is better. Recent deep learning practice has found repeatedly that larger model size, more data, and more computation (resulting in lower training loss) improves performance. In this paper, we give theoretical backing to these empirical observations by showing that these three properties hold in random feature (RF) regression, a class of models equivalent to shallow networks with only the last layer trained. Concretely, we first show that the test risk of RF regression decreases monotonically with both the number of features and the number of samples, provided the ridge penalty is tuned optimally. In particular, this implies that infinite width RF architectures are preferable to those of any finite width. We then proceed to demonstrate that, for a large class of tasks characterized by powerlaw eigenstructure, training to near-zero training loss is obligatory: near-optimal performance can only be achieved when the training error is much smaller than the test error. Grounding our theory in real-world data, we find empirically that standard computer vision tasks with convolutional neural tangent kernels clearly fall into this class. Taken together, our results tell a simple, testable story of the benefits of overparameterization, overfitting, and more data in random feature models.

To improve how neural networks function it is crucial to understand their learning process. The information bottleneck theory of deep learning proposes that neural networks achieve good generalization by compressing their representations to disregard information that is not relevant to the task. However, empirical evidence for this theory is conflicting, as compression was only observed when networks used saturating activation functions. In contrast, networks with non-saturating activation functions achieved comparable levels of task performance but did not show compression. In this paper we developed more robust mutual information estimation techniques, that adapt to hidden activity of neural networks and produce more sensitive measurements of activations from all functions, especially unbounded functions. Using these adaptive estimation techniques, we explored compression in networks with a range of different activation functions. With two improved methods of estimation, firstly, we show that saturation of the activation function is not required for compression, and the amount of compression varies between different activation functions. We also find that there is a large amount of variation in compression between different network initializations. Secondary, we see that L2 regularization leads to significantly increased compression, while preventing overfitting. Finally, we show that only compression of the last layer is positively correlated with generalization.

Deep learning models are challenged by the distribution shift between the training data and test data. Recently, the large models pre-trained on diverse data have demonstrated unprecedented robustness to various distribution shifts. However, fine-tuning these models can lead to a trade-off between in-distribution (ID) performance and out-of-distribution (OOD) robustness. Existing methods for tackling this trade-off do not explicitly address the OOD robustness problem. In this paper, based on causal analysis of the aforementioned problems, we propose a novel fine-tuning method, which uses masked images as counterfactual samples that help improve the robustness of the fine-tuning model. Specifically, we mask either the semantics-related or semantics-unrelated patches of the images based on class activation map to break the spurious correlation, and refill the masked patches with patches from other images. The resulting counterfactual samples are used in feature-based distillation with the pre-trained model. Extensive experiments verify that regularizing the fine-tuning with the proposed masked images can achieve a better trade-off between ID and OOD performance, surpassing previous methods on the OOD performance. Our code is available at https://github.com/Coxy7/robust-finetuning.

Masked visual modeling has attracted much attention due to its promising potential in learning generalizable representations. Typical approaches urge models to predict specific contents of masked tokens, which can be intuitively considered as teaching a student (the model) to solve given problems (predicting masked contents). Under such settings, the performance is highly correlated with mask strategies (the difficulty of provided problems). We argue that it is equally important for the model to stand in the shoes of a teacher to produce challenging problems by itself. Intuitively, patches with high values of reconstruction loss can be regarded as hard samples, and masking those hard patches naturally becomes a demanding reconstruction task. To empower the model as a teacher, we propose Hard Patches Mining (HPM), predicting patch-wise losses and subsequently determining where to mask. Technically, we introduce an auxiliary loss predictor, which is trained with a relative objective to prevent overfitting to exact loss values. Also, to gradually guide the training procedure, we propose an easy-to-hard mask strategy. Empirically, HPM brings significant improvements under both image and video benchmarks. Interestingly, solely incorporating the extra loss prediction objective leads to better representations, verifying the efficacy of determining where is hard to reconstruct. The code is available at https://github.com/Haochen-Wang409/HPM.

We introduce Network Augmentation (NetAug), a new training method for improving the performance of tiny neural networks. Existing regularization techniques (e.g., data augmentation, dropout) have shown much success on large neural networks by adding noise to overcome over-fitting. However, we found these techniques hurt the performance of tiny neural networks. We argue that training tiny models are different from large models: rather than augmenting the data, we should augment the model, since tiny models tend to suffer from under-fitting rather than over-fitting due to limited capacity. To alleviate this issue, NetAug augments the network (reverse dropout) instead of inserting noise into the dataset or the network. It puts the tiny model into larger models and encourages it to work as a sub-model of larger models to get extra supervision, in addition to functioning as an independent model. At test time, only the tiny model is used for inference, incurring zero inference overhead. We demonstrate the effectiveness of NetAug on image classification and object detection. NetAug consistently improves the performance of tiny models, achieving up to 2.2% accuracy improvement on ImageNet. On object detection, achieving the same level of performance, NetAug requires 41% fewer MACs on Pascal VOC and 38% fewer MACs on COCO than the baseline.

Transferability is the property of adversarial examples to be misclassified by other models than the surrogate model for which they were crafted. Previous research has shown that early stopping the training of the surrogate model substantially increases transferability. A common hypothesis to explain this is that deep neural networks (DNNs) first learn robust features, which are more generic, thus a better surrogate. Then, at later epochs, DNNs learn non-robust features, which are more brittle, hence worst surrogate. First, we tend to refute this hypothesis, using transferability as a proxy for representation similarity. We then establish links between transferability and the exploration of the loss landscape in parameter space, focusing on sharpness, which is affected by early stopping. This leads us to evaluate surrogate models trained with seven minimizers that minimize both loss value and loss sharpness. Among them, SAM consistently outperforms early stopping by up to 28.8 percentage points. We discover that the strong SAM regularization from large flat neighborhoods tightly links to transferability. Finally, the best sharpness-aware minimizers prove competitive with other training methods and complement existing transferability techniques.

Batch Normalization is a key component in almost all state-of-the-art image classifiers, but it also introduces practical challenges: it breaks the independence between training examples within a batch, can incur compute and memory overhead, and often results in unexpected bugs. Building on recent theoretical analyses of deep ResNets at initialization, we propose a simple set of analysis tools to characterize signal propagation on the forward pass, and leverage these tools to design highly performant ResNets without activation normalization layers. Crucial to our success is an adapted version of the recently proposed Weight Standardization. Our analysis tools show how this technique preserves the signal in networks with ReLU or Swish activation functions by ensuring that the per-channel activation means do not grow with depth. Across a range of FLOP budgets, our networks attain performance competitive with the state-of-the-art EfficientNets on ImageNet.

We propose an algorithm for inexpensive gradient-based hyperparameter optimization that combines the implicit function theorem (IFT) with efficient inverse Hessian approximations. We present results about the relationship between the IFT and differentiating through optimization, motivating our algorithm. We use the proposed approach to train modern network architectures with millions of weights and millions of hyper-parameters. For example, we learn a data-augmentation network - where every weight is a hyperparameter tuned for validation performance - outputting augmented training examples. Jointly tuning weights and hyperparameters with our approach is only a few times more costly in memory and compute than standard training.

In today's heavily overparameterized models, the value of the training loss provides few guarantees on model generalization ability. Indeed, optimizing only the training loss value, as is commonly done, can easily lead to suboptimal model quality. Motivated by prior work connecting the geometry of the loss landscape and generalization, we introduce a novel, effective procedure for instead simultaneously minimizing loss value and loss sharpness. In particular, our procedure, Sharpness-Aware Minimization (SAM), seeks parameters that lie in neighborhoods having uniformly low loss; this formulation results in a min-max optimization problem on which gradient descent can be performed efficiently. We present empirical results showing that SAM improves model generalization across a variety of benchmark datasets (e.g., CIFAR-10, CIFAR-100, ImageNet, finetuning tasks) and models, yielding novel state-of-the-art performance for several. Additionally, we find that SAM natively provides robustness to label noise on par with that provided by state-of-the-art procedures that specifically target learning with noisy labels. We open source our code at https://github.com/google-research/sam.

We develop an analytical framework to characterize the set of optimal ReLU neural networks by reformulating the non-convex training problem as a convex program. We show that the global optima of the convex parameterization are given by a polyhedral set and then extend this characterization to the optimal set of the non-convex training objective. Since all stationary points of the ReLU training problem can be represented as optima of sub-sampled convex programs, our work provides a general expression for all critical points of the non-convex objective. We then leverage our results to provide an optimal pruning algorithm for computing minimal networks, establish conditions for the regularization path of ReLU networks to be continuous, and develop sensitivity results for minimal ReLU networks.

We introduce for continual learning Autodiff Quadratic Consolidation (AQC), which approximates the previous loss function with a quadratic function, and Neural Consolidation (NC), which approximates the previous loss function with a neural network. Although they are not scalable to large neural networks, they can be used with a fixed pre-trained feature extractor. We empirically study these methods in class-incremental learning, for which regularization-based methods produce unsatisfactory results, unless combined with replay. We find that for small datasets, quadratic approximation of the previous loss function leads to poor results, even with full Hessian computation, and NC could significantly improve the predictive performance, while for large datasets, when used with a fixed pre-trained feature extractor, AQC provides superior predictive performance. We also find that using tanh-output features can improve the predictive performance of AQC. In particular, in class-incremental Split MNIST, when a Convolutional Neural Network (CNN) with tanh-output features is pre-trained on EMNIST Letters and used as a fixed pre-trained feature extractor, AQC can achieve predictive performance comparable to joint training.

Robustness is essential for deep neural networks, especially in security-sensitive applications. To this end, randomized smoothing provides theoretical guarantees for certifying robustness against adversarial perturbations. Recently, diffusion models have been successfully employed for randomized smoothing to purify noise-perturbed samples before making predictions with a standard classifier. While these methods excel at small perturbation radii, they struggle with larger perturbations and incur a significant computational overhead during inference compared to classical methods. To address this, we reformulate the generative modeling task along the diffusion trajectories in pixel space as a discriminative task in the latent space. Specifically, we use instance discrimination to achieve consistent representations along the trajectories by aligning temporally adjacent points. After fine-tuning based on the learned representations, our model enables implicit denoising-then-classification via a single prediction, substantially reducing inference costs. We conduct extensive experiments on various datasets and achieve state-of-the-art performance with minimal computation budget during inference. For example, our method outperforms the certified accuracy of diffusion-based methods on ImageNet across all perturbation radii by 5.3% on average, with up to 11.6% at larger radii, while reducing inference costs by 85times on average. Codes are available at: https://github.com/jiachenlei/rRCM.

Fine-tuning a visual pre-trained model can leverage the semantic information from large-scale pre-training data and mitigate the over-fitting problem on downstream vision tasks with limited training examples. While the problem of catastrophic forgetting in pre-trained backbone has been extensively studied for fine-tuning, its potential bias from the corresponding pre-training task and data, attracts less attention. In this work, we investigate this problem by demonstrating that the obtained classifier after fine-tuning will be close to that induced by the pre-trained model. To reduce the bias in the classifier effectively, we introduce a reference distribution obtained from a fixed text classifier, which can help regularize the learned vision classifier. The proposed method, Text Supervised fine-tuning (TeS), is evaluated with diverse pre-trained vision models including ResNet and ViT, and text encoders including BERT and CLIP, on 11 downstream tasks. The consistent improvement with a clear margin over distinct scenarios confirms the effectiveness of our proposal. Code is available at https://github.com/idstcv/TeS.

Quantization has become a popular technique to compress neural networks and reduce compute cost, but most prior work focuses on studying quantization without changing the network size. Many real-world applications of neural networks have compute cost and memory budgets, which can be traded off with model quality by changing the number of parameters. In this work, we use ResNet as a case study to systematically investigate the effects of quantization on inference compute cost-quality tradeoff curves. Our results suggest that for each bfloat16 ResNet model, there are quantized models with lower cost and higher accuracy; in other words, the bfloat16 compute cost-quality tradeoff curve is Pareto-dominated by the 4-bit and 8-bit curves, with models primarily quantized to 4-bit yielding the best Pareto curve. Furthermore, we achieve state-of-the-art results on ImageNet for 4-bit ResNet-50 with quantization-aware training, obtaining a top-1 eval accuracy of 77.09%. We demonstrate the regularizing effect of quantization by measuring the generalization gap. The quantization method we used is optimized for practicality: It requires little tuning and is designed with hardware capabilities in mind. Our work motivates further research into optimal numeric formats for quantization, as well as the development of machine learning accelerators supporting these formats. As part of this work, we contribute a quantization library written in JAX, which is open-sourced at https://github.com/google-research/google-research/tree/master/aqt.

Grokking is the intriguing phenomenon where a model learns to generalize long after it has fit the training data. We show both analytically and numerically that grokking can surprisingly occur in linear networks performing linear tasks in a simple teacher-student setup with Gaussian inputs. In this setting, the full training dynamics is derived in terms of the training and generalization data covariance matrix. We present exact predictions on how the grokking time depends on input and output dimensionality, train sample size, regularization, and network initialization. We demonstrate that the sharp increase in generalization accuracy may not imply a transition from "memorization" to "understanding", but can simply be an artifact of the accuracy measure. We provide empirical verification for our calculations, along with preliminary results indicating that some predictions also hold for deeper networks, with non-linear activations.

Current tools for machine learning fairness only admit a limited range of fairness definitions and have seen little integration with automatic differentiation libraries, despite the central role these libraries play in modern machine learning pipelines. We introduce a framework of fairness regularization terms (fairrets) which quantify bias as modular objectives that are easily integrated in automatic differentiation pipelines. By employing a general definition of fairness in terms of linear-fractional statistics, a wide class of fairrets can be computed efficiently. Experiments show the behavior of their gradients and their utility in enforcing fairness with minimal loss of predictive power compared to baselines. Our contribution includes a PyTorch implementation of the fairret framework.

A lot of recent work has focused on sparse learned indexes that use deep neural architectures to significantly improve retrieval quality while keeping the efficiency benefits of the inverted index. While such sparse learned structures achieve effectiveness far beyond those of traditional inverted index-based rankers, there is still a gap in effectiveness to the best dense retrievers, or even to sparse methods that leverage more expensive optimizations such as query expansion and query term weighting. We focus on narrowing this gap by revisiting and optimizing DeepImpact, a sparse retrieval approach that uses DocT5Query for document expansion followed by a BERT language model to learn impact scores for document terms. We first reinvestigate the expansion process and find that the recently proposed Doc2Query query filtration does not enhance retrieval quality when used with DeepImpact. Instead, substituting T5 with a fine-tuned Llama 2 model for query prediction results in a considerable improvement. Subsequently, we study training strategies that have proven effective for other models, in particular the use of hard negatives, distillation, and pre-trained CoCondenser model initialization. Our results significantly narrow the effectiveness gap with the most effective versions of SPLADE.

Sharpness-aware minimization (SAM) was proposed to reduce sharpness of minima and has been shown to enhance generalization performance in various settings. In this work we show that perturbing only the affine normalization parameters (typically comprising 0.1% of the total parameters) in the adversarial step of SAM can outperform perturbing all of the parameters.This finding generalizes to different SAM variants and both ResNet (Batch Normalization) and Vision Transformer (Layer Normalization) architectures. We consider alternative sparse perturbation approaches and find that these do not achieve similar performance enhancement at such extreme sparsity levels, showing that this behaviour is unique to the normalization layers. Although our findings reaffirm the effectiveness of SAM in improving generalization performance, they cast doubt on whether this is solely caused by reduced sharpness.

Given a sample of size N, it is often useful to select a subsample of smaller size n<N to be used for statistical estimation or learning. Such a data selection step is useful to reduce the requirements of data labeling and the computational complexity of learning. We assume to be given N unlabeled samples {{boldsymbol x}_i}_{ile N}, and to be given access to a `surrogate model' that can predict labels y_i better than random guessing. Our goal is to select a subset of the samples, to be denoted by {{boldsymbol x}_i}_{iin G}, of size |G|=n<N. We then acquire labels for this set and we use them to train a model via regularized empirical risk minimization. By using a mixture of numerical experiments on real and synthetic data, and mathematical derivations under low- and high- dimensional asymptotics, we show that: (i)~Data selection can be very effective, in particular beating training on the full sample in some cases; (ii)~Certain popular choices in data selection methods (e.g. unbiased reweighted subsampling, or influence function-based subsampling) can be substantially suboptimal.

Despite their tremendous success in modelling high-dimensional data manifolds, deep neural networks suffer from the threat of adversarial attacks - Existence of perceptually valid input-like samples obtained through careful perturbation that lead to degradation in the performance of the underlying model. Major concerns with existing defense mechanisms include non-generalizability across different attacks, models and large inference time. In this paper, we propose a generalized defense mechanism capitalizing on the expressive power of regularized latent space based generative models. We design an adversarial filter, devoid of access to classifier and adversaries, which makes it usable in tandem with any classifier. The basic idea is to learn a Lipschitz constrained mapping from the data manifold, incorporating adversarial perturbations, to a quantized latent space and re-map it to the true data manifold. Specifically, we simultaneously auto-encode the data manifold and its perturbations implicitly through the perturbations of the regularized and quantized generative latent space, realized using variational inference. We demonstrate the efficacy of the proposed formulation in providing resilience against multiple attack types (black and white box) and methods, while being almost real-time. Our experiments show that the proposed method surpasses the state-of-the-art techniques in several cases.

Despite the significant recent progress in deep generative models, the underlying structure of their latent spaces is still poorly understood, thereby making the task of performing semantically meaningful latent traversals an open research challenge. Most prior work has aimed to solve this challenge by modeling latent structures linearly, and finding corresponding linear directions which result in `disentangled' generations. In this work, we instead propose to model latent structures with a learned dynamic potential landscape, thereby performing latent traversals as the flow of samples down the landscape's gradient. Inspired by physics, optimal transport, and neuroscience, these potential landscapes are learned as physically realistic partial differential equations, thereby allowing them to flexibly vary over both space and time. To achieve disentanglement, multiple potentials are learned simultaneously, and are constrained by a classifier to be distinct and semantically self-consistent. Experimentally, we demonstrate that our method achieves both more qualitatively and quantitatively disentangled trajectories than state-of-the-art baselines. Further, we demonstrate that our method can be integrated as a regularization term during training, thereby acting as an inductive bias towards the learning of structured representations, ultimately improving model likelihood on similarly structured data.

Parameter-efficient fine-tuning optimizes large, pre-trained foundation models by updating a subset of parameters; in this class, Low-Rank Adaptation (LoRA) is particularly effective. Inspired by an effort to investigate the different roles of LoRA matrices during fine-tuning, this paper characterizes and leverages unexpected asymmetry in the importance of low-rank adapter matrices. Specifically, when updating the parameter matrices of a neural network by adding a product BA, we observe that the B and A matrices have distinct functions: A extracts features from the input, while B uses these features to create the desired output. Based on this observation, we demonstrate that fine-tuning B is inherently more effective than fine-tuning A, and that a random untrained A should perform nearly as well as a fine-tuned one. Using an information-theoretic lens, we also bound the generalization of low-rank adapters, showing that the parameter savings of exclusively training B improves the bound. We support our conclusions with experiments on RoBERTa, BART-Large, LLaMA-2, and ViTs.

Various data augmentation techniques have been recently proposed in image-based deep reinforcement learning (DRL). Although they empirically demonstrate the effectiveness of data augmentation for improving sample efficiency or generalization, which technique should be preferred is not always clear. To tackle this question, we analyze existing methods to better understand them and to uncover how they are connected. Notably, by expressing the variance of the Q-targets and that of the empirical actor/critic losses of these methods, we can analyze the effects of their different components and compare them. We furthermore formulate an explanation about how these methods may be affected by choosing different data augmentation transformations in calculating the target Q-values. This analysis suggests recommendations on how to exploit data augmentation in a more principled way. In addition, we include a regularization term called tangent prop, previously proposed in computer vision, but whose adaptation to DRL is novel to the best of our knowledge. We evaluate our proposition and validate our analysis in several domains. Compared to different relevant baselines, we demonstrate that it achieves state-of-the-art performance in most environments and shows higher sample efficiency and better generalization ability in some complex environments.

The vast work in Deep Learning (DL) has led to a leap in image denoising research. Most DL solutions for this task have chosen to put their efforts on the denoiser's architecture while maximizing distortion performance. However, distortion driven solutions lead to blurry results with sub-optimal perceptual quality, especially in immoderate noise levels. In this paper we propose a different perspective, aiming to produce sharp and visually pleasing denoised images that are still faithful to their clean sources. Formally, our goal is to achieve high perceptual quality with acceptable distortion. This is attained by a stochastic denoiser that samples from the posterior distribution, trained as a generator in the framework of conditional generative adversarial networks (CGAN). Contrary to distortion-based regularization terms that conflict with perceptual quality, we introduce to the CGAN objective a theoretically founded penalty term that does not force a distortion requirement on individual samples, but rather on their mean. We showcase our proposed method with a novel denoiser architecture that achieves the reformed denoising goal and produces vivid and diverse outcomes in immoderate noise levels.

The extensive need for computational resources poses a significant obstacle to deploying large-scale Deep Neural Networks (DNN) on devices with constrained resources. At the same time, studies have demonstrated that a significant number of these DNN parameters are redundant and extraneous. In this paper, we introduce a novel approach for learning structured sparse neural networks, aimed at bridging the DNN hardware deployment challenges. We develop a novel regularization technique, termed Weighted Group Sparse Envelope Function (WGSEF), generalizing the Sparse Envelop Function (SEF), to select (or nullify) neuron groups, thereby reducing redundancy and enhancing computational efficiency. The method speeds up inference time and aims to reduce memory demand and power consumption, thanks to its adaptability which lets any hardware specify group definitions, such as filters, channels, filter shapes, layer depths, a single parameter (unstructured), etc. The properties of the WGSEF enable the pre-definition of a desired sparsity level to be achieved at the training convergence. In the case of redundant parameters, this approach maintains negligible network accuracy degradation or can even lead to improvements in accuracy. Our method efficiently computes the WGSEF regularizer and its proximal operator, in a worst-case linear complexity relative to the number of group variables. Employing a proximal-gradient-based optimization technique, to train the model, it tackles the non-convex minimization problem incorporating the neural network loss and the WGSEF. Finally, we experiment and illustrate the efficiency of our proposed method in terms of the compression ratio, accuracy, and inference latency.

In class incremental learning, neural networks typically suffer from catastrophic forgetting. We show that an MLP featuring a sparse activation function and an adaptive learning rate optimizer can compete with established regularization techniques in the Split-MNIST task. We highlight the effectiveness of the Adaptive SwisH (ASH) activation function in this context and introduce a novel variant, Hard Adaptive SwisH (Hard ASH) to further enhance the learning retention.

The primary goal in recommendation is to suggest relevant content to users, but optimizing for accuracy often results in recommendations that lack diversity. To remedy this, conventional approaches such as re-ranking improve diversity by presenting more diverse items. Here we argue that to promote inherent and prolonged diversity, the system must encourage its creation. Towards this, we harness the performative nature of recommendation, and show how learning can incentivize strategic content creators to create diverse content. Our approach relies on a novel form of regularization that anticipates strategic changes to content, and penalizes for content homogeneity. We provide analytic and empirical results that demonstrate when and how diversity can be incentivized, and experimentally demonstrate the utility of our approach on synthetic and semi-synthetic data.

Sparse neural networks have shown similar or better generalization performance than their dense counterparts while having higher parameter efficiency. This has motivated a number of works to learn or search for high performing sparse networks. While reports of task performance or efficiency gains are impressive, standard baselines are lacking leading to poor comparability and unreliable reproducibility across methods. In this work, we propose Random Search as a baseline algorithm for finding good sparse configurations and study its performance. We apply Random Search on the node space of an overparameterized network with the goal of finding better initialized sparse sub-networks that are positioned more advantageously in the loss landscape. We record the post-training performances of the found sparse networks and at various levels of sparsity, and compare against both their fully connected parent networks and random sparse configurations at the same sparsity levels. First, we demonstrate performance at different levels of sparsity and highlight that a significant level of performance can still be preserved even when the network is highly sparse. Second, we observe that for this sparse architecture search task, initialized sparse networks found by Random Search neither perform better nor converge more efficiently than their random counterparts. Thus we conclude that Random Search may be viewed as a reasonable neutral baseline for sparsity search methods.

We study the data selection problem, whose aim is to select a small representative subset of data that can be used to efficiently train a machine learning model. We present a new data selection approach based on k-means clustering and sensitivity sampling. Assuming access to an embedding representation of the data with respect to which the model loss is H\"older continuous, our approach provably allows selecting a set of ``typical'' k + 1/varepsilon^2 elements whose average loss corresponds to the average loss of the whole dataset, up to a multiplicative (1pmvarepsilon) factor and an additive varepsilon lambda Phi_k, where Phi_k represents the k-means cost for the input embeddings and lambda is the H\"older constant. We furthermore demonstrate the performance and scalability of our approach on fine-tuning foundation models and show that it outperforms state-of-the-art methods. We also show how it can be applied on linear regression, leading to a new sampling strategy that surprisingly matches the performances of leverage score sampling, while being conceptually simpler and more scalable.

Model pruning is a popular approach to enable the deployment of large deep learning models on edge devices with restricted computational or storage capacities. Although sparse models achieve performance comparable to that of their dense counterparts at the level of the entire dataset, they exhibit high accuracy drops for some data sub-groups. Existing methods to mitigate this disparate impact induced by pruning (i) rely on surrogate metrics that address the problem indirectly and have limited interpretability; or (ii) scale poorly with the number of protected sub-groups in terms of computational cost. We propose a constrained optimization approach that directly addresses the disparate impact of pruning: our formulation bounds the accuracy change between the dense and sparse models, for each sub-group. This choice of constraints provides an interpretable success criterion to determine if a pruned model achieves acceptable disparity levels. Experimental results demonstrate that our technique scales reliably to problems involving large models and hundreds of protected sub-groups.

Combining simple elements from the literature, we define a linear model that is geared toward sparse data, in particular implicit feedback data for recommender systems. We show that its training objective has a closed-form solution, and discuss the resulting conceptual insights. Surprisingly, this simple model achieves better ranking accuracy than various state-of-the-art collaborative-filtering approaches, including deep non-linear models, on most of the publicly available data-sets used in our experiments.

Supervised learning is often affected by a covariate shift in which the marginal distributions of instances (covariates x) of training and testing samples p_tr(x) and p_te(x) are different but the label conditionals coincide. Existing approaches address such covariate shift by either using the ratio p_te(x)/p_tr(x) to weight training samples (reweighted methods) or using the ratio p_tr(x)/p_te(x) to weight testing samples (robust methods). However, the performance of such approaches can be poor under support mismatch or when the above ratios take large values. We propose a minimax risk classification (MRC) approach for covariate shift adaptation that avoids such limitations by weighting both training and testing samples. In addition, we develop effective techniques that obtain both sets of weights and generalize the conventional kernel mean matching method. We provide novel generalization bounds for our method that show a significant increase in the effective sample size compared with reweighted methods. The proposed method also achieves enhanced classification performance in both synthetic and empirical experiments.

Fine-tuning the entire set of parameters of a large pretrained model has become the mainstream approach for transfer learning. To increase its efficiency and prevent catastrophic forgetting and interference, techniques like adapters and sparse fine-tuning have been developed. Adapters are modular, as they can be combined to adapt a model towards different facets of knowledge (e.g., dedicated language and/or task adapters). Sparse fine-tuning is expressive, as it controls the behavior of all model components. In this work, we introduce a new fine-tuning method with both these desirable properties. In particular, we learn sparse, real-valued masks based on a simple variant of the Lottery Ticket Hypothesis. Task-specific masks are obtained from annotated data in a source language, and language-specific masks from masked language modeling in a target language. Both these masks can then be composed with the pretrained model. Unlike adapter-based fine-tuning, this method neither increases the number of parameters at inference time nor alters the original model architecture. Most importantly, it outperforms adapters in zero-shot cross-lingual transfer by a large margin in a series of multilingual benchmarks, including Universal Dependencies, MasakhaNER, and AmericasNLI. Based on an in-depth analysis, we additionally find that sparsity is crucial to prevent both 1) interference between the fine-tunings to be composed and 2) overfitting. We release the code and models at https://github.com/cambridgeltl/composable-sft.

Training deep neural networks is a challenging non-convex optimization problem. Recent work has proven that the strong duality holds (which means zero duality gap) for regularized finite-width two-layer ReLU networks and consequently provided an equivalent convex training problem. However, extending this result to deeper networks remains to be an open problem. In this paper, we prove that the duality gap for deeper linear networks with vector outputs is non-zero. In contrast, we show that the zero duality gap can be obtained by stacking standard deep networks in parallel, which we call a parallel architecture, and modifying the regularization. Therefore, we prove the strong duality and existence of equivalent convex problems that enable globally optimal training of deep networks. As a by-product of our analysis, we demonstrate that the weight decay regularization on the network parameters explicitly encourages low-rank solutions via closed-form expressions. In addition, we show that strong duality holds for three-layer standard ReLU networks given rank-1 data matrices.

While task-specific finetuning of pretrained networks has led to significant empirical advances in NLP, the large size of networks makes finetuning difficult to deploy in multi-task, memory-constrained settings. We propose diff pruning as a simple approach to enable parameter-efficient transfer learning within the pretrain-finetune framework. This approach views finetuning as learning a task-specific diff vector that is applied on top of the pretrained parameter vector, which remains fixed and is shared across different tasks. The diff vector is adaptively pruned during training with a differentiable approximation to the L0-norm penalty to encourage sparsity. Diff pruning becomes parameter-efficient as the number of tasks increases, as it requires storing only the nonzero positions and weights of the diff vector for each task, while the cost of storing the shared pretrained model remains constant. It further does not require access to all tasks during training, which makes it attractive in settings where tasks arrive in stream or the set of tasks is unknown. We find that models finetuned with diff pruning can match the performance of fully finetuned baselines on the GLUE benchmark while only modifying 0.5% of the pretrained model's parameters per task.

Dynamic model pruning is a recent direction that allows for the inference of a different sub-network for each input sample during deployment. However, current dynamic methods rely on learning a continuous channel gating through regularization by inducing sparsity loss. This formulation introduces complexity in balancing different losses (e.g task loss, regularization loss). In addition, regularization based methods lack transparent tradeoff hyperparameter selection to realize a computational budget. Our contribution is two-fold: 1) decoupled task and pruning losses. 2) Simple hyperparameter selection that enables FLOPs reduction estimation before training. Inspired by the Hebbian theory in Neuroscience: "neurons that fire together wire together", we propose to predict a mask to process k filters in a layer based on the activation of its previous layer. We pose the problem as a self-supervised binary classification problem. Each mask predictor module is trained to predict if the log-likelihood for each filter in the current layer belongs to the top-k activated filters. The value k is dynamically estimated for each input based on a novel criterion using the mass of heatmaps. We show experiments on several neural architectures, such as VGG, ResNet and MobileNet on CIFAR and ImageNet datasets. On CIFAR, we reach similar accuracy to SOTA methods with 15% and 24% higher FLOPs reduction. Similarly in ImageNet, we achieve lower drop in accuracy with up to 13% improvement in FLOPs reduction.

During typical gradient-based training of deep neural networks, all of the model's parameters are updated at each iteration. Recent work has shown that it is possible to update only a small subset of the model's parameters during training, which can alleviate storage and communication requirements. In this paper, we show that it is possible to induce a fixed sparse mask on the model's parameters that selects a subset to update over many iterations. Our method constructs the mask out of the k parameters with the largest Fisher information as a simple approximation as to which parameters are most important for the task at hand. In experiments on parameter-efficient transfer learning and distributed training, we show that our approach matches or exceeds the performance of other methods for training with sparse updates while being more efficient in terms of memory usage and communication costs. We release our code publicly to promote further applications of our approach.

Training Deep Neural Networks is complicated by the fact that the distribution of each layer's inputs changes during training, as the parameters of the previous layers change. This slows down the training by requiring lower learning rates and careful parameter initialization, and makes it notoriously hard to train models with saturating nonlinearities. We refer to this phenomenon as internal covariate shift, and address the problem by normalizing layer inputs. Our method draws its strength from making normalization a part of the model architecture and performing the normalization for each training mini-batch. Batch Normalization allows us to use much higher learning rates and be less careful about initialization. It also acts as a regularizer, in some cases eliminating the need for Dropout. Applied to a state-of-the-art image classification model, Batch Normalization achieves the same accuracy with 14 times fewer training steps, and beats the original model by a significant margin. Using an ensemble of batch-normalized networks, we improve upon the best published result on ImageNet classification: reaching 4.9% top-5 validation error (and 4.8% test error), exceeding the accuracy of human raters.

Sparse Neural Networks (SNNs) can potentially demonstrate similar performance to their dense counterparts while saving significant energy and memory at inference. However, the accuracy drop incurred by SNNs, especially at high pruning ratios, can be an issue in critical deployment conditions. While recent works mitigate this issue through sophisticated pruning techniques, we shift our focus to an overlooked factor: hyperparameters and activation functions. Our analyses have shown that the accuracy drop can additionally be attributed to (i) Using ReLU as the default choice for activation functions unanimously, and (ii) Fine-tuning SNNs with the same hyperparameters as dense counterparts. Thus, we focus on learning a novel way to tune activation functions for sparse networks and combining these with a separate hyperparameter optimization (HPO) regime for sparse networks. By conducting experiments on popular DNN models (LeNet-5, VGG-16, ResNet-18, and EfficientNet-B0) trained on MNIST, CIFAR-10, and ImageNet-16 datasets, we show that the novel combination of these two approaches, dubbed Sparse Activation Function Search, short: SAFS, results in up to 15.53%, 8.88%, and 6.33% absolute improvement in the accuracy for LeNet-5, VGG-16, and ResNet-18 over the default training protocols, especially at high pruning ratios. Our code can be found at https://github.com/automl/SAFS

We consider the problem of estimating (diagonally dominant) M-matrices as precision matrices in Gaussian graphical models. These models exhibit intriguing properties, such as the existence of the maximum likelihood estimator with merely two observations for M-matrices lauritzen2019maximum,slawski2015estimation and even one observation for diagonally dominant M-matrices truell2021maximum. We propose an adaptive multiple-stage estimation method that refines the estimate by solving a weighted ell_1-regularized problem at each stage. Furthermore, we develop a unified framework based on the gradient projection method to solve the regularized problem, incorporating distinct projections to handle the constraints of M-matrices and diagonally dominant M-matrices. A theoretical analysis of the estimation error is provided. Our method outperforms state-of-the-art methods in precision matrix estimation and graph edge identification, as evidenced by synthetic and financial time-series data sets.

In recent years, denoising diffusion models have become a crucial area of research due to their abundance in the rapidly expanding field of generative AI. While recent statistical advances have delivered explanations for the generation ability of idealised denoising diffusion models for high-dimensional target data, implementations introduce thresholding procedures for the generating process to overcome issues arising from the unbounded state space of such models. This mismatch between theoretical design and implementation of diffusion models has been addressed empirically by using a reflected diffusion process as the driver of noise instead. In this paper, we study statistical guarantees of these denoising reflected diffusion models. In particular, we establish minimax optimal rates of convergence in total variation, up to a polylogarithmic factor, under Sobolev smoothness assumptions. Our main contributions include the statistical analysis of this novel class of denoising reflected diffusion models and a refined score approximation method in both time and space, leveraging spectral decomposition and rigorous neural network analysis.

Generative convolutional deep neural networks, e.g. popular GAN architectures, are relying on convolution based up-sampling methods to produce non-scalar outputs like images or video sequences. In this paper, we show that common up-sampling methods, i.e. known as up-convolution or transposed convolution, are causing the inability of such models to reproduce spectral distributions of natural training data correctly. This effect is independent of the underlying architecture and we show that it can be used to easily detect generated data like deepfakes with up to 100% accuracy on public benchmarks. To overcome this drawback of current generative models, we propose to add a novel spectral regularization term to the training optimization objective. We show that this approach not only allows to train spectral consistent GANs that are avoiding high frequency errors. Also, we show that a correct approximation of the frequency spectrum has positive effects on the training stability and output quality of generative networks.

Diffusion models excel in generating images that closely resemble their training data but are also susceptible to data memorization, raising privacy, ethical, and legal concerns, particularly in sensitive domains such as medical imaging. We hypothesize that this memorization stems from the overparameterization of deep models and propose that regularizing model capacity during fine-tuning can mitigate this issue. Firstly, we empirically show that regulating the model capacity via Parameter-efficient fine-tuning (PEFT) mitigates memorization to some extent, however, it further requires the identification of the exact parameter subsets to be fine-tuned for high-quality generation. To identify these subsets, we introduce a bi-level optimization framework, MemControl, that automates parameter selection using memorization and generation quality metrics as rewards during fine-tuning. The parameter subsets discovered through MemControl achieve a superior tradeoff between generation quality and memorization. For the task of medical image generation, our approach outperforms existing state-of-the-art memorization mitigation strategies by fine-tuning as few as 0.019% of model parameters. Moreover, we demonstrate that the discovered parameter subsets are transferable to non-medical domains. Our framework is scalable to large datasets, agnostic to reward functions, and can be integrated with existing approaches for further memorization mitigation. To the best of our knowledge, this is the first study to empirically evaluate memorization in medical images and propose a targeted yet universal mitigation strategy. The code is available at https://github.com/Raman1121/Diffusion_Memorization_HPO.

Click-through rate prediction is an essential task in industrial applications, such as online advertising. Recently deep learning based models have been proposed, which follow a similar Embedding\&MLP paradigm. In these methods large scale sparse input features are first mapped into low dimensional embedding vectors, and then transformed into fixed-length vectors in a group-wise manner, finally concatenated together to fed into a multilayer perceptron (MLP) to learn the nonlinear relations among features. In this way, user features are compressed into a fixed-length representation vector, in regardless of what candidate ads are. The use of fixed-length vector will be a bottleneck, which brings difficulty for Embedding\&MLP methods to capture user's diverse interests effectively from rich historical behaviors. In this paper, we propose a novel model: Deep Interest Network (DIN) which tackles this challenge by designing a local activation unit to adaptively learn the representation of user interests from historical behaviors with respect to a certain ad. This representation vector varies over different ads, improving the expressive ability of model greatly. Besides, we develop two techniques: mini-batch aware regularization and data adaptive activation function which can help training industrial deep networks with hundreds of millions of parameters. Experiments on two public datasets as well as an Alibaba real production dataset with over 2 billion samples demonstrate the effectiveness of proposed approaches, which achieve superior performance compared with state-of-the-art methods. DIN now has been successfully deployed in the online display advertising system in Alibaba, serving the main traffic.

The interest of the deep learning community in image synthesis has grown massively in recent years. Nowadays, deep generative methods, and especially Generative Adversarial Networks (GANs), are leading to state-of-the-art performance, capable of synthesizing images that appear realistic. While the efforts for improving the quality of the generated images are extensive, most attempts still consider the generator part as an uncorroborated "black-box". In this paper, we aim to provide a better understanding and design of the image generation process. We interpret existing generators as implicitly relying on sparsity-inspired models. More specifically, we show that generators can be viewed as manifestations of the Convolutional Sparse Coding (CSC) and its Multi-Layered version (ML-CSC) synthesis processes. We leverage this observation by explicitly enforcing a sparsifying regularization on appropriately chosen activation layers in the generator, and demonstrate that this leads to improved image synthesis. Furthermore, we show that the same rationale and benefits apply to generators serving inverse problems, demonstrated on the Deep Image Prior (DIP) method.

To enable DNNs on edge devices like mobile phones, low-rank approximation has been widely adopted because of its solid theoretical rationale and efficient implementations. Several previous works attempted to directly approximate a pretrained model by low-rank decomposition; however, small approximation errors in parameters can ripple over a large prediction loss. As a result, performance usually drops significantly and a sophisticated effort on fine-tuning is required to recover accuracy. Apparently, it is not optimal to separate low-rank approximation from training. Unlike previous works, this paper integrates low rank approximation and regularization into the training process. We propose Trained Rank Pruning (TRP), which alternates between low rank approximation and training. TRP maintains the capacity of the original network while imposing low-rank constraints during training. A nuclear regularization optimized by stochastic sub-gradient descent is utilized to further promote low rank in TRP. The TRP trained network inherently has a low-rank structure, and is approximated with negligible performance loss, thus eliminating the fine-tuning process after low rank decomposition. The proposed method is comprehensively evaluated on CIFAR-10 and ImageNet, outperforming previous compression methods using low rank approximation.

The premise of identifiable and causal representation learning is to improve the current representation learning paradigm in terms of generalizability or robustness. Despite recent progress in questions of identifiability, more theoretical results demonstrating concrete advantages of these methods for downstream tasks are needed. In this paper, we consider the task of intervention extrapolation: predicting how interventions affect an outcome, even when those interventions are not observed at training time, and show that identifiable representations can provide an effective solution to this task even if the interventions affect the outcome non-linearly. Our setup includes an outcome Y, observed features X, which are generated as a non-linear transformation of latent features Z, and exogenous action variables A, which influence Z. The objective of intervention extrapolation is to predict how interventions on A that lie outside the training support of A affect Y. Here, extrapolation becomes possible if the effect of A on Z is linear and the residual when regressing Z on A has full support. As Z is latent, we combine the task of intervention extrapolation with identifiable representation learning, which we call Rep4Ex: we aim to map the observed features X into a subspace that allows for non-linear extrapolation in A. We show that the hidden representation is identifiable up to an affine transformation in Z-space, which is sufficient for intervention extrapolation. The identifiability is characterized by a novel constraint describing the linearity assumption of A on Z. Based on this insight, we propose a method that enforces the linear invariance constraint and can be combined with any type of autoencoder. We validate our theoretical findings through synthetic experiments and show that our approach succeeds in predicting the effects of unseen interventions.

We propose algorithms for approximate filtering and smoothing in high-dimensional Factorial hidden Markov models. The approximation involves discarding, in a principled way, likelihood factors according to a notion of locality in a factor graph associated with the emission distribution. This allows the exponential-in-dimension cost of exact filtering and smoothing to be avoided. We prove that the approximation accuracy, measured in a local total variation norm, is "dimension-free" in the sense that as the overall dimension of the model increases the error bounds we derive do not necessarily degrade. A key step in the analysis is to quantify the error introduced by localizing the likelihood function in a Bayes' rule update. The factorial structure of the likelihood function which we exploit arises naturally when data have known spatial or network structure. We demonstrate the new algorithms on synthetic examples and a London Underground passenger flow problem, where the factor graph is effectively given by the train network.

Kernel continual learning by derakhshani2021kernel has recently emerged as a strong continual learner due to its non-parametric ability to tackle task interference and catastrophic forgetting. Unfortunately its success comes at the expense of an explicit memory to store samples from past tasks, which hampers scalability to continual learning settings with a large number of tasks. In this paper, we introduce generative kernel continual learning, which explores and exploits the synergies between generative models and kernels for continual learning. The generative model is able to produce representative samples for kernel learning, which removes the dependence on memory in kernel continual learning. Moreover, as we replay only on the generative model, we avoid task interference while being computationally more efficient compared to previous methods that need replay on the entire model. We further introduce a supervised contrastive regularization, which enables our model to generate even more discriminative samples for better kernel-based classification performance. We conduct extensive experiments on three widely-used continual learning benchmarks that demonstrate the abilities and benefits of our contributions. Most notably, on the challenging SplitCIFAR100 benchmark, with just a simple linear kernel we obtain the same accuracy as kernel continual learning with variational random features for one tenth of the memory, or a 10.1\% accuracy gain for the same memory budget.

We consider the distributionally robust optimization (DRO) problem with spectral risk-based uncertainty set and f-divergence penalty. This formulation includes common risk-sensitive learning objectives such as regularized condition value-at-risk (CVaR) and average top-k loss. We present Prospect, a stochastic gradient-based algorithm that only requires tuning a single learning rate hyperparameter, and prove that it enjoys linear convergence for smooth regularized losses. This contrasts with previous algorithms that either require tuning multiple hyperparameters or potentially fail to converge due to biased gradient estimates or inadequate regularization. Empirically, we show that Prospect can converge 2-3times faster than baselines such as stochastic gradient and stochastic saddle-point methods on distribution shift and fairness benchmarks spanning tabular, vision, and language domains.

A number of different architectures and loss functions have been applied to the problem of self-supervised learning (SSL), with the goal of developing embeddings that provide the best possible pre-training for as-yet-unknown, lightly supervised downstream tasks. One of these SSL criteria is to maximize the entropy of a set of embeddings in some compact space. But the goal of maximizing the embedding entropy often depends--whether explicitly or implicitly--upon high dimensional entropy estimates, which typically perform poorly in more than a few dimensions. In this paper, we motivate an effective entropy maximization criterion (E2MC), defined in terms of easy-to-estimate, low-dimensional constraints. We demonstrate that using it to continue training an already-trained SSL model for only a handful of epochs leads to a consistent and, in some cases, significant improvement in downstream performance. We perform careful ablation studies to show that the improved performance is due to the proposed add-on criterion. We also show that continued pre-training with alternative criteria does not lead to notable improvements, and in some cases, even degrades performance.

A variety of methods have been proposed to try to explain how deep neural networks make their decisions. Key to those approaches is the need to sample the pixel space efficiently in order to derive importance maps. However, it has been shown that the sampling methods used to date introduce biases and other artifacts, leading to inaccurate estimates of the importance of individual pixels and severely limit the reliability of current explainability methods. Unfortunately, the alternative -- to exhaustively sample the image space is computationally prohibitive. In this paper, we introduce EVA (Explaining using Verified perturbation Analysis) -- the first explainability method guarantee to have an exhaustive exploration of a perturbation space. Specifically, we leverage the beneficial properties of verified perturbation analysis -- time efficiency, tractability and guaranteed complete coverage of a manifold -- to efficiently characterize the input variables that are most likely to drive the model decision. We evaluate the approach systematically and demonstrate state-of-the-art results on multiple benchmarks.

Transformers have emerged as a preferred model for many tasks in natural langugage processing and vision. Recent efforts on training and deploying Transformers more efficiently have identified many strategies to approximate the self-attention matrix, a key module in a Transformer architecture. Effective ideas include various prespecified sparsity patterns, low-rank basis expansions and combinations thereof. In this paper, we revisit classical Multiresolution Analysis (MRA) concepts such as Wavelets, whose potential value in this setting remains underexplored thus far. We show that simple approximations based on empirical feedback and design choices informed by modern hardware and implementation challenges, eventually yield a MRA-based approach for self-attention with an excellent performance profile across most criteria of interest. We undertake an extensive set of experiments and demonstrate that this multi-resolution scheme outperforms most efficient self-attention proposals and is favorable for both short and long sequences. Code is available at https://github.com/mlpen/mra-attention.

Online Normalization is a new technique for normalizing the hidden activations of a neural network. Like Batch Normalization, it normalizes the sample dimension. While Online Normalization does not use batches, it is as accurate as Batch Normalization. We resolve a theoretical limitation of Batch Normalization by introducing an unbiased technique for computing the gradient of normalized activations. Online Normalization works with automatic differentiation by adding statistical normalization as a primitive. This technique can be used in cases not covered by some other normalizers, such as recurrent networks, fully connected networks, and networks with activation memory requirements prohibitive for batching. We show its applications to image classification, image segmentation, and language modeling. We present formal proofs and experimental results on ImageNet, CIFAR, and PTB datasets.

In this work, we investigate the implicit regularization induced by teacher-student learning dynamics in self-distillation. To isolate its effect, we describe a simple experiment where we consider teachers at random initialization instead of trained teachers. Surprisingly, when distilling a student into such a random teacher, we observe that the resulting model and its representations already possess very interesting characteristics; (1) we observe a strong improvement of the distilled student over its teacher in terms of probing accuracy. (2) The learned representations are data-dependent and transferable between different tasks but deteriorate strongly if trained on random inputs. (3) The student checkpoint contains sparse subnetworks, so-called lottery tickets, and lies on the border of linear basins in the supervised loss landscape. These observations have interesting consequences for several important areas in machine learning: (1) Self-distillation can work solely based on the implicit regularization present in the gradient dynamics without relying on any dark knowledge, (2) self-supervised learning can learn features even in the absence of data augmentation and (3) training dynamics during the early phase of supervised training do not necessarily require label information. Finally, we shed light on an intriguing local property of the loss landscape: the process of feature learning is strongly amplified if the student is initialized closely to the teacher. These results raise interesting questions about the nature of the landscape that have remained unexplored so far. Code is available at https://github.com/safelix/dinopl.

Existing methods of pruning deep neural networks focus on removing unnecessary parameters of the trained network and fine tuning the model afterwards to find a good solution that recovers the initial performance of the trained model. Unlike other works, our method pays special attention to the quality of the solution in the compressed model and inference computation time by pruning neurons. The proposed algorithm directs the parameters of the compressed model toward a flatter solution by exploring the spectral radius of Hessian which results in better generalization on unseen data. Moreover, the method does not work with a pre-trained network and performs training and pruning simultaneously. Our result shows that it improves the state-of-the-art results on neuron compression. The method is able to achieve very small networks with small accuracy degradation across different neural network models.