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Mar 14

Weight Compander: A Simple Weight Reparameterization for Regularization

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.

Adaptively Weighted Data Augmentation Consistency Regularization for Robust Optimization under Concept Shift

Concept shift is a prevailing problem in natural tasks like medical image segmentation where samples usually come from different subpopulations with variant correlations between features and labels. One common type of concept shift in medical image segmentation is the "information imbalance" between label-sparse samples with few (if any) segmentation labels and label-dense samples with plentiful labeled pixels. Existing distributionally robust algorithms have focused on adaptively truncating/down-weighting the "less informative" (i.e., label-sparse in our context) samples. To exploit data features of label-sparse samples more efficiently, we propose an adaptively weighted online optimization algorithm -- AdaWAC -- to incorporate data augmentation consistency regularization in sample reweighting. Our method introduces a set of trainable weights to balance the supervised loss and unsupervised consistency regularization of each sample separately. At the saddle point of the underlying objective, the weights assign label-dense samples to the supervised loss and label-sparse samples to the unsupervised consistency regularization. We provide a convergence guarantee by recasting the optimization as online mirror descent on a saddle point problem. Our empirical results demonstrate that AdaWAC not only enhances the segmentation performance and sample efficiency but also improves the robustness to concept shift on various medical image segmentation tasks with different UNet-style backbones.

DR-Tune: Improving Fine-tuning of Pretrained Visual Models by Distribution Regularization with Semantic Calibration

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.

Minimizing the Accumulated Trajectory Error to Improve Dataset Distillation

Model-based deep learning has achieved astounding successes due in part to the availability of large-scale real-world data. However, processing such massive amounts of data comes at a considerable cost in terms of computations, storage, training and the search for good neural architectures. Dataset distillation has thus recently come to the fore. This paradigm involves distilling information from large real-world datasets into tiny and compact synthetic datasets such that processing the latter ideally yields similar performances as the former. State-of-the-art methods primarily rely on learning the synthetic dataset by matching the gradients obtained during training between the real and synthetic data. However, these gradient-matching methods suffer from the so-called accumulated trajectory error caused by the discrepancy between the distillation and subsequent evaluation. To mitigate the adverse impact of this accumulated trajectory error, we propose a novel approach that encourages the optimization algorithm to seek a flat trajectory. We show that the weights trained on synthetic data are robust against the accumulated errors perturbations with the regularization towards the flat trajectory. Our method, called Flat Trajectory Distillation (FTD), is shown to boost the performance of gradient-matching methods by up to 4.7% on a subset of images of the ImageNet dataset with higher resolution images. We also validate the effectiveness and generalizability of our method with datasets of different resolutions and demonstrate its applicability to neural architecture search. Code is available at https://github.com/AngusDujw/FTD-distillation.

Hard-Attention Gates with Gradient Routing for Endoscopic Image Computing

To address overfitting and enhance model generalization in gastroenterological polyp size assessment, our study introduces Feature-Selection Gates (FSG) or Hard-Attention Gates (HAG) alongside Gradient Routing (GR) for dynamic feature selection. This technique aims to boost Convolutional Neural Networks (CNNs) and Vision Transformers (ViTs) by promoting sparse connectivity, thereby reducing overfitting and enhancing generalization. HAG achieves this through sparsification with learnable weights, serving as a regularization strategy. GR further refines this process by optimizing HAG parameters via dual forward passes, independently from the main model, to improve feature re-weighting. Our evaluation spanned multiple datasets, including CIFAR-100 for a broad impact assessment and specialized endoscopic datasets (REAL-Colon, Misawa, and SUN) focusing on polyp size estimation, covering over 200 polyps in more than 370,000 frames. The findings indicate that our HAG-enhanced networks substantially enhance performance in both binary and triclass classification tasks related to polyp sizing. Specifically, CNNs experienced an F1 Score improvement to 87.8% in binary classification, while in triclass classification, the ViT-T model reached an F1 Score of 76.5%, outperforming traditional CNNs and ViT-T models. To facilitate further research, we are releasing our codebase, which includes implementations for CNNs, multistream CNNs, ViT, and HAG-augmented variants. This resource aims to standardize the use of endoscopic datasets, providing public training-validation-testing splits for reliable and comparable research in gastroenterological polyp size estimation. The codebase is available at github.com/cosmoimd/feature-selection-gates.

Self-Tuning Networks: Bilevel Optimization of Hyperparameters using Structured Best-Response Functions

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).

EQ-Net: Elastic Quantization Neural Networks

Current model quantization methods have shown their promising capability in reducing storage space and computation complexity. However, due to the diversity of quantization forms supported by different hardware, one limitation of existing solutions is that usually require repeated optimization for different scenarios. How to construct a model with flexible quantization forms has been less studied. In this paper, we explore a one-shot network quantization regime, named Elastic Quantization Neural Networks (EQ-Net), which aims to train a robust weight-sharing quantization supernet. First of all, we propose an elastic quantization space (including elastic bit-width, granularity, and symmetry) to adapt to various mainstream quantitative forms. Secondly, we propose the Weight Distribution Regularization Loss (WDR-Loss) and Group Progressive Guidance Loss (GPG-Loss) to bridge the inconsistency of the distribution for weights and output logits in the elastic quantization space gap. Lastly, we incorporate genetic algorithms and the proposed Conditional Quantization-Aware Accuracy Predictor (CQAP) as an estimator to quickly search mixed-precision quantized neural networks in supernet. Extensive experiments demonstrate that our EQ-Net is close to or even better than its static counterparts as well as state-of-the-art robust bit-width methods. Code can be available at https://github.com/xuke225/EQ-Net.git{https://github.com/xuke225/EQ-Net}.

Enhanced Aspect-Based Sentiment Analysis Models with Progressive Self-supervised Attention Learning

In aspect-based sentiment analysis (ABSA), many neural models are equipped with an attention mechanism to quantify the contribution of each context word to sentiment prediction. However, such a mechanism suffers from one drawback: only a few frequent words with sentiment polarities are tended to be taken into consideration for final sentiment decision while abundant infrequent sentiment words are ignored by models. To deal with this issue, we propose a progressive self-supervised attention learning approach for attentional ABSA models. In this approach, we iteratively perform sentiment prediction on all training instances, and continually learn useful attention supervision information in the meantime. During training, at each iteration, context words with the highest impact on sentiment prediction, identified based on their attention weights or gradients, are extracted as words with active/misleading influence on the correct/incorrect prediction for each instance. Words extracted in this way are masked for subsequent iterations. To exploit these extracted words for refining ABSA models, we augment the conventional training objective with a regularization term that encourages ABSA models to not only take full advantage of the extracted active context words but also decrease the weights of those misleading words. We integrate the proposed approach into three state-of-the-art neural ABSA models. Experiment results and in-depth analyses show that our approach yields better attention results and significantly enhances the performance of all three models. We release the source code and trained models at https://github.com/DeepLearnXMU/PSSAttention.

MEAL V2: Boosting Vanilla ResNet-50 to 80%+ Top-1 Accuracy on ImageNet without Tricks

We introduce a simple yet effective distillation framework that is able to boost the vanilla ResNet-50 to 80%+ Top-1 accuracy on ImageNet without tricks. We construct such a framework through analyzing the problems in the existing classification system and simplify the base method ensemble knowledge distillation via discriminators by: (1) adopting the similarity loss and discriminator only on the final outputs and (2) using the average of softmax probabilities from all teacher ensembles as the stronger supervision. Intriguingly, three novel perspectives are presented for distillation: (1) weight decay can be weakened or even completely removed since the soft label also has a regularization effect; (2) using a good initialization for students is critical; and (3) one-hot/hard label is not necessary in the distillation process if the weights are well initialized. We show that such a straight-forward framework can achieve state-of-the-art results without involving any commonly-used techniques, such as architecture modification; outside training data beyond ImageNet; autoaug/randaug; cosine learning rate; mixup/cutmix training; label smoothing; etc. Our method obtains 80.67% top-1 accuracy on ImageNet using a single crop-size of 224x224 with vanilla ResNet-50, outperforming the previous state-of-the-arts by a significant margin under the same network structure. Our result can be regarded as a strong baseline using knowledge distillation, and to our best knowledge, this is also the first method that is able to boost vanilla ResNet-50 to surpass 80% on ImageNet without architecture modification or additional training data. On smaller ResNet-18, our distillation framework consistently improves from 69.76% to 73.19%, which shows tremendous practical values in real-world applications. Our code and models are available at: https://github.com/szq0214/MEAL-V2.

Even your Teacher Needs Guidance: Ground-Truth Targets Dampen Regularization Imposed by Self-Distillation

Knowledge distillation is classically a procedure where a neural network is trained on the output of another network along with the original targets in order to transfer knowledge between the architectures. The special case of self-distillation, where the network architectures are identical, has been observed to improve generalization accuracy. In this paper, we consider an iterative variant of self-distillation in a kernel regression setting, in which successive steps incorporate both model outputs and the ground-truth targets. This allows us to provide the first theoretical results on the importance of using the weighted ground-truth targets in self-distillation. Our focus is on fitting nonlinear functions to training data with a weighted mean square error objective function suitable for distillation, subject to ell_2 regularization of the model parameters. We show that any such function obtained with self-distillation can be calculated directly as a function of the initial fit, and that infinite distillation steps yields the same optimization problem as the original with amplified regularization. Furthermore, we provide a closed form solution for the optimal choice of weighting parameter at each step, and show how to efficiently estimate this weighting parameter for deep learning and significantly reduce the computational requirements compared to a grid search.

Learning k-Level Structured Sparse Neural Networks Using Group Envelope Regularization

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.

Sparsity-Constrained Optimal Transport

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.

Early-Learning Regularization Prevents Memorization of Noisy Labels

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.

Doubly Robust Instance-Reweighted Adversarial Training

Assigning importance weights to adversarial data has achieved great success in training adversarially robust networks under limited model capacity. However, existing instance-reweighted adversarial training (AT) methods heavily depend on heuristics and/or geometric interpretations to determine those importance weights, making these algorithms lack rigorous theoretical justification/guarantee. Moreover, recent research has shown that adversarial training suffers from a severe non-uniform robust performance across the training distribution, e.g., data points belonging to some classes can be much more vulnerable to adversarial attacks than others. To address both issues, in this paper, we propose a novel doubly-robust instance reweighted AT framework, which allows to obtain the importance weights via exploring distributionally robust optimization (DRO) techniques, and at the same time boosts the robustness on the most vulnerable examples. In particular, our importance weights are obtained by optimizing the KL-divergence regularized loss function, which allows us to devise new algorithms with a theoretical convergence guarantee. Experiments on standard classification datasets demonstrate that our proposed approach outperforms related state-of-the-art baseline methods in terms of average robust performance, and at the same time improves the robustness against attacks on the weakest data points. Codes will be available soon.

Self-Knowledge Distillation with Progressive Refinement of Targets

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.

To grok or not to grok: Disentangling generalization and memorization on corrupted algorithmic datasets

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)%.

Train longer, generalize better: closing the generalization gap in large batch training of neural networks

Background: Deep learning models are typically trained using stochastic gradient descent or one of its variants. These methods update the weights using their gradient, estimated from a small fraction of the training data. It has been observed that when using large batch sizes there is a persistent degradation in generalization performance - known as the "generalization gap" phenomena. Identifying the origin of this gap and closing it had remained an open problem. Contributions: We examine the initial high learning rate training phase. We find that the weight distance from its initialization grows logarithmically with the number of weight updates. We therefore propose a "random walk on random landscape" statistical model which is known to exhibit similar "ultra-slow" diffusion behavior. Following this hypothesis we conducted experiments to show empirically that the "generalization gap" stems from the relatively small number of updates rather than the batch size, and can be completely eliminated by adapting the training regime used. We further investigate different techniques to train models in the large-batch regime and present a novel algorithm named "Ghost Batch Normalization" which enables significant decrease in the generalization gap without increasing the number of updates. To validate our findings we conduct several additional experiments on MNIST, CIFAR-10, CIFAR-100 and ImageNet. Finally, we reassess common practices and beliefs concerning training of deep models and suggest they may not be optimal to achieve good generalization.

Parameter-Efficient Sparsity for Large Language Models Fine-Tuning

With the dramatically increased number of parameters in language models, sparsity methods have received ever-increasing research focus to compress and accelerate the models. While most research focuses on how to accurately retain appropriate weights while maintaining the performance of the compressed model, there are challenges in the computational overhead and memory footprint of sparse training when compressing large-scale language models. To address this problem, we propose a Parameter-efficient Sparse Training (PST) method to reduce the number of trainable parameters during sparse-aware training in downstream tasks. Specifically, we first combine the data-free and data-driven criteria to efficiently and accurately measure the importance of weights. Then we investigate the intrinsic redundancy of data-driven weight importance and derive two obvious characteristics i.e., low-rankness and structuredness. Based on that, two groups of small matrices are introduced to compute the data-driven importance of weights, instead of using the original large importance score matrix, which therefore makes the sparse training resource-efficient and parameter-efficient. Experiments with diverse networks (i.e., BERT, RoBERTa and GPT-2) on dozens of datasets demonstrate PST performs on par or better than previous sparsity methods, despite only training a small number of parameters. For instance, compared with previous sparsity methods, our PST only requires 1.5% trainable parameters to achieve comparable performance on BERT.

Self-supervised Learning for Large-scale Item Recommendations

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.

Learning from Aggregate responses: Instance Level versus Bag Level Loss Functions

Due to the rise of privacy concerns, in many practical applications the training data is aggregated before being shared with the learner, in order to protect privacy of users' sensitive responses. In an aggregate learning framework, the dataset is grouped into bags of samples, where each bag is available only with an aggregate response, providing a summary of individuals' responses in that bag. In this paper, we study two natural loss functions for learning from aggregate responses: bag-level loss and the instance-level loss. In the former, the model is learnt by minimizing a loss between aggregate responses and aggregate model predictions, while in the latter the model aims to fit individual predictions to the aggregate responses. In this work, we show that the instance-level loss can be perceived as a regularized form of the bag-level loss. This observation lets us compare the two approaches with respect to bias and variance of the resulting estimators, and introduce a novel interpolating estimator which combines the two approaches. For linear regression tasks, we provide a precise characterization of the risk of the interpolating estimator in an asymptotic regime where the size of the training set grows in proportion to the features dimension. Our analysis allows us to theoretically understand the effect of different factors, such as bag size on the model prediction risk. In addition, we propose a mechanism for differentially private learning from aggregate responses and derive the optimal bag size in terms of prediction risk-privacy trade-off. We also carry out thorough experiments to corroborate our theory and show the efficacy of the interpolating estimator.

QuantNAS for super resolution: searching for efficient quantization-friendly architectures against quantization noise

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.

A Boundary Tilting Persepective on the Phenomenon of Adversarial Examples

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.

Class-relation Knowledge Distillation for Novel Class Discovery

We tackle the problem of novel class discovery, which aims to learn novel classes without supervision based on labeled data from known classes. A key challenge lies in transferring the knowledge in the known-class data to the learning of novel classes. Previous methods mainly focus on building a shared representation space for knowledge transfer and often ignore modeling class relations. To address this, we introduce a class relation representation for the novel classes based on the predicted class distribution of a model trained on known classes. Empirically, we find that such class relation becomes less informative during typical discovery training. To prevent such information loss, we propose a novel knowledge distillation framework, which utilizes our class-relation representation to regularize the learning of novel classes. In addition, to enable a flexible knowledge distillation scheme for each data point in novel classes, we develop a learnable weighting function for the regularization, which adaptively promotes knowledge transfer based on the semantic similarity between the novel and known classes. To validate the effectiveness and generalization of our method, we conduct extensive experiments on multiple benchmarks, including CIFAR100, Stanford Cars, CUB, and FGVC-Aircraft datasets. Our results demonstrate that the proposed method outperforms the previous state-of-the-art methods by a significant margin on almost all benchmarks. Code is available at https://github.com/kleinzcy/Cr-KD-NCD{here}.

Imbalanced Adversarial Training with Reweighting

Adversarial training has been empirically proven to be one of the most effective and reliable defense methods against adversarial attacks. However, almost all existing studies about adversarial training are focused on balanced datasets, where each class has an equal amount of training examples. Research on adversarial training with imbalanced training datasets is rather limited. As the initial effort to investigate this problem, we reveal the facts that adversarially trained models present two distinguished behaviors from naturally trained models in imbalanced datasets: (1) Compared to natural training, adversarially trained models can suffer much worse performance on under-represented classes, when the training dataset is extremely imbalanced. (2) Traditional reweighting strategies may lose efficacy to deal with the imbalance issue for adversarial training. For example, upweighting the under-represented classes will drastically hurt the model's performance on well-represented classes, and as a result, finding an optimal reweighting value can be tremendously challenging. In this paper, to further understand our observations, we theoretically show that the poor data separability is one key reason causing this strong tension between under-represented and well-represented classes. Motivated by this finding, we propose Separable Reweighted Adversarial Training (SRAT) to facilitate adversarial training under imbalanced scenarios, by learning more separable features for different classes. Extensive experiments on various datasets verify the effectiveness of the proposed framework.

Pareto-Optimal Quantized ResNet Is Mostly 4-bit

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.

Compressing Features for Learning with Noisy Labels

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/.

Threshold-Consistent Margin Loss for Open-World Deep Metric Learning

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.

Improved Active Multi-Task Representation Learning via Lasso

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.

Spurious Feature Diversification Improves Out-of-distribution Generalization

Generalization to out-of-distribution (OOD) data is a critical challenge in machine learning. Ensemble-based methods, like weight space ensembles that interpolate model parameters, have been shown to achieve superior OOD performance. However, the underlying mechanism for their effectiveness remains unclear. In this study, we closely examine WiSE-FT, a popular weight space ensemble method that interpolates between a pre-trained and a fine-tuned model. We observe an unexpected phenomenon, in which WiSE-FT successfully corrects many cases where each individual model makes incorrect predictions, which contributes significantly to its OOD effectiveness. To gain further insights, we conduct theoretical analysis in a multi-class setting with a large number of spurious features. Our analysis predicts the above phenomenon and it further shows that ensemble-based models reduce prediction errors in the OOD settings by utilizing a more diverse set of spurious features. Contrary to the conventional wisdom that focuses on learning invariant features for better OOD performance, our findings suggest that incorporating a large number of diverse spurious features weakens their individual contributions, leading to improved overall OOD generalization performance. Empirically we demonstrate the effectiveness of utilizing diverse spurious features on a MultiColorMNIST dataset, and our experimental results are consistent with the theoretical analysis. Building upon the new theoretical insights into the efficacy of ensemble methods, we further identify an issue of WiSE-FT caused by the overconfidence of fine-tuned models in OOD situations. This overconfidence magnifies the fine-tuned model's incorrect prediction, leading to deteriorated OOD ensemble performance. To remedy this problem, we propose a novel method called BAlaNced averaGing (BANG), which significantly enhances the OOD performance of WiSE-FT.

AdamP: Slowing Down the Slowdown for Momentum Optimizers on Scale-invariant Weights

Normalization techniques are a boon for modern deep learning. They let weights converge more quickly with often better generalization performances. It has been argued that the normalization-induced scale invariance among the weights provides an advantageous ground for gradient descent (GD) optimizers: the effective step sizes are automatically reduced over time, stabilizing the overall training procedure. It is often overlooked, however, that the additional introduction of momentum in GD optimizers results in a far more rapid reduction in effective step sizes for scale-invariant weights, a phenomenon that has not yet been studied and may have caused unwanted side effects in the current practice. This is a crucial issue because arguably the vast majority of modern deep neural networks consist of (1) momentum-based GD (e.g. SGD or Adam) and (2) scale-invariant parameters. In this paper, we verify that the widely-adopted combination of the two ingredients lead to the premature decay of effective step sizes and sub-optimal model performances. We propose a simple and effective remedy, SGDP and AdamP: get rid of the radial component, or the norm-increasing direction, at each optimizer step. Because of the scale invariance, this modification only alters the effective step sizes without changing the effective update directions, thus enjoying the original convergence properties of GD optimizers. Given the ubiquity of momentum GD and scale invariance in machine learning, we have evaluated our methods against the baselines on 13 benchmarks. They range from vision tasks like classification (e.g. ImageNet), retrieval (e.g. CUB and SOP), and detection (e.g. COCO) to language modelling (e.g. WikiText) and audio classification (e.g. DCASE) tasks. We verify that our solution brings about uniform gains in those benchmarks. Source code is available at https://github.com/clovaai/AdamP.

Opening the Blackbox: Accelerating Neural Differential Equations by Regularizing Internal Solver Heuristics

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.

Deep Learning on a Data Diet: Finding Important Examples Early in Training

Recent success in deep learning has partially been driven by training increasingly overparametrized networks on ever larger datasets. It is therefore natural to ask: how much of the data is superfluous, which examples are important for generalization, and how do we find them? In this work, we make the striking observation that, in standard vision datasets, simple scores averaged over several weight initializations can be used to identify important examples very early in training. We propose two such scores -- the Gradient Normed (GraNd) and the Error L2-Norm (EL2N) scores -- and demonstrate their efficacy on a range of architectures and datasets by pruning significant fractions of training data without sacrificing test accuracy. In fact, using EL2N scores calculated a few epochs into training, we can prune half of the CIFAR10 training set while slightly improving test accuracy. Furthermore, for a given dataset, EL2N scores from one architecture or hyperparameter configuration generalize to other configurations. Compared to recent work that prunes data by discarding examples that are rarely forgotten over the course of training, our scores use only local information early in training. We also use our scores to detect noisy examples and study training dynamics through the lens of important examples -- we investigate how the data distribution shapes the loss surface and identify subspaces of the model's data representation that are relatively stable over training.

NUPES : Non-Uniform Post-Training Quantization via Power Exponent Search

Deep neural network (DNN) deployment has been confined to larger hardware devices due to their expensive computational requirements. This challenge has recently reached another scale with the emergence of large language models (LLMs). In order to reduce both their memory footprint and latency, a promising technique is quantization. It consists in converting floating point representations to low bit-width fixed point representations, usually by assuming a uniform mapping onto a regular grid. This process, referred to in the literature as uniform quantization, may however be ill-suited as most DNN weights and activations follow a bell-shaped distribution. This is even worse on LLMs whose weight distributions are known to exhibit large, high impact, outlier values. In this work, we propose an improvement over the most commonly adopted way to tackle this limitation in deep learning models quantization, namely, non-uniform quantization. NUPES leverages automorphisms to preserve the scalar multiplications. Such transformations are derived from power functions. However, the optimization of the exponent parameter and weight values remains a challenging and novel problem which could not be solved with previous post training optimization techniques which only learn to round up or down weight values in order to preserve the predictive function. We circumvent this limitation with a new paradigm: learning new quantized weights over the entire quantized space. Similarly, we enable the optimization of the power exponent, i.e. the optimization of the quantization operator itself during training by alleviating all the numerical instabilities. The resulting predictive function is compatible with integer-only low-bit inference. We show the ability of the method to achieve state-of-the-art compression rates in both, data-free and data-driven configurations.

T-JEPA: Augmentation-Free Self-Supervised Learning for Tabular Data

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.

Refined Regret for Adversarial MDPs with Linear Function Approximation

We consider learning in an adversarial Markov Decision Process (MDP) where the loss functions can change arbitrarily over K episodes and the state space can be arbitrarily large. We assume that the Q-function of any policy is linear in some known features, that is, a linear function approximation exists. The best existing regret upper bound for this setting (Luo et al., 2021) is of order mathcal O(K^{2/3}) (omitting all other dependencies), given access to a simulator. This paper provides two algorithms that improve the regret to mathcal O(sqrt K) in the same setting. Our first algorithm makes use of a refined analysis of the Follow-the-Regularized-Leader (FTRL) algorithm with the log-barrier regularizer. This analysis allows the loss estimators to be arbitrarily negative and might be of independent interest. Our second algorithm develops a magnitude-reduced loss estimator, further removing the polynomial dependency on the number of actions in the first algorithm and leading to the optimal regret bound (up to logarithmic terms and dependency on the horizon). Moreover, we also extend the first algorithm to simulator-free linear MDPs, which achieves mathcal O(K^{8/9}) regret and greatly improves over the best existing bound mathcal O(K^{14/15}). This algorithm relies on a better alternative to the Matrix Geometric Resampling procedure by Neu & Olkhovskaya (2020), which could again be of independent interest.

Grokking at the Edge of Numerical Stability

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.

Wide and Deep Neural Networks Achieve Optimality for Classification

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.

What's in a Prior? Learned Proximal Networks for Inverse Problems

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.

Investigating the Benefits of Projection Head for Representation Learning

An effective technique for obtaining high-quality representations is adding a projection head on top of the encoder during training, then discarding it and using the pre-projection representations. Despite its proven practical effectiveness, the reason behind the success of this technique is poorly understood. The pre-projection representations are not directly optimized by the loss function, raising the question: what makes them better? In this work, we provide a rigorous theoretical answer to this question. We start by examining linear models trained with self-supervised contrastive loss. We reveal that the implicit bias of training algorithms leads to layer-wise progressive feature weighting, where features become increasingly unequal as we go deeper into the layers. Consequently, lower layers tend to have more normalized and less specialized representations. We theoretically characterize scenarios where such representations are more beneficial, highlighting the intricate interplay between data augmentation and input features. Additionally, we demonstrate that introducing non-linearity into the network allows lower layers to learn features that are completely absent in higher layers. Finally, we show how this mechanism improves the robustness in supervised contrastive learning and supervised learning. We empirically validate our results through various experiments on CIFAR-10/100, UrbanCars and shifted versions of ImageNet. We also introduce a potential alternative to projection head, which offers a more interpretable and controllable design.

Let's Make Block Coordinate Descent Converge Faster: Faster Greedy Rules, Message-Passing, Active-Set Complexity, and Superlinear Convergence

Block coordinate descent (BCD) methods are widely used for large-scale numerical optimization because of their cheap iteration costs, low memory requirements, amenability to parallelization, and ability to exploit problem structure. Three main algorithmic choices influence the performance of BCD methods: the block partitioning strategy, the block selection rule, and the block update rule. In this paper we explore all three of these building blocks and propose variations for each that can significantly improve the progress made by each BCD iteration. We (i) propose new greedy block-selection strategies that guarantee more progress per iteration than the Gauss-Southwell rule; (ii) explore practical issues like how to implement the new rules when using "variable" blocks; (iii) explore the use of message-passing to compute matrix or Newton updates efficiently on huge blocks for problems with sparse dependencies between variables; and (iv) consider optimal active manifold identification, which leads to bounds on the "active-set complexity" of BCD methods and leads to superlinear convergence for certain problems with sparse solutions (and in some cases finite termination at an optimal solution). We support all of our findings with numerical results for the classic machine learning problems of least squares, logistic regression, multi-class logistic regression, label propagation, and L1-regularization.

SaRA: High-Efficient Diffusion Model Fine-tuning with Progressive Sparse Low-Rank Adaptation

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.

Predicting Rare Events by Shrinking Towards Proportional Odds

Training classifiers is difficult with severe class imbalance, but many rare events are the culmination of a sequence with much more common intermediate outcomes. For example, in online marketing a user first sees an ad, then may click on it, and finally may make a purchase; estimating the probability of purchases is difficult because of their rarity. We show both theoretically and through data experiments that the more abundant data in earlier steps may be leveraged to improve estimation of probabilities of rare events. We present PRESTO, a relaxation of the proportional odds model for ordinal regression. Instead of estimating weights for one separating hyperplane that is shifted by separate intercepts for each of the estimated Bayes decision boundaries between adjacent pairs of categorical responses, we estimate separate weights for each of these transitions. We impose an L1 penalty on the differences between weights for the same feature in adjacent weight vectors in order to shrink towards the proportional odds model. We prove that PRESTO consistently estimates the decision boundary weights under a sparsity assumption. Synthetic and real data experiments show that our method can estimate rare probabilities in this setting better than both logistic regression on the rare category, which fails to borrow strength from more abundant categories, and the proportional odds model, which is too inflexible.

Efficient Joint Optimization of Layer-Adaptive Weight Pruning in Deep Neural Networks

In this paper, we propose a novel layer-adaptive weight-pruning approach for Deep Neural Networks (DNNs) that addresses the challenge of optimizing the output distortion minimization while adhering to a target pruning ratio constraint. Our approach takes into account the collective influence of all layers to design a layer-adaptive pruning scheme. We discover and utilize a very important additivity property of output distortion caused by pruning weights on multiple layers. This property enables us to formulate the pruning as a combinatorial optimization problem and efficiently solve it through dynamic programming. By decomposing the problem into sub-problems, we achieve linear time complexity, making our optimization algorithm fast and feasible to run on CPUs. Our extensive experiments demonstrate the superiority of our approach over existing methods on the ImageNet and CIFAR-10 datasets. On CIFAR-10, our method achieves remarkable improvements, outperforming others by up to 1.0% for ResNet-32, 0.5% for VGG-16, and 0.7% for DenseNet-121 in terms of top-1 accuracy. On ImageNet, we achieve up to 4.7% and 4.6% higher top-1 accuracy compared to other methods for VGG-16 and ResNet-50, respectively. These results highlight the effectiveness and practicality of our approach for enhancing DNN performance through layer-adaptive weight pruning. Code will be available on https://github.com/Akimoto-Cris/RD_VIT_PRUNE.

Revisiting Discriminative vs. Generative Classifiers: Theory and Implications

A large-scale deep model pre-trained on massive labeled or unlabeled data transfers well to downstream tasks. Linear evaluation freezes parameters in the pre-trained model and trains a linear classifier separately, which is efficient and attractive for transfer. However, little work has investigated the classifier in linear evaluation except for the default logistic regression. Inspired by the statistical efficiency of naive Bayes, the paper revisits the classical topic on discriminative vs. generative classifiers. Theoretically, the paper considers the surrogate loss instead of the zero-one loss in analyses and generalizes the classical results from binary cases to multiclass ones. We show that, under mild assumptions, multiclass naive Bayes requires O(log n) samples to approach its asymptotic error while the corresponding multiclass logistic regression requires O(n) samples, where n is the feature dimension. To establish it, we present a multiclass H-consistency bound framework and an explicit bound for logistic loss, which are of independent interests. Simulation results on a mixture of Gaussian validate our theoretical findings. Experiments on various pre-trained deep vision models show that naive Bayes consistently converges faster as the number of data increases. Besides, naive Bayes shows promise in few-shot cases and we observe the "two regimes" phenomenon in pre-trained supervised models. Our code is available at https://github.com/ML-GSAI/Revisiting-Dis-vs-Gen-Classifiers.

Fire Together Wire Together: A Dynamic Pruning Approach with Self-Supervised Mask Prediction

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.

The Monge Gap: A Regularizer to Learn All Transport Maps

Optimal transport (OT) theory has been been used in machine learning to study and characterize maps that can push-forward efficiently a probability measure onto another. Recent works have drawn inspiration from Brenier's theorem, which states that when the ground cost is the squared-Euclidean distance, the ``best'' map to morph a continuous measure in P(Rd) into another must be the gradient of a convex function. To exploit that result, [Makkuva+ 2020, Korotin+2020] consider maps T=nabla f_theta, where f_theta is an input convex neural network (ICNN), as defined by Amos+2017, and fit theta with SGD using samples. Despite their mathematical elegance, fitting OT maps with ICNNs raises many challenges, due notably to the many constraints imposed on theta; the need to approximate the conjugate of f_theta; or the limitation that they only work for the squared-Euclidean cost. More generally, we question the relevance of using Brenier's result, which only applies to densities, to constrain the architecture of candidate maps fitted on samples. Motivated by these limitations, we propose a radically different approach to estimating OT maps: Given a cost c and a reference measure rho, we introduce a regularizer, the Monge gap M^c_{rho}(T) of a map T. That gap quantifies how far a map T deviates from the ideal properties we expect from a c-OT map. In practice, we drop all architecture requirements for T and simply minimize a distance (e.g., the Sinkhorn divergence) between Tsharpmu and nu, regularized by M^c_rho(T). We study M^c_{rho}, and show how our simple pipeline outperforms significantly other baselines in practice.

How Powerful are Shallow Neural Networks with Bandlimited Random Weights?

We investigate the expressive power of depth-2 bandlimited random neural networks. A random net is a neural network where the hidden layer parameters are frozen with random assignment, and only the output layer parameters are trained by loss minimization. Using random weights for a hidden layer is an effective method to avoid non-convex optimization in standard gradient descent learning. It has also been adopted in recent deep learning theories. Despite the well-known fact that a neural network is a universal approximator, in this study, we mathematically show that when hidden parameters are distributed in a bounded domain, the network may not achieve zero approximation error. In particular, we derive a new nontrivial approximation error lower bound. The proof utilizes the technique of ridgelet analysis, a harmonic analysis method designed for neural networks. This method is inspired by fundamental principles in classical signal processing, specifically the idea that signals with limited bandwidth may not always be able to perfectly recreate the original signal. We corroborate our theoretical results with various simulation studies, and generally, two main take-home messages are offered: (i) Not any distribution for selecting random weights is feasible to build a universal approximator; (ii) A suitable assignment of random weights exists but to some degree is associated with the complexity of the target function.

Probabilistic Imputation for Time-series Classification with Missing Data

Multivariate time series data for real-world applications typically contain a significant amount of missing values. The dominant approach for classification with such missing values is to impute them heuristically with specific values (zero, mean, values of adjacent time-steps) or learnable parameters. However, these simple strategies do not take the data generative process into account, and more importantly, do not effectively capture the uncertainty in prediction due to the multiple possibilities for the missing values. In this paper, we propose a novel probabilistic framework for classification with multivariate time series data with missing values. Our model consists of two parts; a deep generative model for missing value imputation and a classifier. Extending the existing deep generative models to better capture structures of time-series data, our deep generative model part is trained to impute the missing values in multiple plausible ways, effectively modeling the uncertainty of the imputation. The classifier part takes the time series data along with the imputed missing values and classifies signals, and is trained to capture the predictive uncertainty due to the multiple possibilities of imputations. Importantly, we show that na\"ively combining the generative model and the classifier could result in trivial solutions where the generative model does not produce meaningful imputations. To resolve this, we present a novel regularization technique that can promote the model to produce useful imputation values that help classification. Through extensive experiments on real-world time series data with missing values, we demonstrate the effectiveness of our method.

Rethinking Conventional Wisdom in Machine Learning: From Generalization to Scaling

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?

Global Convergence of Sub-gradient Method for Robust Matrix Recovery: Small Initialization, Noisy Measurements, and Over-parameterization

In this work, we study the performance of sub-gradient method (SubGM) on a natural nonconvex and nonsmooth formulation of low-rank matrix recovery with ell_1-loss, where the goal is to recover a low-rank matrix from a limited number of measurements, a subset of which may be grossly corrupted with noise. We study a scenario where the rank of the true solution is unknown and over-estimated instead. The over-estimation of the rank gives rise to an over-parameterized model in which there are more degrees of freedom than needed. Such over-parameterization may lead to overfitting, or adversely affect the performance of the algorithm. We prove that a simple SubGM with small initialization is agnostic to both over-parameterization and noise in the measurements. In particular, we show that small initialization nullifies the effect of over-parameterization on the performance of SubGM, leading to an exponential improvement in its convergence rate. Moreover, we provide the first unifying framework for analyzing the behavior of SubGM under both outlier and Gaussian noise models, showing that SubGM converges to the true solution, even under arbitrarily large and arbitrarily dense noise values, and--perhaps surprisingly--even if the globally optimal solutions do not correspond to the ground truth. At the core of our results is a robust variant of restricted isometry property, called Sign-RIP, which controls the deviation of the sub-differential of the ell_1-loss from that of an ideal, expected loss. As a byproduct of our results, we consider a subclass of robust low-rank matrix recovery with Gaussian measurements, and show that the number of required samples to guarantee the global convergence of SubGM is independent of the over-parameterized rank.

The Implicit Regularization of Dynamical Stability in Stochastic Gradient Descent

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.

Understanding Certified Training with Interval Bound Propagation

As robustness verification methods are becoming more precise, training certifiably robust neural networks is becoming ever more relevant. To this end, certified training methods compute and then optimize an upper bound on the worst-case loss over a robustness specification. Curiously, training methods based on the imprecise interval bound propagation (IBP) consistently outperform those leveraging more precise bounding methods. Still, we lack an understanding of the mechanisms making IBP so successful. In this work, we thoroughly investigate these mechanisms by leveraging a novel metric measuring the tightness of IBP bounds. We first show theoretically that, for deep linear models, tightness decreases with width and depth at initialization, but improves with IBP training, given sufficient network width. We, then, derive sufficient and necessary conditions on weight matrices for IBP bounds to become exact and demonstrate that these impose strong regularization, explaining the empirically observed trade-off between robustness and accuracy in certified training. Our extensive experimental evaluation validates our theoretical predictions for ReLU networks, including that wider networks improve performance, yielding state-of-the-art results. Interestingly, we observe that while all IBP-based training methods lead to high tightness, this is neither sufficient nor necessary to achieve high certifiable robustness. This hints at the existence of new training methods that do not induce the strong regularization required for tight IBP bounds, leading to improved robustness and standard accuracy.

Policy Gradient-Driven Noise Mask

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.

Accelerating Sinkhorn Algorithm with Sparse Newton Iterations

Computing the optimal transport distance between statistical distributions is a fundamental task in machine learning. One remarkable recent advancement is entropic regularization and the Sinkhorn algorithm, which utilizes only matrix scaling and guarantees an approximated solution with near-linear runtime. Despite the success of the Sinkhorn algorithm, its runtime may still be slow due to the potentially large number of iterations needed for convergence. To achieve possibly super-exponential convergence, we present Sinkhorn-Newton-Sparse (SNS), an extension to the Sinkhorn algorithm, by introducing early stopping for the matrix scaling steps and a second stage featuring a Newton-type subroutine. Adopting the variational viewpoint that the Sinkhorn algorithm maximizes a concave Lyapunov potential, we offer the insight that the Hessian matrix of the potential function is approximately sparse. Sparsification of the Hessian results in a fast O(n^2) per-iteration complexity, the same as the Sinkhorn algorithm. In terms of total iteration count, we observe that the SNS algorithm converges orders of magnitude faster across a wide range of practical cases, including optimal transportation between empirical distributions and calculating the Wasserstein W_1, W_2 distance of discretized densities. The empirical performance is corroborated by a rigorous bound on the approximate sparsity of the Hessian matrix.

Oscillation-free Quantization for Low-bit Vision Transformers

Weight oscillation is an undesirable side effect of quantization-aware training, in which quantized weights frequently jump between two quantized levels, resulting in training instability and a sub-optimal final model. We discover that the learnable scaling factor, a widely-used de facto setting in quantization aggravates weight oscillation. In this study, we investigate the connection between the learnable scaling factor and quantized weight oscillation and use ViT as a case driver to illustrate the findings and remedies. In addition, we also found that the interdependence between quantized weights in query and key of a self-attention layer makes ViT vulnerable to oscillation. We, therefore, propose three techniques accordingly: statistical weight quantization (rm StatsQ) to improve quantization robustness compared to the prevalent learnable-scale-based method; confidence-guided annealing (rm CGA) that freezes the weights with high confidence and calms the oscillating weights; and query-key reparameterization (rm QKR) to resolve the query-key intertwined oscillation and mitigate the resulting gradient misestimation. Extensive experiments demonstrate that these proposed techniques successfully abate weight oscillation and consistently achieve substantial accuracy improvement on ImageNet. Specifically, our 2-bit DeiT-T/DeiT-S algorithms outperform the previous state-of-the-art by 9.8% and 7.7%, respectively. Code and models are available at: https://github.com/nbasyl/OFQ.

From Logistic Regression to the Perceptron Algorithm: Exploring Gradient Descent with Large Step Sizes

We focus on the classification problem with a separable dataset, one of the most important and classical problems from machine learning. The standard approach to this task is logistic regression with gradient descent (LR+GD). Recent studies have observed that LR+GD can find a solution with arbitrarily large step sizes, defying conventional optimization theory. Our work investigates this phenomenon and makes three interconnected key observations about LR+GD with large step sizes. First, we find a remarkably simple explanation of why LR+GD with large step sizes solves the classification problem: LR+GD reduces to a batch version of the celebrated perceptron algorithm when the step size gamma to infty. Second, we observe that larger step sizes lead LR+GD to higher logistic losses when it tends to the perceptron algorithm, but larger step sizes also lead to faster convergence to a solution for the classification problem, meaning that logistic loss is an unreliable metric of the proximity to a solution. Surprisingly, high loss values can actually indicate faster convergence. Third, since the convergence rate in terms of loss function values of LR+GD is unreliable, we examine the iteration complexity required by LR+GD with large step sizes to solve the classification problem and prove that this complexity is suboptimal. To address this, we propose a new method, Normalized LR+GD - based on the connection between LR+GD and the perceptron algorithm - with much better theoretical guarantees.

Towards Exact Computation of Inductive Bias

Much research in machine learning involves finding appropriate inductive biases (e.g. convolutional neural networks, momentum-based optimizers, transformers) to promote generalization on tasks. However, quantification of the amount of inductive bias associated with these architectures and hyperparameters has been limited. We propose a novel method for efficiently computing the inductive bias required for generalization on a task with a fixed training data budget; formally, this corresponds to the amount of information required to specify well-generalizing models within a specific hypothesis space of models. Our approach involves modeling the loss distribution of random hypotheses drawn from a hypothesis space to estimate the required inductive bias for a task relative to these hypotheses. Unlike prior work, our method provides a direct estimate of inductive bias without using bounds and is applicable to diverse hypothesis spaces. Moreover, we derive approximation error bounds for our estimation approach in terms of the number of sampled hypotheses. Consistent with prior results, our empirical results demonstrate that higher dimensional tasks require greater inductive bias. We show that relative to other expressive model classes, neural networks as a model class encode large amounts of inductive bias. Furthermore, our measure quantifies the relative difference in inductive bias between different neural network architectures. Our proposed inductive bias metric provides an information-theoretic interpretation of the benefits of specific model architectures for certain tasks and provides a quantitative guide to developing tasks requiring greater inductive bias, thereby encouraging the development of more powerful inductive biases.

Lottery Jackpots Exist in Pre-trained Models

Network pruning is an effective approach to reduce network complexity with acceptable performance compromise. Existing studies achieve the sparsity of neural networks via time-consuming weight training or complex searching on networks with expanded width, which greatly limits the applications of network pruning. In this paper, we show that high-performing and sparse sub-networks without the involvement of weight training, termed "lottery jackpots", exist in pre-trained models with unexpanded width. Furthermore, we improve the efficiency for searching lottery jackpots from two perspectives. Firstly, we observe that the sparse masks derived from many existing pruning criteria have a high overlap with the searched mask of our lottery jackpot, among which, the magnitude-based pruning results in the most similar mask with ours. Consequently, our searched lottery jackpot removes 90% weights in ResNet-50, while it easily obtains more than 70% top-1 accuracy using only 5 searching epochs on ImageNet. In compliance with this insight, we initialize our sparse mask using the magnitude-based pruning, resulting in at least 3x cost reduction on the lottery jackpot searching while achieving comparable or even better performance. Secondly, we conduct an in-depth analysis of the searching process for lottery jackpots. Our theoretical result suggests that the decrease in training loss during weight searching can be disturbed by the dependency between weights in modern networks. To mitigate this, we propose a novel short restriction method to restrict change of masks that may have potential negative impacts on the training loss. Our code is available at https://github.com/zyxxmu/lottery-jackpots.

Energy Confused Adversarial Metric Learning for Zero-Shot Image Retrieval and Clustering

Deep metric learning has been widely applied in many computer vision tasks, and recently, it is more attractive in zero-shot image retrieval and clustering(ZSRC) where a good embedding is requested such that the unseen classes can be distinguished well. Most existing works deem this 'good' embedding just to be the discriminative one and thus race to devise powerful metric objectives or hard-sample mining strategies for leaning discriminative embedding. However, in this paper, we first emphasize that the generalization ability is a core ingredient of this 'good' embedding as well and largely affects the metric performance in zero-shot settings as a matter of fact. Then, we propose the Energy Confused Adversarial Metric Learning(ECAML) framework to explicitly optimize a robust metric. It is mainly achieved by introducing an interesting Energy Confusion regularization term, which daringly breaks away from the traditional metric learning idea of discriminative objective devising, and seeks to 'confuse' the learned model so as to encourage its generalization ability by reducing overfitting on the seen classes. We train this confusion term together with the conventional metric objective in an adversarial manner. Although it seems weird to 'confuse' the network, we show that our ECAML indeed serves as an efficient regularization technique for metric learning and is applicable to various conventional metric methods. This paper empirically and experimentally demonstrates the importance of learning embedding with good generalization, achieving state-of-the-art performances on the popular CUB, CARS, Stanford Online Products and In-Shop datasets for ZSRC tasks. \textcolor[rgb]{1, 0, 0}{Code available at http://www.bhchen.cn/}.