Daily Papers

Despite their great success, there is still no comprehensive theoretical understanding of learning with Deep Neural Networks (DNNs) or their inner organization. Previous work proposed to analyze DNNs in the Information Plane; i.e., the plane of the Mutual Information values that each layer preserves on the input and output variables. They suggested that the goal of the network is to optimize the Information Bottleneck (IB) tradeoff between compression and prediction, successively, for each layer. In this work we follow up on this idea and demonstrate the effectiveness of the Information-Plane visualization of DNNs. Our main results are: (i) most of the training epochs in standard DL are spent on {\emph compression} of the input to efficient representation and not on fitting the training labels. (ii) The representation compression phase begins when the training errors becomes small and the Stochastic Gradient Decent (SGD) epochs change from a fast drift to smaller training error into a stochastic relaxation, or random diffusion, constrained by the training error value. (iii) The converged layers lie on or very close to the Information Bottleneck (IB) theoretical bound, and the maps from the input to any hidden layer and from this hidden layer to the output satisfy the IB self-consistent equations. This generalization through noise mechanism is unique to Deep Neural Networks and absent in one layer networks. (iv) The training time is dramatically reduced when adding more hidden layers. Thus the main advantage of the hidden layers is computational. This can be explained by the reduced relaxation time, as this it scales super-linearly (exponentially for simple diffusion) with the information compression from the previous layer.

The generalization with respect to domain shifts, as they frequently appear in applications such as autonomous driving, is one of the remaining big challenges for deep learning models. Therefore, we propose an intra-source style augmentation (ISSA) method to improve domain generalization in semantic segmentation. Our method is based on a novel masked noise encoder for StyleGAN2 inversion. The model learns to faithfully reconstruct the image preserving its semantic layout through noise prediction. Random masking of the estimated noise enables the style mixing capability of our model, i.e. it allows to alter the global appearance without affecting the semantic layout of an image. Using the proposed masked noise encoder to randomize style and content combinations in the training set, ISSA effectively increases the diversity of training data and reduces spurious correlation. As a result, we achieve up to 12.4% mIoU improvements on driving-scene semantic segmentation under different types of data shifts, i.e., changing geographic locations, adverse weather conditions, and day to night. ISSA is model-agnostic and straightforwardly applicable with CNNs and Transformers. It is also complementary to other domain generalization techniques, e.g., it improves the recent state-of-the-art solution RobustNet by 3% mIoU in Cityscapes to Dark Z\"urich.

The generalization with respect to domain shifts, as they frequently appear in applications such as autonomous driving, is one of the remaining big challenges for deep learning models. Therefore, we propose an exemplar-based style synthesis pipeline to improve domain generalization in semantic segmentation. Our method is based on a novel masked noise encoder for StyleGAN2 inversion. The model learns to faithfully reconstruct the image, preserving its semantic layout through noise prediction. Using the proposed masked noise encoder to randomize style and content combinations in the training set, i.e., intra-source style augmentation (ISSA) effectively increases the diversity of training data and reduces spurious correlation. As a result, we achieve up to 12.4% mIoU improvements on driving-scene semantic segmentation under different types of data shifts, i.e., changing geographic locations, adverse weather conditions, and day to night. ISSA is model-agnostic and straightforwardly applicable with CNNs and Transformers. It is also complementary to other domain generalization techniques, e.g., it improves the recent state-of-the-art solution RobustNet by 3% mIoU in Cityscapes to Dark Z\"urich. In addition, we demonstrate the strong plug-n-play ability of the proposed style synthesis pipeline, which is readily usable for extra-source exemplars e.g., web-crawled images, without any retraining or fine-tuning. Moreover, we study a new use case to indicate neural network's generalization capability by building a stylized proxy validation set. This application has significant practical sense for selecting models to be deployed in the open-world environment. Our code is available at https://github.com/boschresearch/ISSA.

Despite the rapid development of machine learning algorithms for domain generalization (DG), there is no clear empirical evidence that the existing DG algorithms outperform the classic empirical risk minimization (ERM) across standard benchmarks. To better understand this phenomenon, we investigate whether there are benefits of DG algorithms over ERM through the lens of label noise. Specifically, our finite-sample analysis reveals that label noise exacerbates the effect of spurious correlations for ERM, undermining generalization. Conversely, we illustrate that DG algorithms exhibit implicit label-noise robustness during finite-sample training even when spurious correlation is present. Such desirable property helps mitigate spurious correlations and improve generalization in synthetic experiments. However, additional comprehensive experiments on real-world benchmark datasets indicate that label-noise robustness does not necessarily translate to better performance compared to ERM. We conjecture that the failure mode of ERM arising from spurious correlations may be less pronounced in practice.

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

We consider the learning from noisy labels (NL) problem which emerges in many real-world applications. In addition to the widely-studied synthetic noise in the NL literature, we also consider the pseudo labels in semi-supervised learning (Semi-SL) as a special case of NL. For both types of noise, we argue that the generalization performance of existing methods is highly coupled with the quality of noisy labels. Therefore, we counter the problem from a novel and unified perspective: learning from the auxiliary clean labels. Specifically, we propose the Rotational-Decoupling Consistency Regularization (RDCR) framework that integrates the consistency-based methods with the self-supervised rotation task to learn noise-tolerant representations. The experiments show that RDCR achieves comparable or superior performance than the state-of-the-art methods under small noise, while outperforms the existing methods significantly when there is large noise.

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.

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

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

Neural networks often learn simple explanations that fit the majority of the data while memorizing exceptions that deviate from these explanations.This behavior leads to poor generalization when the learned explanations rely on spurious correlations. In this work, we formalize the interplay between memorization and generalization, showing that spurious correlations would particularly lead to poor generalization when are combined with memorization. Memorization can reduce training loss to zero, leaving no incentive to learn robust, generalizable patterns. To address this, we propose memorization-aware training (MAT), which uses held-out predictions as a signal of memorization to shift a model's logits. MAT encourages learning robust patterns invariant across distributions, improving generalization under distribution shifts.

Reliable generalization lies at the heart of safe ML and AI. However, understanding when and how neural networks generalize remains one of the most important unsolved problems in the field. In this work, we conduct an extensive empirical study (20'910 models, 15 tasks) to investigate whether insights from the theory of computation can predict the limits of neural network generalization in practice. We demonstrate that grouping tasks according to the Chomsky hierarchy allows us to forecast whether certain architectures will be able to generalize to out-of-distribution inputs. This includes negative results where even extensive amounts of data and training time never lead to any non-trivial generalization, despite models having sufficient capacity to fit the training data perfectly. Our results show that, for our subset of tasks, RNNs and Transformers fail to generalize on non-regular tasks, LSTMs can solve regular and counter-language tasks, and only networks augmented with structured memory (such as a stack or memory tape) can successfully generalize on context-free and context-sensitive tasks.

During both pretraining and fine-tuning, Large Language Models (LLMs) are trained on trillions of tokens of text of widely varying quality. Both phases of training typically involve heuristically filtering out ``low-quality'' or noisy training samples, yet little is known quantitatively about how the type or intensity of noise affects downstream performance. In this work, we study how noise in chain of thought (CoT) impacts task performance in the highly-controlled setting of algorithmically solvable tasks. First, we develop the Traced Integer (TInt) framework to generate highly customizable noised execution traces for any arithmetic function on lists of integers. We then define two types of noise: static noise, a local form of noise which is applied after the CoT trace is computed, and dynamic noise, a global form of noise which propagates errors in the trace as it is computed. We then evaluate the test performance of pretrained models both prompted and fine-tuned on noised datasets with varying levels of dataset contamination and intensity. We find fine-tuned models are extremely robust to high levels of static noise but struggle significantly more with lower levels of dynamic noise. In contrast, few-shot prompted models appear more sensitive to even static noise. We conclude with a discussion of how our findings impact noise filtering best-practices, in particular emphasizing the importance of removing samples containing destructive dynamic noise with global errors.

Current vision systems are trained on huge datasets, and these datasets come with costs: curation is expensive, they inherit human biases, and there are concerns over privacy and usage rights. To counter these costs, interest has surged in learning from cheaper data sources, such as unlabeled images. In this paper we go a step further and ask if we can do away with real image datasets entirely, instead learning from noise processes. We investigate a suite of image generation models that produce images from simple random processes. These are then used as training data for a visual representation learner with a contrastive loss. We study two types of noise processes, statistical image models and deep generative models under different random initializations. Our findings show that it is important for the noise to capture certain structural properties of real data but that good performance can be achieved even with processes that are far from realistic. We also find that diversity is a key property to learn good representations. Datasets, models, and code are available at https://mbaradad.github.io/learning_with_noise.

The ability for a machine learning model to cope with differences in training and deployment conditions--e.g. in the presence of distribution shift or the generalization to new classes altogether--is crucial for real-world use cases. However, most empirical work in this area has focused on the image domain with artificial benchmarks constructed to measure individual aspects of generalization. We present BIRB, a complex benchmark centered on the retrieval of bird vocalizations from passively-recorded datasets given focal recordings from a large citizen science corpus available for training. We propose a baseline system for this collection of tasks using representation learning and a nearest-centroid search. Our thorough empirical evaluation and analysis surfaces open research directions, suggesting that BIRB fills the need for a more realistic and complex benchmark to drive progress on robustness to distribution shifts and generalization of ML models.

This work explores whether language models encode meaningfully grounded representations of sounds of objects. We learn a linear probe that retrieves the correct text representation of an object given a snippet of audio related to that object, where the sound representation is given by a pretrained audio model. This probe is trained via a contrastive loss that pushes the language representations and sound representations of an object to be close to one another. After training, the probe is tested on its ability to generalize to objects that were not seen during training. Across different language models and audio models, we find that the probe generalization is above chance in many cases, indicating that despite being trained only on raw text, language models encode grounded knowledge of sounds for some objects.

Recent diagnostic datasets on compositional generalization, such as SCAN (Lake and Baroni, 2018) and COGS (Kim and Linzen, 2020), expose severe problems in models trained from scratch on these datasets. However, in contrast to this poor performance, state-of-the-art models trained on larger and more general datasets show better generalization ability. In this work, to reconcile this inconsistency, we conduct an empirical analysis by training Transformer models on a variety of training sets with different data factors, including dataset scale, pattern complexity, example difficulty, etc. First, we show that increased dataset complexity can lead to better generalization behavior on multiple different generalization challenges. To further understand this improvement, we show two axes of the benefit from more complex datasets: they provide more diverse examples so compositional understanding becomes more effective, and they also prevent ungeneralizable memorization of the examples due to reduced example repetition frequency. Finally, we explore how training examples of different difficulty levels influence generalization differently. On synthetic datasets, simple examples invoke stronger compositionality than hard examples do. On larger-scale real language datasets, while hard examples become more important potentially to ensure decent data coverage, a balanced mixture of simple and hard examples manages to induce the strongest generalizability. The code and data for this work are available at https://github.com/owenzx/data4comp

When capturing and storing images, devices inevitably introduce noise. Reducing this noise is a critical task called image denoising. Deep learning has become the de facto method for image denoising, especially with the emergence of Transformer-based models that have achieved notable state-of-the-art results on various image tasks. However, deep learning-based methods often suffer from a lack of generalization ability. For example, deep models trained on Gaussian noise may perform poorly when tested on other noise distributions. To address this issue, we present a novel approach to enhance the generalization performance of denoising networks, known as masked training. Our method involves masking random pixels of the input image and reconstructing the missing information during training. We also mask out the features in the self-attention layers to avoid the impact of training-testing inconsistency. Our approach exhibits better generalization ability than other deep learning models and is directly applicable to real-world scenarios. Additionally, our interpretability analysis demonstrates the superiority of our method.

Large Language Models trained on web-scale text acquire language generation abilities that can solve a wide range of tasks, particularly when task knowledge is refined into the generative prior using in-context examples. However, spurious features learned from noisy data hinder their generalizability. Supervised finetuning can introduce task specificity, but introduce data inefficiency. Prior studies indicate that (i) noisy neural circuitries coexist with generalizable ones within LLMs, and (ii) finetuning typically enhances (or suppresses) existing abilities without introducing newer ones. Building upon these, we propose TaRot, a novel method for task adaptation. TaRot intervenes in the neural circuitries using learnable rotation matrices that are optimized using Bayesian Optimization, on labelled samples in the order of standard few-shot prompting examples. Experiments on multiple classification and generation tasks using LLMs of varying sizes reveal the efficacy of TaRot, improving upon both zero- as well as few-shot performance, with average improvements (across models and tasks) of 23.81% and 11.15%, respectively. The source code is available at https://github.com/joykirat18/TaRot

Pre-training on large-scale datasets and then fine-tuning on downstream tasks have become a standard practice in deep learning. However, pre-training data often contain label noise that may adversely affect the generalization of the model. This paper aims to understand the nature of noise in pre-training datasets and to mitigate its impact on downstream tasks. More specifically, through extensive experiments of supervised pre-training models on synthetic noisy ImageNet-1K and YFCC15M datasets, we demonstrate that while slight noise in pre-training can benefit in-domain (ID) transfer performance, where the training and testing data share the same distribution, it always deteriorates out-of-domain (OOD) performance, where training and testing data distribution are different. We empirically verify that the reason behind is noise in pre-training shapes the feature space differently. We then propose a light-weight black-box tuning method (NMTune) to affine the feature space to mitigate the malignant effect of noise and improve generalization on both ID and OOD tasks, considering one may not be able to fully fine-tune or even access the pre-trained models. We conduct practical experiments on popular vision and language models that are pre-trained on noisy data for evaluation of our approach. Our analysis and results show the importance of this interesting and novel research direction, which we term Noisy Model Learning.

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

In this work, we build upon our previous publication and use diffusion-based generative models for speech enhancement. We present a detailed overview of the diffusion process that is based on a stochastic differential equation and delve into an extensive theoretical examination of its implications. Opposed to usual conditional generation tasks, we do not start the reverse process from pure Gaussian noise but from a mixture of noisy speech and Gaussian noise. This matches our forward process which moves from clean speech to noisy speech by including a drift term. We show that this procedure enables using only 30 diffusion steps to generate high-quality clean speech estimates. By adapting the network architecture, we are able to significantly improve the speech enhancement performance, indicating that the network, rather than the formalism, was the main limitation of our original approach. In an extensive cross-dataset evaluation, we show that the improved method can compete with recent discriminative models and achieves better generalization when evaluating on a different corpus than used for training. We complement the results with an instrumental evaluation using real-world noisy recordings and a listening experiment, in which our proposed method is rated best. Examining different sampler configurations for solving the reverse process allows us to balance the performance and computational speed of the proposed method. Moreover, we show that the proposed method is also suitable for dereverberation and thus not limited to additive background noise removal. Code and audio examples are available online, see https://github.com/sp-uhh/sgmse

Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the denoising diffusion model in the function space which also allows us to naturally handle irregularly-sampled observations. The forward process gradually adds noise to functions, preserving their continuity, while the learned reverse process removes the noise and returns functions as new samples. To this end, we define suitable noise sources and introduce novel denoising and score-matching models. We show how our method can be used for multivariate probabilistic forecasting and imputation, and how our model can be interpreted as a neural process.

Despite extensive studies, the underlying reason as to why overparameterized neural networks can generalize remains elusive. Existing theory shows that common stochastic optimizers prefer flatter minimizers of the training loss, and thus a natural potential explanation is that flatness implies generalization. This work critically examines this explanation. Through theoretical and empirical investigation, we identify the following three scenarios for two-layer ReLU networks: (1) flatness provably implies generalization; (2) there exist non-generalizing flattest models and sharpness minimization algorithms fail to generalize, and (3) perhaps most surprisingly, there exist non-generalizing flattest models, but sharpness minimization algorithms still generalize. Our results suggest that the relationship between sharpness and generalization subtly depends on the data distributions and the model architectures and sharpness minimization algorithms do not only minimize sharpness to achieve better generalization. This calls for the search for other explanations for the generalization of over-parameterized neural networks.

Learning representations that generalize under distribution shifts is critical for building robust machine learning models. However, despite significant efforts in recent years, algorithmic advances in this direction have been limited. In this work, we seek to understand the fundamental difficulty of out-of-distribution generalization with deep neural networks. We first empirically show that perhaps surprisingly, even allowing a neural network to explicitly fit the representations obtained from a teacher network that can generalize out-of-distribution is insufficient for the generalization of the student network. Then, by a theoretical study of two-layer ReLU networks optimized by stochastic gradient descent (SGD) under a structured feature model, we identify a fundamental yet unexplored feature learning proclivity of neural networks, feature contamination: neural networks can learn uncorrelated features together with predictive features, resulting in generalization failure under distribution shifts. Notably, this mechanism essentially differs from the prevailing narrative in the literature that attributes the generalization failure to spurious correlations. Overall, our results offer new insights into the non-linear feature learning dynamics of neural networks and highlight the necessity of considering inductive biases in out-of-distribution generalization.

Distant and weak supervision allow to obtain large amounts of labeled training data quickly and cheaply, but these automatic annotations tend to contain a high amount of errors. A popular technique to overcome the negative effects of these noisy labels is noise modelling where the underlying noise process is modelled. In this work, we study the quality of these estimated noise models from the theoretical side by deriving the expected error of the noise model. Apart from evaluating the theoretical results on commonly used synthetic noise, we also publish NoisyNER, a new noisy label dataset from the NLP domain that was obtained through a realistic distant supervision technique. It provides seven sets of labels with differing noise patterns to evaluate different noise levels on the same instances. Parallel, clean labels are available making it possible to study scenarios where a small amount of gold-standard data can be leveraged. Our theoretical results and the corresponding experiments give insights into the factors that influence the noise model estimation like the noise distribution and the sampling technique.

The generalization mystery in deep learning is the following: Why do over-parameterized neural networks trained with gradient descent (GD) generalize well on real datasets even though they are capable of fitting random datasets of comparable size? Furthermore, from among all solutions that fit the training data, how does GD find one that generalizes well (when such a well-generalizing solution exists)? We argue that the answer to both questions lies in the interaction of the gradients of different examples during training. Intuitively, if the per-example gradients are well-aligned, that is, if they are coherent, then one may expect GD to be (algorithmically) stable, and hence generalize well. We formalize this argument with an easy to compute and interpretable metric for coherence, and show that the metric takes on very different values on real and random datasets for several common vision networks. The theory also explains a number of other phenomena in deep learning, such as why some examples are reliably learned earlier than others, why early stopping works, and why it is possible to learn from noisy labels. Moreover, since the theory provides a causal explanation of how GD finds a well-generalizing solution when one exists, it motivates a class of simple modifications to GD that attenuate memorization and improve generalization. Generalization in deep learning is an extremely broad phenomenon, and therefore, it requires an equally general explanation. We conclude with a survey of alternative lines of attack on this problem, and argue that the proposed approach is the most viable one on this basis.

Text-to-image synthesis (T2I) has advanced remarkably with the emergence of large-scale diffusion models. In the conventional setup, the text prompt provides explicit, user-defined guidance, directing the generation process by denoising a randomly sampled Gaussian noise. In this work, we reveal that the often-overlooked noise itself encodes inherent generative tendencies, acting as a "silent prompt" that implicitly guides the output. This implicit guidance, embedded in the noise scheduler design of diffusion model formulations and their training stages, generalizes across a wide range of T2I models and backbones. Building on this insight, we introduce NoiseQuery, a novel strategy that selects optimal initial noise from a pre-built noise library to meet diverse user needs. Our approach not only enhances high-level semantic alignment with text prompts, but also allows for nuanced adjustments of low-level visual attributes, such as texture, sharpness, shape, and color, which are typically challenging to control through text alone. Extensive experiments across various models and target attributes demonstrate the strong performance and zero-shot transferability of our approach, requiring no additional optimization.

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

The proliferation of pretrained models, as a result of advancements in pretraining techniques, has led to the emergence of a vast zoo of publicly available models. Effectively utilizing these resources to obtain models with robust out-of-distribution generalization capabilities for downstream tasks has become a crucial area of research. Previous research has primarily focused on identifying the most powerful models within the model zoo, neglecting to fully leverage the diverse inductive biases contained within. This paper argues that the knowledge contained in weaker models is valuable and presents a method for leveraging the diversity within the model zoo to improve out-of-distribution generalization capabilities. Specifically, we investigate the behaviors of various pretrained models across different domains of downstream tasks by characterizing the variations in their encoded representations in terms of two dimensions: diversity shift and correlation shift. This characterization enables us to propose a new algorithm for integrating diverse pretrained models, not limited to the strongest models, in order to achieve enhanced out-of-distribution generalization performance. Our proposed method demonstrates state-of-the-art empirical results on a variety of datasets, thus validating the benefits of utilizing diverse knowledge.

We study the class of location-scale or heteroscedastic noise models (LSNMs), in which the effect Y can be written as a function of the cause X and a noise source N independent of X, which may be scaled by a positive function g over the cause, i.e., Y = f(X) + g(X)N. Despite the generality of the model class, we show the causal direction is identifiable up to some pathological cases. To empirically validate these theoretical findings, we propose two estimators for LSNMs: an estimator based on (non-linear) feature maps, and one based on neural networks. Both model the conditional distribution of Y given X as a Gaussian parameterized by its natural parameters. When the feature maps are correctly specified, we prove that our estimator is jointly concave, and a consistent estimator for the cause-effect identification task. Although the the neural network does not inherit those guarantees, it can fit functions of arbitrary complexity, and reaches state-of-the-art performance across benchmarks.

Instruction tuning -- fine-tuning a large language model (LLM) on pairs of instructions and desired outcomes -- is an approach that enables pre-trained language models to perform real-world tasks and follow human instructions. Its practical success depends on the model learning a broader set of instructions than those it was trained on. Yet the factors that determine model generalization to such unseen tasks are not well understood. %To understand the driving factors of generalization, In this paper, we experiment with string rewrites, a symbolic task that serves as a building block for Turing complete Markov algorithms while allowing experimental control of "inputs" and "instructions". We investigate the trade-off between the number of instructions the model is trained on and the number of training samples provided for each instruction and observe that the diversity of the instruction set determines generalization. Generalization emerges once a diverse enough set of tasks is provided, even though very few examples are provided for each task. Instruction diversity also ensures robustness with respect to non-uniform distributions of instructions in the training set.

The continued release of new and better image generation models increases the demand for synthetic image detectors. In such a dynamic field, detectors need to be able to generalize widely and be robust to uncontrolled alterations. The present work is motivated by this setting, when looking at the role of time, image transformations and data sources, for detector generalization. In these experiments, none of the evaluated detectors is found universal, but results indicate an ensemble could be. Experiments on data collected in the wild show this task to be more challenging than the one defined by large-scale datasets, pointing to a gap between experimentation and actual practice. Finally, we observe a race equilibrium effect, where better generators lead to better detectors, and vice versa. We hypothesize this pushes the field towards a perpetually close race between generators and detectors.

We expect the generalization error to improve with more samples from a similar task, and to deteriorate with more samples from an out-of-distribution (OOD) task. In this work, we show a counter-intuitive phenomenon: the generalization error of a task can be a non-monotonic function of the number of OOD samples. As the number of OOD samples increases, the generalization error on the target task improves before deteriorating beyond a threshold. In other words, there is value in training on small amounts of OOD data. We use Fisher's Linear Discriminant on synthetic datasets and deep networks on computer vision benchmarks such as MNIST, CIFAR-10, CINIC-10, PACS and DomainNet to demonstrate and analyze this phenomenon. In the idealistic setting where we know which samples are OOD, we show that these non-monotonic trends can be exploited using an appropriately weighted objective of the target and OOD empirical risk. While its practical utility is limited, this does suggest that if we can detect OOD samples, then there may be ways to benefit from them. When we do not know which samples are OOD, we show how a number of go-to strategies such as data-augmentation, hyper-parameter optimization, and pre-training are not enough to ensure that the target generalization error does not deteriorate with the number of OOD samples in the dataset.

The measure of a machine learning algorithm is the difficulty of the tasks it can perform, and sufficiently difficult tasks are critical drivers of strong machine learning models. However, quantifying the generalization difficulty of machine learning benchmarks has remained challenging. We propose what is to our knowledge the first model-agnostic measure of the inherent generalization difficulty of tasks. Our inductive bias complexity measure quantifies the total information required to generalize well on a task minus the information provided by the data. It does so by measuring the fractional volume occupied by hypotheses that generalize on a task given that they fit the training data. It scales exponentially with the intrinsic dimensionality of the space over which the model must generalize but only polynomially in resolution per dimension, showing that tasks which require generalizing over many dimensions are drastically more difficult than tasks involving more detail in fewer dimensions. Our measure can be applied to compute and compare supervised learning, reinforcement learning and meta-learning generalization difficulties against each other. We show that applied empirically, it formally quantifies intuitively expected trends, e.g. that in terms of required inductive bias, MNIST < CIFAR10 < Imagenet and fully observable Markov decision processes (MDPs) < partially observable MDPs. Further, we show that classification of complex images < few-shot meta-learning with simple images. Our measure provides a quantitative metric to guide the construction of more complex tasks requiring greater inductive bias, and thereby encourages the development of more sophisticated architectures and learning algorithms with more powerful generalization capabilities.

Diffusion models are a class of generative models that learn to synthesize samples by inverting a diffusion process that gradually maps data into noise. While these models have enjoyed great success recently, a full theoretical understanding of their observed properties is still lacking, in particular, their weak sensitivity to the choice of noise family and the role of adequate scheduling of noise levels for good synthesis. By identifying a correspondence between diffusion models and a well-known paradigm in cognitive science known as serial reproduction, whereby human agents iteratively observe and reproduce stimuli from memory, we show how the aforementioned properties of diffusion models can be explained as a natural consequence of this correspondence. We then complement our theoretical analysis with simulations that exhibit these key features. Our work highlights how classic paradigms in cognitive science can shed light on state-of-the-art machine learning problems.

In crowded settings, the human brain can focus on speech from a target speaker, given prior knowledge of how they sound. We introduce a novel intelligent hearable system that achieves this capability, enabling target speech hearing to ignore all interfering speech and noise, but the target speaker. A naive approach is to require a clean speech example to enroll the target speaker. This is however not well aligned with the hearable application domain since obtaining a clean example is challenging in real world scenarios, creating a unique user interface problem. We present the first enrollment interface where the wearer looks at the target speaker for a few seconds to capture a single, short, highly noisy, binaural example of the target speaker. This noisy example is used for enrollment and subsequent speech extraction in the presence of interfering speakers and noise. Our system achieves a signal quality improvement of 7.01 dB using less than 5 seconds of noisy enrollment audio and can process 8 ms of audio chunks in 6.24 ms on an embedded CPU. Our user studies demonstrate generalization to real-world static and mobile speakers in previously unseen indoor and outdoor multipath environments. Finally, our enrollment interface for noisy examples does not cause performance degradation compared to clean examples, while being convenient and user-friendly. Taking a step back, this paper takes an important step towards enhancing the human auditory perception with artificial intelligence. We provide code and data at: https://github.com/vb000/LookOnceToHear.

Several works have proposed Simplicity Bias (SB)---the tendency of standard training procedures such as Stochastic Gradient Descent (SGD) to find simple models---to justify why neural networks generalize well [Arpit et al. 2017, Nakkiran et al. 2019, Soudry et al. 2018]. However, the precise notion of simplicity remains vague. Furthermore, previous settings that use SB to theoretically justify why neural networks generalize well do not simultaneously capture the non-robustness of neural networks---a widely observed phenomenon in practice [Goodfellow et al. 2014, Jo and Bengio 2017]. We attempt to reconcile SB and the superior standard generalization of neural networks with the non-robustness observed in practice by designing datasets that (a) incorporate a precise notion of simplicity, (b) comprise multiple predictive features with varying levels of simplicity, and (c) capture the non-robustness of neural networks trained on real data. Through theory and empirics on these datasets, we make four observations: (i) SB of SGD and variants can be extreme: neural networks can exclusively rely on the simplest feature and remain invariant to all predictive complex features. (ii) The extreme aspect of SB could explain why seemingly benign distribution shifts and small adversarial perturbations significantly degrade model performance. (iii) Contrary to conventional wisdom, SB can also hurt generalization on the same data distribution, as SB persists even when the simplest feature has less predictive power than the more complex features. (iv) Common approaches to improve generalization and robustness---ensembles and adversarial training---can fail in mitigating SB and its pitfalls. Given the role of SB in training neural networks, we hope that the proposed datasets and methods serve as an effective testbed to evaluate novel algorithmic approaches aimed at avoiding the pitfalls of SB.

We prove a new upper bound on the generalization gap of classifiers that are obtained by first using self-supervision to learn a representation r of the training data, and then fitting a simple (e.g., linear) classifier g to the labels. Specifically, we show that (under the assumptions described below) the generalization gap of such classifiers tends to zero if C(g) ll n, where C(g) is an appropriately-defined measure of the simple classifier g's complexity, and n is the number of training samples. We stress that our bound is independent of the complexity of the representation r. We do not make any structural or conditional-independence assumptions on the representation-learning task, which can use the same training dataset that is later used for classification. Rather, we assume that the training procedure satisfies certain natural noise-robustness (adding small amount of label noise causes small degradation in performance) and rationality (getting the wrong label is not better than getting no label at all) conditions that widely hold across many standard architectures. We show that our bound is non-vacuous for many popular representation-learning based classifiers on CIFAR-10 and ImageNet, including SimCLR, AMDIM and MoCo.

The ability of deep neural networks to generalise well even when they interpolate their training data has been explained using various "simplicity biases". These theories postulate that neural networks avoid overfitting by first learning simple functions, say a linear classifier, before learning more complex, non-linear functions. Meanwhile, data structure is also recognised as a key ingredient for good generalisation, yet its role in simplicity biases is not yet understood. Here, we show that neural networks trained using stochastic gradient descent initially classify their inputs using lower-order input statistics, like mean and covariance, and exploit higher-order statistics only later during training. We first demonstrate this distributional simplicity bias (DSB) in a solvable model of a neural network trained on synthetic data. We empirically demonstrate DSB in a range of deep convolutional networks and visual transformers trained on CIFAR10, and show that it even holds in networks pre-trained on ImageNet. We discuss the relation of DSB to other simplicity biases and consider its implications for the principle of Gaussian universality in learning.

We establish a new theoretical framework for learning under multi-class, instance-dependent label noise. This framework casts learning with label noise as a form of domain adaptation, in particular, domain adaptation under posterior drift. We introduce the concept of relative signal strength (RSS), a pointwise measure that quantifies the transferability from noisy to clean posterior. Using RSS, we establish nearly matching upper and lower bounds on the excess risk. Our theoretical findings support the simple Noise Ignorant Empirical Risk Minimization (NI-ERM) principle, which minimizes empirical risk while ignoring label noise. Finally, we translate this theoretical insight into practice: by using NI-ERM to fit a linear classifier on top of a self-supervised feature extractor, we achieve state-of-the-art performance on the CIFAR-N data challenge.

It is not fully understood why adversarial examples can deceive neural networks and transfer between different networks. To elucidate this, several studies have hypothesized that adversarial perturbations, while appearing as noises, contain class features. This is supported by empirical evidence showing that networks trained on mislabeled adversarial examples can still generalize well to correctly labeled test samples. However, a theoretical understanding of how perturbations include class features and contribute to generalization is limited. In this study, we provide a theoretical framework for understanding learning from perturbations using a one-hidden-layer network trained on mutually orthogonal samples. Our results highlight that various adversarial perturbations, even perturbations of a few pixels, contain sufficient class features for generalization. Moreover, we reveal that the decision boundary when learning from perturbations matches that from standard samples except for specific regions under mild conditions. The code is available at https://github.com/s-kumano/learning-from-adversarial-perturbations.

Standard training datasets for deep learning often contain objects in common settings (e.g., "a horse on grass" or "a ship in water") since they are usually collected by randomly scraping the web. Uncommon and rare settings (e.g., "a plane on water", "a car in snowy weather") are thus severely under-represented in the training data. This can lead to an undesirable bias in model predictions towards common settings and create a false sense of accuracy. In this paper, we introduce FOCUS (Familiar Objects in Common and Uncommon Settings), a dataset for stress-testing the generalization power of deep image classifiers. By leveraging the power of modern search engines, we deliberately gather data containing objects in common and uncommon settings in a wide range of locations, weather conditions, and time of day. We present a detailed analysis of the performance of various popular image classifiers on our dataset and demonstrate a clear drop in performance when classifying images in uncommon settings. By analyzing deep features of these models, we show that such errors can be due to the use of spurious features in model predictions. We believe that our dataset will aid researchers in understanding the inability of deep models to generalize well to uncommon settings and drive future work on improving their distributional robustness.

A major goal of unsupervised learning is to discover data representations that are useful for subsequent tasks, without access to supervised labels during training. Typically, this involves minimizing a surrogate objective, such as the negative log likelihood of a generative model, with the hope that representations useful for subsequent tasks will arise as a side effect. In this work, we propose instead to directly target later desired tasks by meta-learning an unsupervised learning rule which leads to representations useful for those tasks. Specifically, we target semi-supervised classification performance, and we meta-learn an algorithm -- an unsupervised weight update rule -- that produces representations useful for this task. Additionally, we constrain our unsupervised update rule to a be a biologically-motivated, neuron-local function, which enables it to generalize to different neural network architectures, datasets, and data modalities. We show that the meta-learned update rule produces useful features and sometimes outperforms existing unsupervised learning techniques. We further show that the meta-learned unsupervised update rule generalizes to train networks with different widths, depths, and nonlinearities. It also generalizes to train on data with randomly permuted input dimensions and even generalizes from image datasets to a text task.

Unsupervised pretraining, which learns a useful representation using a large amount of unlabeled data to facilitate the learning of downstream tasks, is a critical component of modern large-scale machine learning systems. Despite its tremendous empirical success, the rigorous theoretical understanding of why unsupervised pretraining generally helps remains rather limited -- most existing results are restricted to particular methods or approaches for unsupervised pretraining with specialized structural assumptions. This paper studies a generic framework, where the unsupervised representation learning task is specified by an abstract class of latent variable models Phi and the downstream task is specified by a class of prediction functions Psi. We consider a natural approach of using Maximum Likelihood Estimation (MLE) for unsupervised pretraining and Empirical Risk Minimization (ERM) for learning downstream tasks. We prove that, under a mild ''informative'' condition, our algorithm achieves an excess risk of mathcal{O}(mathcal{C_Phi/m} + mathcal{C_Psi/n}) for downstream tasks, where C_Phi, C_Psi are complexity measures of function classes Phi, Psi, and m, n are the number of unlabeled and labeled data respectively. Comparing to the baseline of mathcal{O}(mathcal{C_{Phi circ Psi}/n}) achieved by performing supervised learning using only the labeled data, our result rigorously shows the benefit of unsupervised pretraining when m gg n and C_{Phicirc Psi} > C_Psi. This paper further shows that our generic framework covers a wide range of approaches for unsupervised pretraining, including factor models, Gaussian mixture models, and contrastive learning.

We present Noisy Student Training, a semi-supervised learning approach that works well even when labeled data is abundant. Noisy Student Training achieves 88.4% top-1 accuracy on ImageNet, which is 2.0% better than the state-of-the-art model that requires 3.5B weakly labeled Instagram images. On robustness test sets, it improves ImageNet-A top-1 accuracy from 61.0% to 83.7%, reduces ImageNet-C mean corruption error from 45.7 to 28.3, and reduces ImageNet-P mean flip rate from 27.8 to 12.2. Noisy Student Training extends the idea of self-training and distillation with the use of equal-or-larger student models and noise added to the student during learning. On ImageNet, we first train an EfficientNet model on labeled images and use it as a teacher to generate pseudo labels for 300M unlabeled images. We then train a larger EfficientNet as a student model on the combination of labeled and pseudo labeled images. We iterate this process by putting back the student as the teacher. During the learning of the student, we inject noise such as dropout, stochastic depth, and data augmentation via RandAugment to the student so that the student generalizes better than the teacher. Models are available at https://github.com/tensorflow/tpu/tree/master/models/official/efficientnet. Code is available at https://github.com/google-research/noisystudent.

Language models (LMs), like other neural networks, often favor shortcut heuristics based on surface-level patterns. Although LMs behave like n-gram models early in training, they must eventually learn hierarchical syntactic representations to correctly apply grammatical rules out-of-distribution (OOD). In this work, we use case studies of English grammar to explore how complex, diverse training data drives models to generalize OOD. We construct a framework that unifies our understanding of random variation with training dynamics, rule selection with memorization, and data diversity with complexity. We show that these factors are nuanced, and that intermediate levels of diversity and complexity lead to inconsistent behavior across random seeds and to unstable training dynamics. Our findings emphasize the critical role of training data in shaping generalization patterns and illuminate how competing model strategies lead to inconsistent generalization outcomes across random seeds. Code is available at https://github.com/sunnytqin/concept_comp.git.

Retrieval-Augmented Generation (RAG) has emerged as a crucial method for addressing hallucinations in large language models (LLMs). While recent research has extended RAG models to complex noisy scenarios, these explorations often confine themselves to limited noise types and presuppose that noise is inherently detrimental to LLMs, potentially deviating from real-world retrieval environments and restricting practical applicability. In this paper, we define seven distinct noise types from a linguistic perspective and establish a Noise RAG Benchmark (NoiserBench), a comprehensive evaluation framework encompassing multiple datasets and reasoning tasks. Through empirical evaluation of eight representative LLMs with diverse architectures and scales, we reveal that these noises can be further categorized into two practical groups: noise that is beneficial to LLMs (aka beneficial noise) and noise that is harmful to LLMs (aka harmful noise). While harmful noise generally impairs performance, beneficial noise may enhance several aspects of model capabilities and overall performance. Our analysis offers insights for developing more robust, adaptable RAG solutions and mitigating hallucinations across diverse retrieval scenarios.

Our understanding of the generalization capabilities of neural networks (NNs) is still incomplete. Prevailing explanations are based on implicit biases of gradient descent (GD) but they cannot account for the capabilities of models from gradient-free methods nor the simplicity bias recently observed in untrained networks. This paper seeks other sources of generalization in NNs. Findings. To understand the inductive biases provided by architectures independently from GD, we examine untrained, random-weight networks. Even simple MLPs show strong inductive biases: uniform sampling in weight space yields a very biased distribution of functions in terms of complexity. But unlike common wisdom, NNs do not have an inherent "simplicity bias". This property depends on components such as ReLUs, residual connections, and layer normalizations. Alternative architectures can be built with a bias for any level of complexity. Transformers also inherit all these properties from their building blocks. Implications. We provide a fresh explanation for the success of deep learning independent from gradient-based training. It points at promising avenues for controlling the solutions implemented by trained models.

While recent work has convincingly showed that sequence-to-sequence models struggle to generalize to new compositions (termed compositional generalization), little is known on what makes compositional generalization hard on a particular test instance. In this work, we investigate what are the factors that make generalization to certain test instances challenging. We first substantiate that indeed some examples are more difficult than others by showing that different models consistently fail or succeed on the same test instances. Then, we propose a criterion for the difficulty of an example: a test instance is hard if it contains a local structure that was not observed at training time. We formulate a simple decision rule based on this criterion and empirically show it predicts instance-level generalization well across 5 different semantic parsing datasets, substantially better than alternative decision rules. Last, we show local structures can be leveraged for creating difficult adversarial compositional splits and also to improve compositional generalization under limited training budgets by strategically selecting examples for the training set.

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.

One of the most surprising puzzles in neural network generalisation is grokking: a network with perfect training accuracy but poor generalisation will, upon further training, transition to perfect generalisation. We propose that grokking occurs when the task admits a generalising solution and a memorising solution, where the generalising solution is slower to learn but more efficient, producing larger logits with the same parameter norm. We hypothesise that memorising circuits become more inefficient with larger training datasets while generalising circuits do not, suggesting there is a critical dataset size at which memorisation and generalisation are equally efficient. We make and confirm four novel predictions about grokking, providing significant evidence in favour of our explanation. Most strikingly, we demonstrate two novel and surprising behaviours: ungrokking, in which a network regresses from perfect to low test accuracy, and semi-grokking, in which a network shows delayed generalisation to partial rather than perfect test accuracy.

Recent empirical works have successfully used unlabeled data to learn feature representations that are broadly useful in downstream classification tasks. Several of these methods are reminiscent of the well-known word2vec embedding algorithm: leveraging availability of pairs of semantically "similar" data points and "negative samples," the learner forces the inner product of representations of similar pairs with each other to be higher on average than with negative samples. The current paper uses the term contrastive learning for such algorithms and presents a theoretical framework for analyzing them by introducing latent classes and hypothesizing that semantically similar points are sampled from the same latent class. This framework allows us to show provable guarantees on the performance of the learned representations on the average classification task that is comprised of a subset of the same set of latent classes. Our generalization bound also shows that learned representations can reduce (labeled) sample complexity on downstream tasks. We conduct controlled experiments in both the text and image domains to support the theory.

Neural networks trained by gradient descent (GD) have exhibited a number of surprising generalization behaviors. First, they can achieve a perfect fit to noisy training data and still generalize near-optimally, showing that overfitting can sometimes be benign. Second, they can undergo a period of classical, harmful overfitting -- achieving a perfect fit to training data with near-random performance on test data -- before transitioning ("grokking") to near-optimal generalization later in training. In this work, we show that both of these phenomena provably occur in two-layer ReLU networks trained by GD on XOR cluster data where a constant fraction of the training labels are flipped. In this setting, we show that after the first step of GD, the network achieves 100% training accuracy, perfectly fitting the noisy labels in the training data, but achieves near-random test accuracy. At a later training step, the network achieves near-optimal test accuracy while still fitting the random labels in the training data, exhibiting a "grokking" phenomenon. This provides the first theoretical result of benign overfitting in neural network classification when the data distribution is not linearly separable. Our proofs rely on analyzing the feature learning process under GD, which reveals that the network implements a non-generalizable linear classifier after one step and gradually learns generalizable features in later steps.

Foundational image-language models have generated considerable interest due to their efficient adaptation to downstream tasks by prompt learning. Prompt learning treats part of the language model input as trainable while freezing the rest, and optimizes an Empirical Risk Minimization objective. However, Empirical Risk Minimization is known to suffer from distributional shifts which hurt generalizability to prompts unseen during training. By leveraging the regularization ability of Bayesian methods, we frame prompt learning from the Bayesian perspective and formulate it as a variational inference problem. Our approach regularizes the prompt space, reduces overfitting to the seen prompts and improves the prompt generalization on unseen prompts. Our framework is implemented by modeling the input prompt space in a probabilistic manner, as an a priori distribution which makes our proposal compatible with prompt learning approaches that are unconditional or conditional on the image. We demonstrate empirically on 15 benchmarks that Bayesian prompt learning provides an appropriate coverage of the prompt space, prevents learning spurious features, and exploits transferable invariant features. This results in better generalization of unseen prompts, even across different datasets and domains. Code available at: https://github.com/saic-fi/Bayesian-Prompt-Learning

We introduce Noise2Music, where a series of diffusion models is trained to generate high-quality 30-second music clips from text prompts. Two types of diffusion models, a generator model, which generates an intermediate representation conditioned on text, and a cascader model, which generates high-fidelity audio conditioned on the intermediate representation and possibly the text, are trained and utilized in succession to generate high-fidelity music. We explore two options for the intermediate representation, one using a spectrogram and the other using audio with lower fidelity. We find that the generated audio is not only able to faithfully reflect key elements of the text prompt such as genre, tempo, instruments, mood, and era, but goes beyond to ground fine-grained semantics of the prompt. Pretrained large language models play a key role in this story -- they are used to generate paired text for the audio of the training set and to extract embeddings of the text prompts ingested by the diffusion models. Generated examples: https://google-research.github.io/noise2music

Text-to-image diffusion model is a popular paradigm that synthesizes personalized images by providing a text prompt and a random Gaussian noise. While people observe that some noises are ``golden noises'' that can achieve better text-image alignment and higher human preference than others, we still lack a machine learning framework to obtain those golden noises. To learn golden noises for diffusion sampling, we mainly make three contributions in this paper. First, we identify a new concept termed the noise prompt, which aims at turning a random Gaussian noise into a golden noise by adding a small desirable perturbation derived from the text prompt. Following the concept, we first formulate the noise prompt learning framework that systematically learns ``prompted'' golden noise associated with a text prompt for diffusion models. Second, we design a noise prompt data collection pipeline and collect a large-scale noise prompt dataset~(NPD) that contains 100k pairs of random noises and golden noises with the associated text prompts. With the prepared NPD as the training dataset, we trained a small noise prompt network~(NPNet) that can directly learn to transform a random noise into a golden noise. The learned golden noise perturbation can be considered as a kind of prompt for noise, as it is rich in semantic information and tailored to the given text prompt. Third, our extensive experiments demonstrate the impressive effectiveness and generalization of NPNet on improving the quality of synthesized images across various diffusion models, including SDXL, DreamShaper-xl-v2-turbo, and Hunyuan-DiT. Moreover, NPNet is a small and efficient controller that acts as a plug-and-play module with very limited additional inference and computational costs, as it just provides a golden noise instead of a random noise without accessing the original pipeline.

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.

The quality of generative models depends on the quality of the data they are trained on. Creating large-scale, high-quality datasets is often expensive and sometimes impossible, e.g. in certain scientific applications where there is no access to clean data due to physical or instrumentation constraints. Ambient Diffusion and related frameworks train diffusion models with solely corrupted data (which are usually cheaper to acquire) but ambient models significantly underperform models trained on clean data. We study this phenomenon at scale by training more than 80 models on data with different corruption levels across three datasets ranging from 30,000 to approx 1.3M samples. We show that it is impossible, at these sample sizes, to match the performance of models trained on clean data when only training on noisy data. Yet, a combination of a small set of clean data (e.g.~10% of the total dataset) and a large set of highly noisy data suffices to reach the performance of models trained solely on similar-size datasets of clean data, and in particular to achieve near state-of-the-art performance. We provide theoretical evidence for our findings by developing novel sample complexity bounds for learning from Gaussian Mixtures with heterogeneous variances. Our theoretical model suggests that, for large enough datasets, the effective marginal utility of a noisy sample is exponentially worse than that of a clean sample. Providing a small set of clean samples can significantly reduce the sample size requirements for noisy data, as we also observe in our experiments.

Available training data for named entity recognition (NER) often contains a significant percentage of incorrect labels for entity types and entity boundaries. Such label noise poses challenges for supervised learning and may significantly deteriorate model quality. To address this, prior work proposed various noise-robust learning approaches capable of learning from data with partially incorrect labels. These approaches are typically evaluated using simulated noise where the labels in a clean dataset are automatically corrupted. However, as we show in this paper, this leads to unrealistic noise that is far easier to handle than real noise caused by human error or semi-automatic annotation. To enable the study of the impact of various types of real noise, we introduce NoiseBench, an NER benchmark consisting of clean training data corrupted with 6 types of real noise, including expert errors, crowdsourcing errors, automatic annotation errors and LLM errors. We present an analysis that shows that real noise is significantly more challenging than simulated noise, and show that current state-of-the-art models for noise-robust learning fall far short of their theoretically achievable upper bound. We release NoiseBench to the research community.

One puzzling artifact in machine learning dubbed grokking is where delayed generalization is achieved tenfolds of iterations after near perfect overfitting to the training data. Focusing on the long delay itself on behalf of machine learning practitioners, our goal is to accelerate generalization of a model under grokking phenomenon. By regarding a series of gradients of a parameter over training iterations as a random signal over time, we can spectrally decompose the parameter trajectories under gradient descent into two components: the fast-varying, overfitting-yielding component and the slow-varying, generalization-inducing component. This analysis allows us to accelerate the grokking phenomenon more than times 50 with only a few lines of code that amplifies the slow-varying components of gradients. The experiments show that our algorithm applies to diverse tasks involving images, languages, and graphs, enabling practical availability of this peculiar artifact of sudden generalization. Our code is available at https://github.com/ironjr/grokfast.

Neural fields, which represent signals as a function parameterized by a neural network, are a promising alternative to traditional discrete vector or grid-based representations. Compared to discrete representations, neural representations both scale well with increasing resolution, are continuous, and can be many-times differentiable. However, given a dataset of signals that we would like to represent, having to optimize a separate neural field for each signal is inefficient, and cannot capitalize on shared information or structures among signals. Existing generalization methods view this as a meta-learning problem and employ gradient-based meta-learning to learn an initialization which is then fine-tuned with test-time optimization, or learn hypernetworks to produce the weights of a neural field. We instead propose a new paradigm that views the large-scale training of neural representations as a part of a partially-observed neural process framework, and leverage neural process algorithms to solve this task. We demonstrate that this approach outperforms both state-of-the-art gradient-based meta-learning approaches and hypernetwork approaches.

The robust generalization of models to rare, in-distribution (ID) samples drawn from the long tail of the training distribution and to out-of-training-distribution (OOD) samples is one of the major challenges of current deep learning methods. For image classification, this manifests in the existence of adversarial attacks, the performance drops on distorted images, and a lack of generalization to concepts such as sketches. The current understanding of generalization in neural networks is very limited, but some biases that differentiate models from human vision have been identified and might be causing these limitations. Consequently, several attempts with varying success have been made to reduce these biases during training to improve generalization. We take a step back and sanity-check these attempts. Fixing the architecture to the well-established ResNet-50, we perform a large-scale study on 48 ImageNet models obtained via different training methods to understand how and if these biases - including shape bias, spectral biases, and critical bands - interact with generalization. Our extensive study results reveal that contrary to previous findings, these biases are insufficient to accurately predict the generalization of a model holistically. We provide access to all checkpoints and evaluation code at https://github.com/paulgavrikov/biases_vs_generalization

While score-based generative models (SGMs) have achieved remarkable success in enormous image generation tasks, their mathematical foundations are still limited. In this paper, we analyze the approximation and generalization of SGMs in learning a family of sub-Gaussian probability distributions. We introduce a notion of complexity for probability distributions in terms of their relative density with respect to the standard Gaussian measure. We prove that if the log-relative density can be locally approximated by a neural network whose parameters can be suitably bounded, then the distribution generated by empirical score matching approximates the target distribution in total variation with a dimension-independent rate. We illustrate our theory through examples, which include certain mixtures of Gaussians. An essential ingredient of our proof is to derive a dimension-free deep neural network approximation rate for the true score function associated with the forward process, which is interesting in its own right.

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

State-of-the-art machine learning methods exhibit limited compositional generalization. At the same time, there is a lack of realistic benchmarks that comprehensively measure this ability, which makes it challenging to find and evaluate improvements. We introduce a novel method to systematically construct such benchmarks by maximizing compound divergence while guaranteeing a small atom divergence between train and test sets, and we quantitatively compare this method to other approaches for creating compositional generalization benchmarks. We present a large and realistic natural language question answering dataset that is constructed according to this method, and we use it to analyze the compositional generalization ability of three machine learning architectures. We find that they fail to generalize compositionally and that there is a surprisingly strong negative correlation between compound divergence and accuracy. We also demonstrate how our method can be used to create new compositionality benchmarks on top of the existing SCAN dataset, which confirms these findings.

The noise transition matrix plays a central role in the problem of learning with noisy labels. Among many other reasons, a large number of existing solutions rely on access to it. Identifying and estimating the transition matrix without ground truth labels is a critical and challenging task. When label noise transition depends on each instance, the problem of identifying the instance-dependent noise transition matrix becomes substantially more challenging. Despite recent works proposing solutions for learning from instance-dependent noisy labels, the field lacks a unified understanding of when such a problem remains identifiable. The goal of this paper is to characterize the identifiability of the label noise transition matrix. Building on Kruskal's identifiability results, we are able to show the necessity of multiple noisy labels in identifying the noise transition matrix for the generic case at the instance level. We further instantiate the results to explain the successes of the state-of-the-art solutions and how additional assumptions alleviated the requirement of multiple noisy labels. Our result also reveals that disentangled features are helpful in the above identification task and we provide empirical evidence.

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.

Generative models have made significant impacts across various domains, largely due to their ability to scale during training by increasing data, computational resources, and model size, a phenomenon characterized by the scaling laws. Recent research has begun to explore inference-time scaling behavior in Large Language Models (LLMs), revealing how performance can further improve with additional computation during inference. Unlike LLMs, diffusion models inherently possess the flexibility to adjust inference-time computation via the number of denoising steps, although the performance gains typically flatten after a few dozen. In this work, we explore the inference-time scaling behavior of diffusion models beyond increasing denoising steps and investigate how the generation performance can further improve with increased computation. Specifically, we consider a search problem aimed at identifying better noises for the diffusion sampling process. We structure the design space along two axes: the verifiers used to provide feedback, and the algorithms used to find better noise candidates. Through extensive experiments on class-conditioned and text-conditioned image generation benchmarks, our findings reveal that increasing inference-time compute leads to substantial improvements in the quality of samples generated by diffusion models, and with the complicated nature of images, combinations of the components in the framework can be specifically chosen to conform with different application scenario.

Machine learning methods can be a valuable aid in the scientific process, but they need to face challenging settings where data come from inhomogeneous experimental conditions. Recent meta-learning methods have made significant progress in multi-task learning, but they rely on black-box neural networks, resulting in high computational costs and limited interpretability. Leveraging the structure of the learning problem, we argue that multi-environment generalization can be achieved using a simpler learning model, with an affine structure with respect to the learning task. Crucially, we prove that this architecture can identify the physical parameters of the system, enabling interpreable learning. We demonstrate the competitive generalization performance and the low computational cost of our method by comparing it to state-of-the-art algorithms on physical systems, ranging from toy models to complex, non-analytical systems. The interpretability of our method is illustrated with original applications to physical-parameter-induced adaptation and to adaptive control.

We introduce Domain-specific Masks for Generalization, a model for improving both in-domain and out-of-domain generalization performance. For domain generalization, the goal is to learn from a set of source domains to produce a single model that will best generalize to an unseen target domain. As such, many prior approaches focus on learning representations which persist across all source domains with the assumption that these domain agnostic representations will generalize well. However, often individual domains contain characteristics which are unique and when leveraged can significantly aid in-domain recognition performance. To produce a model which best generalizes to both seen and unseen domains, we propose learning domain specific masks. The masks are encouraged to learn a balance of domain-invariant and domain-specific features, thus enabling a model which can benefit from the predictive power of specialized features while retaining the universal applicability of domain-invariant features. We demonstrate competitive performance compared to naive baselines and state-of-the-art methods on both PACS and DomainNet.

In this work, we theoretically investigate the generalization properties of neural networks (NN) trained by stochastic gradient descent (SGD) algorithm with large learning rates. Under such a training regime, our finding is that, the oscillation of the NN weights caused by the large learning rate SGD training turns out to be beneficial to the generalization of the NN, which potentially improves over the same NN trained by SGD with small learning rates that converges more smoothly. In view of this finding, we call such a phenomenon "benign oscillation". Our theory towards demystifying such a phenomenon builds upon the feature learning perspective of deep learning. Specifically, we consider a feature-noise data generation model that consists of (i) weak features which have a small ell_2-norm and appear in each data point; (ii) strong features which have a larger ell_2-norm but only appear in a certain fraction of all data points; and (iii) noise. We prove that NNs trained by oscillating SGD with a large learning rate can effectively learn the weak features in the presence of those strong features. In contrast, NNs trained by SGD with a small learning rate can only learn the strong features but makes little progress in learning the weak features. Consequently, when it comes to the new testing data which consist of only weak features, the NN trained by oscillating SGD with a large learning rate could still make correct predictions consistently, while the NN trained by small learning rate SGD fails. Our theory sheds light on how large learning rate training benefits the generalization of NNs. Experimental results demonstrate our finding on "benign oscillation".

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)%.

While many unsupervised learning models focus on one family of tasks, either generative or discriminative, we explore the possibility of a unified representation learner: a model which uses a single pre-training stage to address both families of tasks simultaneously. We identify diffusion models as a prime candidate. Diffusion models have risen to prominence as a state-of-the-art method for image generation, denoising, inpainting, super-resolution, manipulation, etc. Such models involve training a U-Net to iteratively predict and remove noise, and the resulting model can synthesize high fidelity, diverse, novel images. The U-Net architecture, as a convolution-based architecture, generates a diverse set of feature representations in the form of intermediate feature maps. We present our findings that these embeddings are useful beyond the noise prediction task, as they contain discriminative information and can also be leveraged for classification. We explore optimal methods for extracting and using these embeddings for classification tasks, demonstrating promising results on the ImageNet classification task. We find that with careful feature selection and pooling, diffusion models outperform comparable generative-discriminative methods such as BigBiGAN for classification tasks. We investigate diffusion models in the transfer learning regime, examining their performance on several fine-grained visual classification datasets. We compare these embeddings to those generated by competing architectures and pre-trainings for classification tasks.

Attention layers -- which map a sequence of inputs to a sequence of outputs -- are core building blocks of the Transformer architecture which has achieved significant breakthroughs in modern artificial intelligence. This paper presents a rigorous theoretical study on the learning and generalization of a single multi-head attention layer, with a sequence of key vectors and a separate query vector as input. We consider the random feature setting where the attention layer has a large number of heads, with randomly sampled frozen query and key matrices, and trainable value matrices. We show that such a random-feature attention layer can express a broad class of target functions that are permutation invariant to the key vectors. We further provide quantitative excess risk bounds for learning these target functions from finite samples, using random feature attention with finitely many heads. Our results feature several implications unique to the attention structure compared with existing random features theory for neural networks, such as (1) Advantages in the sample complexity over standard two-layer random-feature networks; (2) Concrete and natural classes of functions that can be learned efficiently by a random-feature attention layer; and (3) The effect of the sampling distribution of the query-key weight matrix (the product of the query and key matrix), where Gaussian random weights with a non-zero mean result in better sample complexities over the zero-mean counterpart for learning certain natural target functions. Experiments on simulated data corroborate our theoretical findings and further illustrate the interplay between the sample size and the complexity of the target function.

Whether neural networks can learn abstract reasoning or whether they merely rely on superficial statistics is a topic of recent debate. Here, we propose a dataset and challenge designed to probe abstract reasoning, inspired by a well-known human IQ test. To succeed at this challenge, models must cope with various generalisation `regimes' in which the training and test data differ in clearly-defined ways. We show that popular models such as ResNets perform poorly, even when the training and test sets differ only minimally, and we present a novel architecture, with a structure designed to encourage reasoning, that does significantly better. When we vary the way in which the test questions and training data differ, we find that our model is notably proficient at certain forms of generalisation, but notably weak at others. We further show that the model's ability to generalise improves markedly if it is trained to predict symbolic explanations for its answers. Altogether, we introduce and explore ways to both measure and induce stronger abstract reasoning in neural networks. Our freely-available dataset should motivate further progress in this direction.

Generative models have reached an advanced stage where they can produce remarkably realistic images. However, this remarkable generative capability also introduces the risk of disseminating false or misleading information. Notably, existing image detectors for generated images encounter challenges such as low accuracy and limited generalization. This paper seeks to address this issue by seeking a representation with strong generalization capabilities to enhance the detection of generated images. Our investigation has revealed that real and generated images display distinct latent Gaussian representations when subjected to an inverse diffusion process within a pre-trained diffusion model. Exploiting this disparity, we can amplify subtle artifacts in generated images. Building upon this insight, we introduce a novel image representation known as Diffusion Noise Feature (DNF). DNF is extracted from the estimated noise generated during the inverse diffusion process. A simple classifier, e.g., ResNet50, trained on DNF achieves high accuracy, robustness, and generalization capabilities for detecting generated images (even the corresponding generator is built with datasets/structures that are not seen during the classifier's training). We conducted experiments using four training datasets and five testsets, achieving state-of-the-art detection performance.

Diffusion models have achieved state-of-the-art synthesis quality on both visual and audio tasks, and recent works further adapt them to textual data by diffusing on the embedding space. In this paper, we conduct systematic studies and analyze the challenges between the continuous data space and the embedding space which have not been carefully explored. Firstly, the data distribution is learnable for embeddings, which may lead to the collapse of the loss function. Secondly, as the norm of embeddings varies between popular and rare words, adding the same noise scale will lead to sub-optimal results. In addition, we find the normal level of noise causes insufficient training of the model. To address the above challenges, we propose Difformer, an embedding diffusion model based on Transformer, which consists of three essential modules including an additional anchor loss function, a layer normalization module for embeddings, and a noise factor to the Gaussian noise. Experiments on two seminal text generation tasks including machine translation and text summarization show the superiority of Difformer over compared embedding diffusion baselines.

Modern machine learning requires system designers to specify aspects of the learning pipeline, such as losses, architectures, and optimizers. Meta-learning, or learning-to-learn, instead aims to learn those aspects, and promises to unlock greater capabilities with less manual effort. One particularly ambitious goal of meta-learning is to train general-purpose in-context learning algorithms from scratch, using only black-box models with minimal inductive bias. Such a model takes in training data, and produces test-set predictions across a wide range of problems, without any explicit definition of an inference model, training loss, or optimization algorithm. In this paper we show that Transformers and other black-box models can be meta-trained to act as general-purpose in-context learners. We characterize transitions between algorithms that generalize, algorithms that memorize, and algorithms that fail to meta-train at all, induced by changes in model size, number of tasks, and meta-optimization. We further show that the capabilities of meta-trained algorithms are bottlenecked by the accessible state size (memory) determining the next prediction, unlike standard models which are thought to be bottlenecked by parameter count. Finally, we propose practical interventions such as biasing the training distribution that improve the meta-training and meta-generalization of general-purpose in-context learning algorithms.

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

One of the key challenges of detecting AI-generated images is spotting images that have been created by previously unseen generative models. We argue that the limited diversity of the training data is a major obstacle to addressing this problem, and we propose a new dataset that is significantly larger and more diverse than prior work. As part of creating this dataset, we systematically download thousands of text-to-image latent diffusion models and sample images from them. We also collect images from dozens of popular open source and commercial models. The resulting dataset contains 2.7M images that have been sampled from 4803 different models. These images collectively capture a wide range of scene content, generator architectures, and image processing settings. Using this dataset, we study the generalization abilities of fake image detectors. Our experiments suggest that detection performance improves as the number of models in the training set increases, even when these models have similar architectures. We also find that detection performance improves as the diversity of the models increases, and that our trained detectors generalize better than those trained on other datasets.

Label noise is one of the key factors that lead to the poor generalization of deep learning models. Existing label-noise learning methods usually assume that the ground-truth classes of the training data are balanced. However, the real-world data is often imbalanced, leading to the inconsistency between observed and intrinsic class distribution with label noises. In this case, it is hard to distinguish clean samples from noisy samples on the intrinsic tail classes with the unknown intrinsic class distribution. In this paper, we propose a learning framework for label-noise learning with intrinsically long-tailed data. Specifically, we propose two-stage bi-dimensional sample selection (TABASCO) to better separate clean samples from noisy samples, especially for the tail classes. TABASCO consists of two new separation metrics that complement each other to compensate for the limitation of using a single metric in sample separation. Extensive experiments on benchmarks demonstrate the effectiveness of our method. Our code is available at https://github.com/Wakings/TABASCO.

Generalization is arguably the most important goal of statistical language modeling research. Publicly available benchmarks and papers published with an open-source code have been critical to advancing the field. However, it is often very difficult, and sometimes even impossible, to reproduce the results fully as reported in publications. In this paper, we propose a simple framework that should help advance the state of the art in language modeling in terms of generalization. We propose to publish not just the code, but also probabilities on dev and test sets with future publications so that one can easily add the new model into an ensemble. This has crucial advantages: it is much easier to determine whether a newly proposed model is actually complementary to the current baseline. Therefore, instead of inventing new names for the old tricks, the scientific community can advance faster. Finally, this approach promotes diversity of ideas: one does not need to create an individual model that is the new state of the art to attract attention; it will be sufficient to develop a new model that learns patterns which other models do not. Thus, even a suboptimal model can be found to have value. Remarkably, our approach has yielded new state-of-the-art results across various language modeling benchmarks up to 10%.

Optimization and generalization are two essential aspects of statistical machine learning. In this paper, we propose a framework to connect optimization with generalization by analyzing the generalization error based on the optimization trajectory under the gradient flow algorithm. The key ingredient of this framework is the Uniform-LGI, a property that is generally satisfied when training machine learning models. Leveraging the Uniform-LGI, we first derive convergence rates for gradient flow algorithm, then we give generalization bounds for a large class of machine learning models. We further apply our framework to three distinct machine learning models: linear regression, kernel regression, and two-layer neural networks. Through our approach, we obtain generalization estimates that match or extend previous results.

To build an artificial neural network like the biological intelligence system, recent works have unified numerous tasks into a generalist model, which can process various tasks with shared parameters and do not have any task-specific modules. While generalist models achieve promising results on various benchmarks, they have performance degradation on some tasks compared with task-specialized models. In this work, we find that interference among different tasks and modalities is the main factor to this phenomenon. To mitigate such interference, we introduce the Conditional Mixture-of-Experts (Conditional MoEs) to generalist models. Routing strategies under different levels of conditions are proposed to take both the training/inference cost and generalization ability into account. By incorporating the proposed Conditional MoEs, the recently proposed generalist model Uni-Perceiver can effectively mitigate the interference across tasks and modalities, and achieves state-of-the-art results on a series of downstream tasks via prompt tuning on 1% of downstream data. Moreover, the introduction of Conditional MoEs still holds the generalization ability of generalist models to conduct zero-shot inference on new tasks, e.g., video-text retrieval and video caption. Code and pre-trained generalist models shall be released.

State-of-the-art results on image recognition tasks are achieved using over-parameterized learning algorithms that (nearly) perfectly fit the training set and are known to fit well even random labels. This tendency to memorize the labels of the training data is not explained by existing theoretical analyses. Memorization of the training data also presents significant privacy risks when the training data contains sensitive personal information and thus it is important to understand whether such memorization is necessary for accurate learning. We provide the first conceptual explanation and a theoretical model for this phenomenon. Specifically, we demonstrate that for natural data distributions memorization of labels is necessary for achieving close-to-optimal generalization error. Crucially, even labels of outliers and noisy labels need to be memorized. The model is motivated and supported by the results of several recent empirical works. In our model, data is sampled from a mixture of subpopulations and our results show that memorization is necessary whenever the distribution of subpopulation frequencies is long-tailed. Image and text data is known to be long-tailed and therefore our results establish a formal link between these empirical phenomena. Our results allow to quantify the cost of limiting memorization in learning and explain the disparate effects that privacy and model compression have on different subgroups.

This paper considers the learning of logical (Boolean) functions with focus on the generalization on the unseen (GOTU) setting, a strong case of out-of-distribution generalization. This is motivated by the fact that the rich combinatorial nature of data in certain reasoning tasks (e.g., arithmetic/logic) makes representative data sampling challenging, and learning successfully under GOTU gives a first vignette of an 'extrapolating' or 'reasoning' learner. We then study how different network architectures trained by (S)GD perform under GOTU and provide both theoretical and experimental evidence that for a class of network models including instances of Transformers, random features models, and diagonal linear networks, a min-degree-interpolator (MDI) is learned on the unseen. We also provide evidence that other instances with larger learning rates or mean-field networks reach leaky MDIs. These findings lead to two implications: (1) we provide an explanation to the length generalization problem (e.g., Anil et al. 2022); (2) we introduce a curriculum learning algorithm called Degree-Curriculum that learns monomials more efficiently by incrementing supports.

Inspired by the phenomenon of catastrophic forgetting, we investigate the learning dynamics of neural networks as they train on single classification tasks. Our goal is to understand whether a related phenomenon occurs when data does not undergo a clear distributional shift. We define a `forgetting event' to have occurred when an individual training example transitions from being classified correctly to incorrectly over the course of learning. Across several benchmark data sets, we find that: (i) certain examples are forgotten with high frequency, and some not at all; (ii) a data set's (un)forgettable examples generalize across neural architectures; and (iii) based on forgetting dynamics, a significant fraction of examples can be omitted from the training data set while still maintaining state-of-the-art generalization performance.

It is widely believed that noise conditioning is indispensable for denoising diffusion models to work successfully. This work challenges this belief. Motivated by research on blind image denoising, we investigate a variety of denoising-based generative models in the absence of noise conditioning. To our surprise, most models exhibit graceful degradation, and in some cases, they even perform better without noise conditioning. We provide a theoretical analysis of the error caused by removing noise conditioning and demonstrate that our analysis aligns with empirical observations. We further introduce a noise-unconditional model that achieves a competitive FID of 2.23 on CIFAR-10, significantly narrowing the gap to leading noise-conditional models. We hope our findings will inspire the community to revisit the foundations and formulations of denoising generative models.

Diffusion-based generative models have achieved remarkable success in image generation. Their guidance formulation allows an external model to plug-and-play control the generation process for various tasks without finetuning the diffusion model. However, the direct use of publicly available off-the-shelf models for guidance fails due to their poor performance on noisy inputs. For that, the existing practice is to fine-tune the guidance models with labeled data corrupted with noises. In this paper, we argue that this practice has limitations in two aspects: (1) performing on inputs with extremely various noises is too hard for a single guidance model; (2) collecting labeled datasets hinders scaling up for various tasks. To tackle the limitations, we propose a novel strategy that leverages multiple experts where each expert is specialized in a particular noise range and guides the reverse process of the diffusion at its corresponding timesteps. However, as it is infeasible to manage multiple networks and utilize labeled data, we present a practical guidance framework termed Practical Plug-And-Play (PPAP), which leverages parameter-efficient fine-tuning and data-free knowledge transfer. We exhaustively conduct ImageNet class conditional generation experiments to show that our method can successfully guide diffusion with small trainable parameters and no labeled data. Finally, we show that image classifiers, depth estimators, and semantic segmentation models can guide publicly available GLIDE through our framework in a plug-and-play manner. Our code is available at https://github.com/riiid/PPAP.

Humans can understand and produce new utterances effortlessly, thanks to their compositional skills. Once a person learns the meaning of a new verb "dax," he or she can immediately understand the meaning of "dax twice" or "sing and dax." In this paper, we introduce the SCAN domain, consisting of a set of simple compositional navigation commands paired with the corresponding action sequences. We then test the zero-shot generalization capabilities of a variety of recurrent neural networks (RNNs) trained on SCAN with sequence-to-sequence methods. We find that RNNs can make successful zero-shot generalizations when the differences between training and test commands are small, so that they can apply "mix-and-match" strategies to solve the task. However, when generalization requires systematic compositional skills (as in the "dax" example above), RNNs fail spectacularly. We conclude with a proof-of-concept experiment in neural machine translation, suggesting that lack of systematicity might be partially responsible for neural networks' notorious training data thirst.

Recently, deep neural networks such as RNN, CNN and Transformer have been applied in the task of sequential recommendation, which aims to capture the dynamic preference characteristics from logged user behavior data for accurate recommendation. However, in online platforms, logged user behavior data is inevitable to contain noise, and deep recommendation models are easy to overfit on these logged data. To tackle this problem, we borrow the idea of filtering algorithms from signal processing that attenuates the noise in the frequency domain. In our empirical experiments, we find that filtering algorithms can substantially improve representative sequential recommendation models, and integrating simple filtering algorithms (eg Band-Stop Filter) with an all-MLP architecture can even outperform competitive Transformer-based models. Motivated by it, we propose FMLP-Rec, an all-MLP model with learnable filters for sequential recommendation task. The all-MLP architecture endows our model with lower time complexity, and the learnable filters can adaptively attenuate the noise information in the frequency domain. Extensive experiments conducted on eight real-world datasets demonstrate the superiority of our proposed method over competitive RNN, CNN, GNN and Transformer-based methods. Our code and data are publicly available at the link: blue{https://github.com/RUCAIBox/FMLP-Rec}.

Diffusion models learn to restore noisy data, which is corrupted with different levels of noise, by optimizing the weighted sum of the corresponding loss terms, i.e., denoising score matching loss. In this paper, we show that restoring data corrupted with certain noise levels offers a proper pretext task for the model to learn rich visual concepts. We propose to prioritize such noise levels over other levels during training, by redesigning the weighting scheme of the objective function. We show that our simple redesign of the weighting scheme significantly improves the performance of diffusion models regardless of the datasets, architectures, and sampling strategies.

Diffusion models have emerged as the de facto choice for generating visual signals. However, training a single model to predict noise across various levels poses significant challenges, necessitating numerous iterations and incurring significant computational costs. Various approaches, such as loss weighting strategy design and architectural refinements, have been introduced to expedite convergence. In this study, we propose a novel approach to design the noise schedule for enhancing the training of diffusion models. Our key insight is that the importance sampling of the logarithm of the Signal-to-Noise ratio (logSNR), theoretically equivalent to a modified noise schedule, is particularly beneficial for training efficiency when increasing the sample frequency around log SNR=0. We empirically demonstrate the superiority of our noise schedule over the standard cosine schedule. Furthermore, we highlight the advantages of our noise schedule design on the ImageNet benchmark, showing that the designed schedule consistently benefits different prediction targets.

We build new test sets for the CIFAR-10 and ImageNet datasets. Both benchmarks have been the focus of intense research for almost a decade, raising the danger of overfitting to excessively re-used test sets. By closely following the original dataset creation processes, we test to what extent current classification models generalize to new data. We evaluate a broad range of models and find accuracy drops of 3% - 15% on CIFAR-10 and 11% - 14% on ImageNet. However, accuracy gains on the original test sets translate to larger gains on the new test sets. Our results suggest that the accuracy drops are not caused by adaptivity, but by the models' inability to generalize to slightly "harder" images than those found in the original test sets.

We explore the critical data size in language models, a threshold that marks a fundamental shift from quick memorization to slow generalization. We formalize the phase transition under the grokking configuration into the Data Efficiency Hypothesis and identify data insufficiency, sufficiency, and surplus regimes in language models training dynamics. We develop a grokking configuration to reproduce grokking on simplistic language models stably by rescaling initialization and weight decay. We show that generalization occurs only when language models reach a critical size. We analyze grokking across sample-wise and model-wise, verifying the proposed data efficiency hypothesis. Our experiments reveal smoother phase transitions occurring at the critical dataset size for language datasets. As the model size increases, this critical point also becomes larger, indicating that larger models require more data. Our results deepen the understanding of language model training, offering a novel perspective on the role of data in the learning mechanism of language models.

Effective implementations of sampling-based probabilistic inference often require manually constructed, model-specific proposals. Inspired by recent progresses in meta-learning for training learning agents that can generalize to unseen environments, we propose a meta-learning approach to building effective and generalizable MCMC proposals. We parametrize the proposal as a neural network to provide fast approximations to block Gibbs conditionals. The learned neural proposals generalize to occurrences of common structural motifs across different models, allowing for the construction of a library of learned inference primitives that can accelerate inference on unseen models with no model-specific training required. We explore several applications including open-universe Gaussian mixture models, in which our learned proposals outperform a hand-tuned sampler, and a real-world named entity recognition task, in which our sampler yields higher final F1 scores than classical single-site Gibbs sampling.

Overparametrization often helps improve the generalization performance. This paper proposes a dual view of overparametrization suggesting that downsampling may also help generalize. Motivated by this dual view, we characterize two out-of-sample prediction risks of the sketched ridgeless least square estimator in the proportional regime masymp n asymp p, where m is the sketching size, n the sample size, and p the feature dimensionality. Our results reveal the statistical role of downsampling. Specifically, downsampling does not always hurt the generalization performance, and may actually help improve it in some cases. We identify the optimal sketching sizes that minimize the out-of-sample prediction risks, and find that the optimally sketched estimator has stabler risk curves that eliminates the peaks of those for the full-sample estimator. We then propose a practical procedure to empirically identify the optimal sketching size. Finally, we extend our results to cover central limit theorems and misspecified models. Numerical studies strongly support our theory.

Transformer models can use two fundamentally different kinds of information: information stored in weights during training, and information provided ``in-context'' at inference time. In this work, we show that transformers exhibit different inductive biases in how they represent and generalize from the information in these two sources. In particular, we characterize whether they generalize via parsimonious rules (rule-based generalization) or via direct comparison with observed examples (exemplar-based generalization). This is of important practical consequence, as it informs whether to encode information in weights or in context, depending on how we want models to use that information. In transformers trained on controlled stimuli, we find that generalization from weights is more rule-based whereas generalization from context is largely exemplar-based. In contrast, we find that in transformers pre-trained on natural language, in-context learning is significantly rule-based, with larger models showing more rule-basedness. We hypothesise that rule-based generalization from in-context information might be an emergent consequence of large-scale training on language, which has sparse rule-like structure. Using controlled stimuli, we verify that transformers pretrained on data containing sparse rule-like structure exhibit more rule-based generalization.

Neuroimage processing tasks like segmentation, reconstruction, and registration are central to the study of neuroscience. Robust deep learning strategies and architectures used to solve these tasks are often similar. Yet, when presented with a new task or a dataset with different visual characteristics, practitioners most often need to train a new model, or fine-tune an existing one. This is a time-consuming process that poses a substantial barrier for the thousands of neuroscientists and clinical researchers who often lack the resources or machine-learning expertise to train deep learning models. In practice, this leads to a lack of adoption of deep learning, and neuroscience tools being dominated by classical frameworks. We introduce Neuralizer, a single model that generalizes to previously unseen neuroimaging tasks and modalities without the need for re-training or fine-tuning. Tasks do not have to be known a priori, and generalization happens in a single forward pass during inference. The model can solve processing tasks across multiple image modalities, acquisition methods, and datasets, and generalize to tasks and modalities it has not been trained on. Our experiments on coronal slices show that when few annotated subjects are available, our multi-task network outperforms task-specific baselines without training on the task.

Deep neural networks (DNNs) trained for image denoising are able to generate high-quality samples with score-based reverse diffusion algorithms. These impressive capabilities seem to imply an escape from the curse of dimensionality, but recent reports of memorization of the training set raise the question of whether these networks are learning the "true" continuous density of the data. Here, we show that two DNNs trained on non-overlapping subsets of a dataset learn nearly the same score function, and thus the same density, when the number of training images is large enough. In this regime of strong generalization, diffusion-generated images are distinct from the training set, and are of high visual quality, suggesting that the inductive biases of the DNNs are well-aligned with the data density. We analyze the learned denoising functions and show that the inductive biases give rise to a shrinkage operation in a basis adapted to the underlying image. Examination of these bases reveals oscillating harmonic structures along contours and in homogeneous regions. We demonstrate that trained denoisers are inductively biased towards these geometry-adaptive harmonic bases since they arise not only when the network is trained on photographic images, but also when it is trained on image classes supported on low-dimensional manifolds for which the harmonic basis is suboptimal. Finally, we show that when trained on regular image classes for which the optimal basis is known to be geometry-adaptive and harmonic, the denoising performance of the networks is near-optimal.

Domain Generalization aims to develop models that can generalize to novel and unseen data distributions. In this work, we study how model architectures and pre-training objectives impact feature richness and propose a method to effectively leverage them for domain generalization. Specifically, given a pre-trained feature space, we first discover latent domain structures, referred to as pseudo-domains, that capture domain-specific variations in an unsupervised manner. Next, we augment existing classifiers with these complementary pseudo-domain representations making them more amenable to diverse unseen test domains. We analyze how different pre-training feature spaces differ in the domain-specific variances they capture. Our empirical studies reveal that features from diffusion models excel at separating domains in the absence of explicit domain labels and capture nuanced domain-specific information. On 5 datasets, we show that our very simple framework improves generalization to unseen domains by a maximum test accuracy improvement of over 4% compared to the standard baseline Empirical Risk Minimization (ERM). Crucially, our method outperforms most algorithms that access domain labels during training.

The generalization of language models (LMs) is undergoing active debates, contrasting their potential for general intelligence with their struggles with basic knowledge composition (e.g., reverse/transition curse). This paper uncovers the phenomenon of linear correlations in LMs during knowledge composition. For explanation, there exists a linear transformation between certain related knowledge that maps the next token prediction logits from one prompt to another, e.g., "X lives in the city of" rightarrow "X lives in the country of" for every given X. This mirrors the linearity in human knowledge composition, such as Paris rightarrow France. Our findings indicate that the linear transformation is resilient to large-scale fine-tuning, generalizing updated knowledge when aligned with real-world relationships, but causing hallucinations when it deviates. Empirical results suggest that linear correlation can serve as a potential identifier of LM's generalization. Finally, we show such linear correlations can be learned with a single feedforward network and pre-trained vocabulary representations, indicating LM generalization heavily relies on the latter.

In this work, we provide a characterization of the feature-learning process in two-layer ReLU networks trained by gradient descent on the logistic loss following random initialization. We consider data with binary labels that are generated by an XOR-like function of the input features. We permit a constant fraction of the training labels to be corrupted by an adversary. We show that, although linear classifiers are no better than random guessing for the distribution we consider, two-layer ReLU networks trained by gradient descent achieve generalization error close to the label noise rate. We develop a novel proof technique that shows that at initialization, the vast majority of neurons function as random features that are only weakly correlated with useful features, and the gradient descent dynamics 'amplify' these weak, random features to strong, useful features.

We discover that common diffusion noise schedules do not enforce the last timestep to have zero signal-to-noise ratio (SNR), and some implementations of diffusion samplers do not start from the last timestep. Such designs are flawed and do not reflect the fact that the model is given pure Gaussian noise at inference, creating a discrepancy between training and inference. We show that the flawed design causes real problems in existing implementations. In Stable Diffusion, it severely limits the model to only generate images with medium brightness and prevents it from generating very bright and dark samples. We propose a few simple fixes: (1) rescale the noise schedule to enforce zero terminal SNR; (2) train the model with v prediction; (3) change the sampler to always start from the last timestep; (4) rescale classifier-free guidance to prevent over-exposure. These simple changes ensure the diffusion process is congruent between training and inference and allow the model to generate samples more faithful to the original data distribution.

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

Graph neural networks (GNNs) are the most widely adopted model in graph-structured data oriented learning and representation. Despite their extraordinary success in real-world applications, understanding their working mechanism by theory is still on primary stage. In this paper, we move towards this goal from the perspective of generalization. To be specific, we first establish high probability bounds of generalization gap and gradients in transductive learning with consideration of stochastic optimization. After that, we provide high probability bounds of generalization gap for popular GNNs. The theoretical results reveal the architecture specific factors affecting the generalization gap. Experimental results on benchmark datasets show the consistency between theoretical results and empirical evidence. Our results provide new insights in understanding the generalization of GNNs.

While efficient architectures and a plethora of augmentations for end-to-end image classification tasks have been suggested and heavily investigated, state-of-the-art techniques for audio classifications still rely on numerous representations of the audio signal together with large architectures, fine-tuned from large datasets. By utilizing the inherited lightweight nature of audio and novel audio augmentations, we were able to present an efficient end-to-end network with strong generalization ability. Experiments on a variety of sound classification sets demonstrate the effectiveness and robustness of our approach, by achieving state-of-the-art results in various settings. Public code is available at: https://github.com/Alibaba-MIIL/AudioClassfication{this http url}

While instruction-tuned language models have demonstrated impressive zero-shot generalization, these models often struggle to generate accurate responses when faced with instructions that fall outside their training set. This paper presents Instructive Decoding (ID), a simple yet effective approach that augments the efficacy of instruction-tuned models. Specifically, ID adjusts the logits for next-token prediction in a contrastive manner, utilizing predictions generated from a manipulated version of the original instruction, referred to as a noisy instruction. This noisy instruction aims to elicit responses that could diverge from the intended instruction yet remain plausible. We conduct experiments across a spectrum of such noisy instructions, ranging from those that insert semantic noise via random words to others like 'opposite' that elicit the deviated responses. Our approach achieves considerable performance gains across various instruction-tuned models and tasks without necessitating any additional parameter updates. Notably, utilizing 'opposite' as the noisy instruction in ID, which exhibits the maximum divergence from the original instruction, consistently produces the most significant performance gains across multiple models and tasks.

The advent of the Transformer has led to the development of large language models (LLM), which appear to demonstrate human-like capabilities. To assess the generality of this class of models and a variety of other base neural network architectures to multimodal domains, we evaluated and compared their capacity for multimodal generalization. We introduce a multimodal question-answer benchmark to evaluate three specific types of out-of-distribution (OOD) generalization performance: distractor generalization (generalization in the presence of distractors), systematic compositional generalization (generalization to new task permutations), and productive compositional generalization (generalization to more complex tasks structures). We found that across model architectures (e.g., RNNs, Transformers, Perceivers, etc.), models with multiple attention layers, or models that leveraged cross-attention mechanisms between input domains, fared better. Our positive results demonstrate that for multimodal distractor and systematic generalization, either cross-modal attention or models with deeper attention layers are key architectural features required to integrate multimodal inputs. On the other hand, neither of these architectural features led to productive generalization, suggesting fundamental limitations of existing architectures for specific types of multimodal generalization. These results demonstrate the strengths and limitations of specific architectural components underlying modern neural models for multimodal reasoning. Finally, we provide Generic COG (gCOG), a configurable benchmark with several multimodal generalization splits, for future studies to explore.

Understanding when the noise in stochastic gradient descent (SGD) affects generalization of deep neural networks remains a challenge, complicated by the fact that networks can operate in distinct training regimes. Here we study how the magnitude of this noise T affects performance as the size of the training set P and the scale of initialization alpha are varied. For gradient descent, alpha is a key parameter that controls if the network is `lazy'(alphagg1) or instead learns features (alphall1). For classification of MNIST and CIFAR10 images, our central results are: (i) obtaining phase diagrams for performance in the (alpha,T) plane. They show that SGD noise can be detrimental or instead useful depending on the training regime. Moreover, although increasing T or decreasing alpha both allow the net to escape the lazy regime, these changes can have opposite effects on performance. (ii) Most importantly, we find that the characteristic temperature T_c where the noise of SGD starts affecting the trained model (and eventually performance) is a power law of P. We relate this finding with the observation that key dynamical quantities, such as the total variation of weights during training, depend on both T and P as power laws. These results indicate that a key effect of SGD noise occurs late in training by affecting the stopping process whereby all data are fitted. Indeed, we argue that due to SGD noise, nets must develop a stronger `signal', i.e. larger informative weights, to fit the data, leading to a longer training time. A stronger signal and a longer training time are also required when the size of the training set P increases. We confirm these views in the perceptron model, where signal and noise can be precisely measured. Interestingly, exponents characterizing the effect of SGD depend on the density of data near the decision boundary, as we explain.

Learning representations that capture the underlying data generating process is a key problem for data efficient and robust use of neural networks. One key property for robustness which the learned representation should capture and which recently received a lot of attention is described by the notion of invariance. In this work we provide a causal perspective and new algorithm for learning invariant representations. Empirically we show that this algorithm works well on a diverse set of tasks and in particular we observe state-of-the-art performance on domain generalization, where we are able to significantly boost the score of existing models.

This paper provides theoretical insights into why and how deep learning can generalize well, despite its large capacity, complexity, possible algorithmic instability, nonrobustness, and sharp minima, responding to an open question in the literature. We also discuss approaches to provide non-vacuous generalization guarantees for deep learning. Based on theoretical observations, we propose new open problems and discuss the limitations of our results.

This study addresses the challenge of noise in training datasets for Direct Preference Optimization (DPO), a method for aligning Large Language Models (LLMs) with human preferences. We categorize noise into pointwise noise, which includes low-quality data points, and pairwise noise, which encompasses erroneous data pair associations that affect preference rankings. Utilizing Distributionally Robust Optimization (DRO), we enhance DPO's resilience to these types of noise. Our theoretical insights reveal that DPO inherently embeds DRO principles, conferring robustness to pointwise noise, with the regularization coefficient beta playing a critical role in its noise resistance. Extending this framework, we introduce Distributionally Robustifying DPO (Dr. DPO), which integrates pairwise robustness by optimizing against worst-case pairwise scenarios. The novel hyperparameter beta' in Dr. DPO allows for fine-tuned control over data pair reliability, providing a strategic balance between exploration and exploitation in noisy training environments. Empirical evaluations demonstrate that Dr. DPO substantially improves the quality of generated text and response accuracy in preference datasets, showcasing enhanced performance in both noisy and noise-free settings. The code is available at https://github.com/junkangwu/Dr_DPO.

This paper focuses on over-parameterized deep neural networks (DNNs) with ReLU activation functions and proves that when the data distribution is well-separated, DNNs can achieve Bayes-optimal test error for classification while obtaining (nearly) zero-training error under the lazy training regime. For this purpose, we unify three interrelated concepts of overparameterization, benign overfitting, and the Lipschitz constant of DNNs. Our results indicate that interpolating with smoother functions leads to better generalization. Furthermore, we investigate the special case where interpolating smooth ground-truth functions is performed by DNNs under the Neural Tangent Kernel (NTK) regime for generalization. Our result demonstrates that the generalization error converges to a constant order that only depends on label noise and initialization noise, which theoretically verifies benign overfitting. Our analysis provides a tight lower bound on the normalized margin under non-smooth activation functions, as well as the minimum eigenvalue of NTK under high-dimensional settings, which has its own interest in learning theory.

We identify a new phenomenon in neural network optimization which arises from the interaction of depth and a particular heavy-tailed structure in natural data. Our result offers intuitive explanations for several previously reported observations about network training dynamics. In particular, it implies a conceptually new cause for progressive sharpening and the edge of stability; we also highlight connections to other concepts in optimization and generalization including grokking, simplicity bias, and Sharpness-Aware Minimization. Experimentally, we demonstrate the significant influence of paired groups of outliers in the training data with strong opposing signals: consistent, large magnitude features which dominate the network output throughout training and provide gradients which point in opposite directions. Due to these outliers, early optimization enters a narrow valley which carefully balances the opposing groups; subsequent sharpening causes their loss to rise rapidly, oscillating between high on one group and then the other, until the overall loss spikes. We describe how to identify these groups, explore what sets them apart, and carefully study their effect on the network's optimization and behavior. We complement these experiments with a mechanistic explanation on a toy example of opposing signals and a theoretical analysis of a two-layer linear network on a simple model. Our finding enables new qualitative predictions of training behavior which we confirm experimentally. It also provides a new lens through which to study and improve modern training practices for stochastic optimization, which we highlight via a case study of Adam versus SGD.

Bayesian optimization is an approach to optimizing objective functions that take a long time (minutes or hours) to evaluate. It is best-suited for optimization over continuous domains of less than 20 dimensions, and tolerates stochastic noise in function evaluations. It builds a surrogate for the objective and quantifies the uncertainty in that surrogate using a Bayesian machine learning technique, Gaussian process regression, and then uses an acquisition function defined from this surrogate to decide where to sample. In this tutorial, we describe how Bayesian optimization works, including Gaussian process regression and three common acquisition functions: expected improvement, entropy search, and knowledge gradient. We then discuss more advanced techniques, including running multiple function evaluations in parallel, multi-fidelity and multi-information source optimization, expensive-to-evaluate constraints, random environmental conditions, multi-task Bayesian optimization, and the inclusion of derivative information. We conclude with a discussion of Bayesian optimization software and future research directions in the field. Within our tutorial material we provide a generalization of expected improvement to noisy evaluations, beyond the noise-free setting where it is more commonly applied. This generalization is justified by a formal decision-theoretic argument, standing in contrast to previous ad hoc modifications.

We study the performance of transformers as a function of the number of repetitions of training examples with algorithmically generated datasets. On three problems of mathematics: the greatest common divisor, modular multiplication, and matrix eigenvalues, we show that for a fixed number of training steps, models trained on smaller sets of repeated examples outperform models trained on larger sets of single-use examples. We also demonstrate that two-set training - repeated use of a small random subset of examples, along normal sampling on the rest of the training set - provides for faster learning and better performance. This highlights that the benefits of repetition can outweigh those of data diversity. These datasets and problems provide a controlled setting to shed light on the still poorly understood interplay between generalization and memorization in deep learning.

Reconstruction of magnetic resonance imaging (MRI) data has been positively affected by deep learning. A key challenge remains: to improve generalisation to distribution shifts between the training and testing data. Most approaches aim to address this via inductive design or data augmentation. However, they can be affected by misleading data, e.g. random noise, and cases where the inference stage data do not match assumptions in the modelled shifts. In this work, by employing a conditional hyperparameter network, we eliminate the need of augmentation, yet maintain robust performance under various levels of Gaussian noise. We demonstrate that our model withstands various input noise levels while producing high-definition reconstructions during the test stage. Moreover, we present a hyperparameter sampling strategy that accelerates the convergence of training. Our proposed method achieves the highest accuracy and image quality in all settings compared to baseline methods.

No free lunch theorems for supervised learning state that no learner can solve all problems or that all learners achieve exactly the same accuracy on average over a uniform distribution on learning problems. Accordingly, these theorems are often referenced in support of the notion that individual problems require specially tailored inductive biases. While virtually all uniformly sampled datasets have high complexity, real-world problems disproportionately generate low-complexity data, and we argue that neural network models share this same preference, formalized using Kolmogorov complexity. Notably, we show that architectures designed for a particular domain, such as computer vision, can compress datasets on a variety of seemingly unrelated domains. Our experiments show that pre-trained and even randomly initialized language models prefer to generate low-complexity sequences. Whereas no free lunch theorems seemingly indicate that individual problems require specialized learners, we explain how tasks that often require human intervention such as picking an appropriately sized model when labeled data is scarce or plentiful can be automated into a single learning algorithm. These observations justify the trend in deep learning of unifying seemingly disparate problems with an increasingly small set of machine learning models.

We study pre-training representations for decision-making using video data, which is abundantly available for tasks such as game agents and software testing. Even though significant empirical advances have been made on this problem, a theoretical understanding remains absent. We initiate the theoretical investigation into principled approaches for representation learning and focus on learning the latent state representations of the underlying MDP using video data. We study two types of settings: one where there is iid noise in the observation, and a more challenging setting where there is also the presence of exogenous noise, which is non-iid noise that is temporally correlated, such as the motion of people or cars in the background. We study three commonly used approaches: autoencoding, temporal contrastive learning, and forward modeling. We prove upper bounds for temporal contrastive learning and forward modeling in the presence of only iid noise. We show that these approaches can learn the latent state and use it to do efficient downstream RL with polynomial sample complexity. When exogenous noise is also present, we establish a lower bound result showing that the sample complexity of learning from video data can be exponentially worse than learning from action-labeled trajectory data. This partially explains why reinforcement learning with video pre-training is hard. We evaluate these representational learning methods in two visual domains, yielding results that are consistent with our theoretical findings.

This paper explores the scenarios under which an attacker can claim that 'Noise and access to the softmax layer of the model is all you need' to steal the weights of a convolutional neural network whose architecture is already known. We were able to achieve 96% test accuracy using the stolen MNIST model and 82% accuracy using the stolen KMNIST model learned using only i.i.d. Bernoulli noise inputs. We posit that this theft-susceptibility of the weights is indicative of the complexity of the dataset and propose a new metric that captures the same. The goal of this dissemination is to not just showcase how far knowing the architecture can take you in terms of model stealing, but to also draw attention to this rather idiosyncratic weight learnability aspects of CNNs spurred by i.i.d. noise input. We also disseminate some initial results obtained with using the Ising probability distribution in lieu of the i.i.d. Bernoulli distribution.

We present a machine sound dataset to benchmark domain generalization techniques for anomalous sound detection (ASD). Domain shifts are differences in data distributions that can degrade the detection performance, and handling them is a major issue for the application of ASD systems. While currently available datasets for ASD tasks assume that occurrences of domain shifts are known, in practice, they can be difficult to detect. To handle such domain shifts, domain generalization techniques that perform well regardless of the domains should be investigated. In this paper, we present the first ASD dataset for the domain generalization techniques, called MIMII DG. The dataset consists of five machine types and three domain shift scenarios for each machine type. The dataset is dedicated to the domain generalization task with features such as multiple different values for parameters that cause domain shifts and introduction of domain shifts that can be difficult to detect, such as shifts in the background noise. Experimental results using two baseline systems indicate that the dataset reproduces domain shift scenarios and is useful for benchmarking domain generalization techniques.

In this paper, we consider a real-world scenario where a model that is trained on pre-defined classes continually encounters unlabeled data that contains both known and novel classes. The goal is to continually discover novel classes while maintaining the performance in known classes. We name the setting Continual Generalized Category Discovery (C-GCD). Existing methods for novel class discovery cannot directly handle the C-GCD setting due to some unrealistic assumptions, such as the unlabeled data only containing novel classes. Furthermore, they fail to discover novel classes in a continual fashion. In this work, we lift all these assumptions and propose an approach, called MetaGCD, to learn how to incrementally discover with less forgetting. Our proposed method uses a meta-learning framework and leverages the offline labeled data to simulate the testing incremental learning process. A meta-objective is defined to revolve around two conflicting learning objectives to achieve novel class discovery without forgetting. Furthermore, a soft neighborhood-based contrastive network is proposed to discriminate uncorrelated images while attracting correlated images. We build strong baselines and conduct extensive experiments on three widely used benchmarks to demonstrate the superiority of our method.

Despite their widespread success, the application of deep neural networks to functional data remains scarce today. The infinite dimensionality of functional data means standard learning algorithms can be applied only after appropriate dimension reduction, typically achieved via basis expansions. Currently, these bases are chosen a priori without the information for the task at hand and thus may not be effective for the designated task. We instead propose to adaptively learn these bases in an end-to-end fashion. We introduce neural networks that employ a new Basis Layer whose hidden units are each basis functions themselves implemented as a micro neural network. Our architecture learns to apply parsimonious dimension reduction to functional inputs that focuses only on information relevant to the target rather than irrelevant variation in the input function. Across numerous classification/regression tasks with functional data, our method empirically outperforms other types of neural networks, and we prove that our approach is statistically consistent with low generalization error. Code is available at: https://github.com/jwyyy/AdaFNN.

The generalization performance of a machine learning algorithm such as a neural network depends in a non-trivial way on the structure of the data distribution. To analyze the influence of data structure on test loss dynamics, we study an exactly solveable model of stochastic gradient descent (SGD) on mean square loss which predicts test loss when training on features with arbitrary covariance structure. We solve the theory exactly for both Gaussian features and arbitrary features and we show that the simpler Gaussian model accurately predicts test loss of nonlinear random-feature models and deep neural networks trained with SGD on real datasets such as MNIST and CIFAR-10. We show that the optimal batch size at a fixed compute budget is typically small and depends on the feature correlation structure, demonstrating the computational benefits of SGD with small batch sizes. Lastly, we extend our theory to the more usual setting of stochastic gradient descent on a fixed subsampled training set, showing that both training and test error can be accurately predicted in our framework on real data.

This paper introduces misinfo-general, a benchmark dataset for evaluating misinformation models' ability to perform out-of-distribution generalisation. Misinformation changes rapidly, much quicker than moderators can annotate at scale, resulting in a shift between the training and inference data distributions. As a result, misinformation models need to be able to perform out-of-distribution generalisation, an understudied problem in existing datasets. We identify 6 axes of generalisation-time, event, topic, publisher, political bias, misinformation type-and design evaluation procedures for each. We also analyse some baseline models, highlighting how these fail important desiderata.

Mixup is a highly successful technique to improve generalization of neural networks by augmenting the training data with combinations of random pairs. Selective mixup is a family of methods that apply mixup to specific pairs, e.g. only combining examples across classes or domains. These methods have claimed remarkable improvements on benchmarks with distribution shifts, but their mechanisms and limitations remain poorly understood. We examine an overlooked aspect of selective mixup that explains its success in a completely new light. We find that the non-random selection of pairs affects the training distribution and improve generalization by means completely unrelated to the mixing. For example in binary classification, mixup across classes implicitly resamples the data for a uniform class distribution - a classical solution to label shift. We show empirically that this implicit resampling explains much of the improvements in prior work. Theoretically, these results rely on a regression toward the mean, an accidental property that we identify in several datasets. We have found a new equivalence between two successful methods: selective mixup and resampling. We identify limits of the former, confirm the effectiveness of the latter, and find better combinations of their respective benefits.

Gradient-based meta-learning has proven to be highly effective at learning model initializations, representations, and update rules that allow fast adaptation from a few samples. The core idea behind these approaches is to use fast adaptation and generalization -- two second-order metrics -- as training signals on a meta-training dataset. However, little attention has been given to other possible second-order metrics. In this paper, we investigate a different training signal -- robustness to catastrophic interference -- and demonstrate that representations learned by directing minimizing interference are more conducive to incremental learning than those learned by just maximizing fast adaptation.

We propose a new framework for estimating generative models via an adversarial process, in which we simultaneously train two models: a generative model G that captures the data distribution, and a discriminative model D that estimates the probability that a sample came from the training data rather than G. The training procedure for G is to maximize the probability of D making a mistake. This framework corresponds to a minimax two-player game. In the space of arbitrary functions G and D, a unique solution exists, with G recovering the training data distribution and D equal to 1/2 everywhere. In the case where G and D are defined by multilayer perceptrons, the entire system can be trained with backpropagation. There is no need for any Markov chains or unrolled approximate inference networks during either training or generation of samples. Experiments demonstrate the potential of the framework through qualitative and quantitative evaluation of the generated samples.

Web-crawled datasets have enabled remarkable generalization capabilities in recent image-text models such as CLIP (Contrastive Language-Image pre-training) or Flamingo, but little is known about the dataset creation processes. In this work, we introduce a testbed of six publicly available data sources - YFCC, LAION, Conceptual Captions, WIT, RedCaps, Shutterstock - to investigate how pre-training distributions induce robustness in CLIP. We find that the performance of the pre-training data varies substantially across distribution shifts, with no single data source dominating. Moreover, we systematically study the interactions between these data sources and find that combining multiple sources does not necessarily yield better models, but rather dilutes the robustness of the best individual data source. We complement our empirical findings with theoretical insights from a simple setting, where combining the training data also results in diluted robustness. In addition, our theoretical model provides a candidate explanation for the success of the CLIP-based data filtering technique recently employed in the LAION dataset. Overall our results demonstrate that simply gathering a large amount of data from the web is not the most effective way to build a pre-training dataset for robust generalization, necessitating further study into dataset design. Code is available at https://github.com/mlfoundations/clip_quality_not_quantity.

Large monolithic generative models trained on massive amounts of data have become an increasingly dominant approach in AI research. In this paper, we argue that we should instead construct large generative systems by composing smaller generative models together. We show how such a compositional generative approach enables us to learn distributions in a more data-efficient manner, enabling generalization to parts of the data distribution unseen at training time. We further show how this enables us to program and construct new generative models for tasks completely unseen at training. Finally, we show that in many cases, we can discover separate compositional components from data.

Grokking, or delayed generalization, is a phenomenon where generalization in a deep neural network (DNN) occurs long after achieving near zero training error. Previous studies have reported the occurrence of grokking in specific controlled settings, such as DNNs initialized with large-norm parameters or transformers trained on algorithmic datasets. We demonstrate that grokking is actually much more widespread and materializes in a wide range of practical settings, such as training of a convolutional neural network (CNN) on CIFAR10 or a Resnet on Imagenette. We introduce the new concept of delayed robustness, whereby a DNN groks adversarial examples and becomes robust, long after interpolation and/or generalization. We develop an analytical explanation for the emergence of both delayed generalization and delayed robustness based on a new measure of the local complexity of a DNN's input-output mapping. Our local complexity measures the density of the so-called 'linear regions' (aka, spline partition regions) that tile the DNN input space, and serves as a utile progress measure for training. We provide the first evidence that for classification problems, the linear regions undergo a phase transition during training whereafter they migrate away from the training samples (making the DNN mapping smoother there) and towards the decision boundary (making the DNN mapping less smooth there). Grokking occurs post phase transition as a robust partition of the input space emerges thanks to the linearization of the DNN mapping around the training points. Website: https://bit.ly/grok-adversarial

Ensembling is among the most popular tools in machine learning (ML) due to its effectiveness in minimizing variance and thus improving generalization. Most ensembling methods for black-box base learners fall under the umbrella of "stacked generalization," namely training an ML algorithm that takes the inferences from the base learners as input. While stacking has been widely applied in practice, its theoretical properties are poorly understood. In this paper, we prove a novel result, showing that choosing the best stacked generalization from a (finite or finite-dimensional) family of stacked generalizations based on cross-validated performance does not perform "much worse" than the oracle best. Our result strengthens and significantly extends the results in Van der Laan et al. (2007). Inspired by the theoretical analysis, we further propose a particular family of stacked generalizations in the context of probabilistic forecasting, each one with a different sensitivity for how much the ensemble weights are allowed to vary across items, timestamps in the forecast horizon, and quantiles. Experimental results demonstrate the performance gain of the proposed method.

A growing body of research has demonstrated the inability of NLP models to generalize compositionally and has tried to alleviate it through specialized architectures, training schemes, and data augmentation, among other approaches. In this work, we study a different approach: training on instances with diverse structures. We propose a model-agnostic algorithm for subsampling such sets of instances from a labeled instance pool with structured outputs. Evaluating on both compositional template splits and traditional IID splits of 5 semantic parsing datasets of varying complexity, we show that structurally diverse training using our algorithm leads to comparable or better generalization than prior algorithms in 9 out of 10 dataset-split type pairs. In general, we find structural diversity to consistently improve sample efficiency compared to random train sets. Moreover, we show that structurally diverse sampling yields comprehensive test sets that are a lot more challenging than IID test sets. Finally, we provide two explanations for improved generalization from diverse train sets: 1) improved coverage of output substructures, and 2) a reduction in spurious correlations between these substructures.

Generalizing to out-of-distribution (OOD) data or unseen domain, termed OOD generalization, still lacks appropriate theoretical guarantees. Canonical OOD bounds focus on different distance measurements between source and target domains but fail to consider the optimization property of the learned model. As empirically shown in recent work, the sharpness of learned minima influences OOD generalization. To bridge this gap between optimization and OOD generalization, we study the effect of sharpness on how a model tolerates data change in domain shift which is usually captured by "robustness" in generalization. In this paper, we give a rigorous connection between sharpness and robustness, which gives better OOD guarantees for robust algorithms. It also provides a theoretical backing for "flat minima leads to better OOD generalization". Overall, we propose a sharpness-based OOD generalization bound by taking robustness into consideration, resulting in a tighter bound than non-robust guarantees. Our findings are supported by the experiments on a ridge regression model, as well as the experiments on deep learning classification tasks.

While state-of-the-art language models achieve impressive results through next-token prediction, they have inherent limitations such as the inability to revise already generated tokens. This has prompted exploration of alternative approaches such as discrete diffusion. However, masked diffusion, which has emerged as a popular choice due to its simplicity and effectiveness, reintroduces this inability to revise words. To overcome this, we generalize masked diffusion and derive the theoretical backbone of a family of general interpolating discrete diffusion (GIDD) processes offering greater flexibility in the design of the noising processes. Leveraging a novel diffusion ELBO, we achieve compute-matched state-of-the-art performance in diffusion language modeling. Exploiting GIDD's flexibility, we explore a hybrid approach combining masking and uniform noise, leading to improved sample quality and unlocking the ability for the model to correct its own mistakes, an area where autoregressive models notoriously have struggled. Our code and models are open-source: https://github.com/dvruette/gidd/

We describe new datasets for studying generalization from easy to hard examples.

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

Understanding how convolutional neural networks (CNNs) can efficiently learn high-dimensional functions remains a fundamental challenge. A popular belief is that these models harness the local and hierarchical structure of natural data such as images. Yet, we lack a quantitative understanding of how such structure affects performance, e.g., the rate of decay of the generalisation error with the number of training samples. In this paper, we study infinitely-wide deep CNNs in the kernel regime. First, we show that the spectrum of the corresponding kernel inherits the hierarchical structure of the network, and we characterise its asymptotics. Then, we use this result together with generalisation bounds to prove that deep CNNs adapt to the spatial scale of the target function. In particular, we find that if the target function depends on low-dimensional subsets of adjacent input variables, then the decay of the error is controlled by the effective dimensionality of these subsets. Conversely, if the target function depends on the full set of input variables, then the error decay is controlled by the input dimension. We conclude by computing the generalisation error of a deep CNN trained on the output of another deep CNN with randomly-initialised parameters. Interestingly, we find that, despite their hierarchical structure, the functions generated by infinitely-wide deep CNNs are too rich to be efficiently learnable in high dimension.

Large language models exhibit surprising emergent generalization properties, yet also struggle on many simple reasoning tasks such as arithmetic and parity. This raises the question of if and when Transformer models can learn the true algorithm for solving a task. We study the scope of Transformers' abilities in the specific setting of length generalization on algorithmic tasks. Here, we propose a unifying framework to understand when and how Transformers can exhibit strong length generalization on a given task. Specifically, we leverage RASP (Weiss et al., 2021) -- a programming language designed for the computational model of a Transformer -- and introduce the RASP-Generalization Conjecture: Transformers tend to length generalize on a task if the task can be solved by a short RASP program which works for all input lengths. This simple conjecture remarkably captures most known instances of length generalization on algorithmic tasks. Moreover, we leverage our insights to drastically improve generalization performance on traditionally hard tasks (such as parity and addition). On the theoretical side, we give a simple example where the "min-degree-interpolator" model of learning from Abbe et al. (2023) does not correctly predict Transformers' out-of-distribution behavior, but our conjecture does. Overall, our work provides a novel perspective on the mechanisms of compositional generalization and the algorithmic capabilities of Transformers.

Knowledge-dependent tasks typically use two sources of knowledge: parametric, learned at training time, and contextual, given as a passage at inference time. To understand how models use these sources together, we formalize the problem of knowledge conflicts, where the contextual information contradicts the learned information. Analyzing the behaviour of popular models, we measure their over-reliance on memorized information (the cause of hallucinations), and uncover important factors that exacerbate this behaviour. Lastly, we propose a simple method to mitigate over-reliance on parametric knowledge, which minimizes hallucination, and improves out-of-distribution generalization by 4%-7%. Our findings demonstrate the importance for practitioners to evaluate model tendency to hallucinate rather than read, and show that our mitigation strategy encourages generalization to evolving information (i.e., time-dependent queries). To encourage these practices, we have released our framework for generating knowledge conflicts.

Recently, denoising diffusion probabilistic models and generative score matching have shown high potential in modelling complex data distributions while stochastic calculus has provided a unified point of view on these techniques allowing for flexible inference schemes. In this paper we introduce Grad-TTS, a novel text-to-speech model with score-based decoder producing mel-spectrograms by gradually transforming noise predicted by encoder and aligned with text input by means of Monotonic Alignment Search. The framework of stochastic differential equations helps us to generalize conventional diffusion probabilistic models to the case of reconstructing data from noise with different parameters and allows to make this reconstruction flexible by explicitly controlling trade-off between sound quality and inference speed. Subjective human evaluation shows that Grad-TTS is competitive with state-of-the-art text-to-speech approaches in terms of Mean Opinion Score. We will make the code publicly available shortly.

The equivalence of realizable and agnostic learnability is a fundamental phenomenon in learning theory. With variants ranging from classical settings like PAC learning and regression to recent trends such as adversarially robust learning, it's surprising that we still lack a unified theory; traditional proofs of the equivalence tend to be disparate, and rely on strong model-specific assumptions like uniform convergence and sample compression. In this work, we give the first model-independent framework explaining the equivalence of realizable and agnostic learnability: a three-line blackbox reduction that simplifies, unifies, and extends our understanding across a wide variety of settings. This includes models with no known characterization of learnability such as learning with arbitrary distributional assumptions and more general loss functions, as well as a host of other popular settings such as robust learning, partial learning, fair learning, and the statistical query model. More generally, we argue that the equivalence of realizable and agnostic learning is actually a special case of a broader phenomenon we call property generalization: any desirable property of a learning algorithm (e.g. noise tolerance, privacy, stability) that can be satisfied over finite hypothesis classes extends (possibly in some variation) to any learnable hypothesis class.

Diffusion models have emerged as a powerful tool rivaling GANs in generating high-quality samples with improved fidelity, flexibility, and robustness. A key component of these models is to learn the score function through score matching. Despite empirical success on various tasks, it remains unclear whether gradient-based algorithms can learn the score function with a provable accuracy. As a first step toward answering this question, this paper establishes a mathematical framework for analyzing score estimation using neural networks trained by gradient descent. Our analysis covers both the optimization and the generalization aspects of the learning procedure. In particular, we propose a parametric form to formulate the denoising score-matching problem as a regression with noisy labels. Compared to the standard supervised learning setup, the score-matching problem introduces distinct challenges, including unbounded input, vector-valued output, and an additional time variable, preventing existing techniques from being applied directly. In this paper, we show that with proper designs, the evolution of neural networks during training can be accurately modeled by a series of kernel regression tasks. Furthermore, by applying an early-stopping rule for gradient descent and leveraging recent developments in neural tangent kernels, we establish the first generalization error (sample complexity) bounds for learning the score function with neural networks, despite the presence of noise in the observations. Our analysis is grounded in a novel parametric form of the neural network and an innovative connection between score matching and regression analysis, facilitating the application of advanced statistical and optimization techniques.

When language models (LMs) are trained to forget (or "unlearn'') a skill, how precisely does their behavior change? We study the behavior of transformer LMs in which tasks have been forgotten via fine-tuning on randomized labels. Such LMs learn to generate near-random predictions for individual examples in the "training'' set used for forgetting. Across tasks, however, LMs exhibit extreme variability in whether LM predictions change on examples outside the training set. In some tasks (like entailment classification), forgetting generalizes robustly, and causes models to produce uninformative predictions on new task instances; in other tasks (like physical commonsense reasoning and scientific question answering) forgetting affects only the training examples, and models continue to perform the "forgotten'' task accurately even for examples very similar to those that appeared in the training set. Dataset difficulty is not predictive of whether a behavior can be forgotten; instead, generalization in forgetting is (weakly) predicted by the confidence of LMs' initial task predictions and the variability of LM representations of training data, with low confidence and low variability both associated with greater generalization. Perhaps most surprisingly, random-label forgetting appears to be somewhat insensitive to the contents of the training set: for example, models trained on science questions with random labels continue to answer other science questions accurately, but begin to produce random labels on entailment classification tasks. Finally, we show that even generalizable forgetting is shallow: linear probes trained on LMs' representations can still perform tasks reliably after forgetting. Our results highlight the difficulty and unpredictability of performing targeted skill removal from models via fine-tuning.

In this work, we present a variety of novel information-theoretic generalization bounds for learning algorithms, from the supersample setting of Steinke & Zakynthinou (2020)-the setting of the "conditional mutual information" framework. Our development exploits projecting the loss pair (obtained from a training instance and a testing instance) down to a single number and correlating loss values with a Rademacher sequence (and its shifted variants). The presented bounds include square-root bounds, fast-rate bounds, including those based on variance and sharpness, and bounds for interpolating algorithms etc. We show theoretically or empirically that these bounds are tighter than all information-theoretic bounds known to date on the same supersample setting.

To process novel sentences, language models (LMs) must generalize compositionally -- combine familiar elements in new ways. What aspects of a model's structure promote compositional generalization? Focusing on transformers, we test the hypothesis, motivated by recent theoretical and empirical work, that transformers generalize more compositionally when they are deeper (have more layers). Because simply adding layers increases the total number of parameters, confounding depth and size, we construct three classes of models which trade off depth for width such that the total number of parameters is kept constant (41M, 134M and 374M parameters). We pretrain all models as LMs and fine-tune them on tasks that test for compositional generalization. We report three main conclusions: (1) after fine-tuning, deeper models generalize better out-of-distribution than shallower models do, but the relative benefit of additional layers diminishes rapidly; (2) within each family, deeper models show better language modeling performance, but returns are similarly diminishing; (3) the benefits of depth for compositional generalization cannot be attributed solely to better performance on language modeling or on in-distribution data.

We derive a minimalist but powerful deterministic denoising-diffusion model. While denoising diffusion has shown great success in many domains, its underlying theory remains largely inaccessible to non-expert users. Indeed, an understanding of graduate-level concepts such as Langevin dynamics or score matching appears to be required to grasp how it works. We propose an alternative approach that requires no more than undergrad calculus and probability. We consider two densities and observe what happens when random samples from these densities are blended (linearly interpolated). We show that iteratively blending and deblending samples produces random paths between the two densities that converge toward a deterministic mapping. This mapping can be evaluated with a neural network trained to deblend samples. We obtain a model that behaves like deterministic denoising diffusion: it iteratively maps samples from one density (e.g., Gaussian noise) to another (e.g., cat images). However, compared to the state-of-the-art alternative, our model is simpler to derive, simpler to implement, more numerically stable, achieves higher quality results in our experiments, and has interesting connections to computer graphics.

Supervised learning datasets may contain multiple cues that explain the training set equally well, i.e., learning any of them would lead to the correct predictions on the training data. However, many of them can be spurious, i.e., lose their predictive power under a distribution shift and consequently fail to generalize to out-of-distribution (OOD) data. Recently developed "diversification" methods (Lee et al., 2023; Pagliardini et al., 2023) approach this problem by finding multiple diverse hypotheses that rely on different features. This paper aims to study this class of methods and identify the key components contributing to their OOD generalization abilities. We show that (1) diversification methods are highly sensitive to the distribution of the unlabeled data used for diversification and can underperform significantly when away from a method-specific sweet spot. (2) Diversification alone is insufficient for OOD generalization. The choice of the used learning algorithm, e.g., the model's architecture and pretraining, is crucial. In standard experiments (classification on Waterbirds and Office-Home datasets), using the second-best choice leads to an up to 20\% absolute drop in accuracy. (3) The optimal choice of learning algorithm depends on the unlabeled data and vice versa i.e. they are co-dependent. (4) Finally, we show that, in practice, the above pitfalls cannot be alleviated by increasing the number of diverse hypotheses, the major feature of diversification methods. These findings provide a clearer understanding of the critical design factors influencing the OOD generalization abilities of diversification methods. They can guide practitioners in how to use the existing methods best and guide researchers in developing new, better ones.

Recent work in mechanistic interpretability has shown that behaviors in language models can be successfully reverse-engineered through circuit analysis. A common criticism, however, is that each circuit is task-specific, and thus such analysis cannot contribute to understanding the models at a higher level. In this work, we present evidence that insights (both low-level findings about specific heads and higher-level findings about general algorithms) can indeed generalize across tasks. Specifically, we study the circuit discovered in Wang et al. (2022) for the Indirect Object Identification (IOI) task and 1.) show that it reproduces on a larger GPT2 model, and 2.) that it is mostly reused to solve a seemingly different task: Colored Objects (Ippolito & Callison-Burch, 2023). We provide evidence that the process underlying both tasks is functionally very similar, and contains about a 78% overlap in in-circuit attention heads. We further present a proof-of-concept intervention experiment, in which we adjust four attention heads in middle layers in order to 'repair' the Colored Objects circuit and make it behave like the IOI circuit. In doing so, we boost accuracy from 49.6% to 93.7% on the Colored Objects task and explain most sources of error. The intervention affects downstream attention heads in specific ways predicted by their interactions in the IOI circuit, indicating that this subcircuit behavior is invariant to the different task inputs. Overall, our results provide evidence that it may yet be possible to explain large language models' behavior in terms of a relatively small number of interpretable task-general algorithmic building blocks and computational components.

Recent work have demonstrated that robustness (to "corruption") can be at odds with generalization. Adversarial training, for instance, aims to reduce the problematic susceptibility of modern neural networks to small data perturbations. Surprisingly, overfitting is a major concern in adversarial training despite being mostly absent in standard training. We provide here theoretical evidence for this peculiar "robust overfitting" phenomenon. Subsequently, we advance a novel distributionally robust loss function bridging robustness and generalization. We demonstrate both theoretically as well as empirically the loss to enjoy a certified level of robustness against two common types of corruption--data evasion and poisoning attacks--while ensuring guaranteed generalization. We show through careful numerical experiments that our resulting holistic robust (HR) training procedure yields SOTA performance. Finally, we indicate that HR training can be interpreted as a direct extension of adversarial training and comes with a negligible additional computational burden. A ready-to-use python library implementing our algorithm is available at https://github.com/RyanLucas3/HR_Neural_Networks.

According to the principle of compositional generalization, the meaning of a complex expression can be understood as a function of the meaning of its parts and of how they are combined. This principle is crucial for human language processing and also, arguably, for NLP models in the face of out-of-distribution data. However, many neural network models, including Transformers, have been shown to struggle with compositional generalization. In this paper, we hypothesize that forcing models to in-context learn can provide an inductive bias to promote compositional generalization. To test this hypothesis, we train a causal Transformer in a setting that renders ordinary learning very difficult: we present it with different orderings of the training instance and shuffle instance labels. This corresponds to training the model on all possible few-shot learning problems attainable from the dataset. The model can solve the task, however, by utilizing earlier examples to generalize to later ones (i.e. in-context learning). In evaluations on the datasets, SCAN, COGS, and GeoQuery, models trained in this manner indeed show improved compositional generalization. This indicates the usefulness of in-context learning problems as an inductive bias for generalization.

Typical generative diffusion models rely on a Gaussian diffusion process for training the backward transformations, which can then be used to generate samples from Gaussian noise. However, real world data often takes place in discrete-state spaces, including many scientific applications. Here, we develop a theoretical formulation for arbitrary discrete-state Markov processes in the forward diffusion process using exact (as opposed to variational) analysis. We relate the theory to the existing continuous-state Gaussian diffusion as well as other approaches to discrete diffusion, and identify the corresponding reverse-time stochastic process and score function in the continuous-time setting, and the reverse-time mapping in the discrete-time setting. As an example of this framework, we introduce ``Blackout Diffusion'', which learns to produce samples from an empty image instead of from noise. Numerical experiments on the CIFAR-10, Binarized MNIST, and CelebA datasets confirm the feasibility of our approach. Generalizing from specific (Gaussian) forward processes to discrete-state processes without a variational approximation sheds light on how to interpret diffusion models, which we discuss.

We introduce a new neural architecture to learn the conditional probability of an output sequence with elements that are discrete tokens corresponding to positions in an input sequence. Such problems cannot be trivially addressed by existent approaches such as sequence-to-sequence and Neural Turing Machines, because the number of target classes in each step of the output depends on the length of the input, which is variable. Problems such as sorting variable sized sequences, and various combinatorial optimization problems belong to this class. Our model solves the problem of variable size output dictionaries using a recently proposed mechanism of neural attention. It differs from the previous attention attempts in that, instead of using attention to blend hidden units of an encoder to a context vector at each decoder step, it uses attention as a pointer to select a member of the input sequence as the output. We call this architecture a Pointer Net (Ptr-Net). We show Ptr-Nets can be used to learn approximate solutions to three challenging geometric problems -- finding planar convex hulls, computing Delaunay triangulations, and the planar Travelling Salesman Problem -- using training examples alone. Ptr-Nets not only improve over sequence-to-sequence with input attention, but also allow us to generalize to variable size output dictionaries. We show that the learnt models generalize beyond the maximum lengths they were trained on. We hope our results on these tasks will encourage a broader exploration of neural learning for discrete problems.

This work aims to advance sound event detection (SED) research by presenting a new large language model (LLM)-powered dataset namely wild domestic environment sound event detection (WildDESED). It is crafted as an extension to the original DESED dataset to reflect diverse acoustic variability and complex noises in home settings. We leveraged LLMs to generate eight different domestic scenarios based on target sound categories of the DESED dataset. Then we enriched the scenarios with a carefully tailored mixture of noises selected from AudioSet and ensured no overlap with target sound. We consider widely popular convolutional neural recurrent network to study WildDESED dataset, which depicts its challenging nature. We then apply curriculum learning by gradually increasing noise complexity to enhance the model's generalization capabilities across various noise levels. Our results with this approach show improvements within the noisy environment, validating the effectiveness on the WildDESED dataset promoting noise-robust SED advancements.

Simulation-free methods for training continuous-time generative models construct probability paths that go between noise distributions and individual data samples. Recent works, such as Flow Matching, derived paths that are optimal for each data sample. However, these algorithms rely on independent data and noise samples, and do not exploit underlying structure in the data distribution for constructing probability paths. We propose Multisample Flow Matching, a more general framework that uses non-trivial couplings between data and noise samples while satisfying the correct marginal constraints. At very small overhead costs, this generalization allows us to (i) reduce gradient variance during training, (ii) obtain straighter flows for the learned vector field, which allows us to generate high-quality samples using fewer function evaluations, and (iii) obtain transport maps with lower cost in high dimensions, which has applications beyond generative modeling. Importantly, we do so in a completely simulation-free manner with a simple minimization objective. We show that our proposed methods improve sample consistency on downsampled ImageNet data sets, and lead to better low-cost sample generation.

Diffusion probabilistic models have been shown to generate state-of-the-art results on several competitive image synthesis benchmarks but lack a low-dimensional, interpretable latent space, and are slow at generation. On the other hand, standard Variational Autoencoders (VAEs) typically have access to a low-dimensional latent space but exhibit poor sample quality. We present DiffuseVAE, a novel generative framework that integrates VAE within a diffusion model framework, and leverage this to design novel conditional parameterizations for diffusion models. We show that the resulting model equips diffusion models with a low-dimensional VAE inferred latent code which can be used for downstream tasks like controllable synthesis. The proposed method also improves upon the speed vs quality tradeoff exhibited in standard unconditional DDPM/DDIM models (for instance, FID of 16.47 vs 34.36 using a standard DDIM on the CelebA-HQ-128 benchmark using T=10 reverse process steps) without having explicitly trained for such an objective. Furthermore, the proposed model exhibits synthesis quality comparable to state-of-the-art models on standard image synthesis benchmarks like CIFAR-10 and CelebA-64 while outperforming most existing VAE-based methods. Lastly, we show that the proposed method exhibits inherent generalization to different types of noise in the conditioning signal. For reproducibility, our source code is publicly available at https://github.com/kpandey008/DiffuseVAE.

The goal of machine learning is generalization. While the No Free Lunch Theorem states that we cannot obtain theoretical guarantees for generalization without further assumptions, in practice we observe that simple models which explain the training data generalize best: a principle called Occam's razor. Despite the need for simple models, most current approaches in machine learning only minimize the training error, and at best indirectly promote simplicity through regularization or architecture design. Here, we draw a connection between Occam's razor and in-context learning: an emergent ability of certain sequence models like Transformers to learn at inference time from past observations in a sequence. In particular, we show that the next-token prediction loss used to train in-context learners is directly equivalent to a data compression technique called prequential coding, and that minimizing this loss amounts to jointly minimizing both the training error and the complexity of the model that was implicitly learned from context. Our theory and the empirical experiments we use to support it not only provide a normative account of in-context learning, but also elucidate the shortcomings of current in-context learning methods, suggesting ways in which they can be improved. We make our code available at https://github.com/3rdCore/PrequentialCode.

Amidst the rapid advancements in generative language models, the investigation of how training data shapes the performance of GPT models is still emerging. This paper presents GPTfluence, a novel approach that leverages a featurized simulation to assess the impact of training examples on the training dynamics of GPT models. Our approach not only traces the influence of individual training instances on performance trajectories, such as loss and other key metrics, on targeted test points but also enables a comprehensive comparison with existing methods across various training scenarios in GPT models, ranging from 14 million to 2.8 billion parameters, across a range of downstream tasks. Contrary to earlier methods that struggle with generalization to new data, GPTfluence introduces a parameterized simulation of training dynamics, demonstrating robust generalization capabilities to unseen training data. This adaptability is evident across both fine-tuning and instruction-tuning scenarios, spanning tasks in natural language understanding and generation. We will make our code and data publicly available.

Large language models are extensively applied across a wide range of tasks, such as customer support, content creation, educational tutoring, and providing financial guidance. However, a well-known drawback is their predisposition to generate hallucinations. This damages the trustworthiness of the information these models provide, impacting decision-making and user confidence. We propose a method to detect hallucinations by looking at the structure of the latent space and finding associations within hallucinated and non-hallucinated generations. We create a graph structure that connects generations that lie closely in the embedding space. Moreover, we employ a Graph Attention Network which utilizes message passing to aggregate information from neighboring nodes and assigns varying degrees of importance to each neighbor based on their relevance. Our findings show that 1) there exists a structure in the latent space that differentiates between hallucinated and non-hallucinated generations, 2) Graph Attention Networks can learn this structure and generalize it to unseen generations, and 3) the robustness of our method is enhanced when incorporating contrastive learning. When evaluated against evidence-based benchmarks, our model performs similarly without access to search-based methods.

We present a dynamic model in which the weights are conditioned on an input sample x and are learned to match those that would be obtained by finetuning a base model on x and its label y. This mapping between an input sample and network weights is approximated by a denoising diffusion model. The diffusion model we employ focuses on modifying a single layer of the base model and is conditioned on the input, activations, and output of this layer. Since the diffusion model is stochastic in nature, multiple initializations generate different networks, forming an ensemble, which leads to further improvements. Our experiments demonstrate the wide applicability of the method for image classification, 3D reconstruction, tabular data, speech separation, and natural language processing. Our code is available at https://github.com/ShaharLutatiPersonal/OCD

Many machine learning algorithms are trained and evaluated by splitting data from a single source into training and test sets. While such focus on in-distribution learning scenarios has led to interesting advancement, it has not been able to tell if models are relying on dataset biases as shortcuts for successful prediction (e.g., using snow cues for recognising snowmobiles), resulting in biased models that fail to generalise when the bias shifts to a different class. The cross-bias generalisation problem has been addressed by de-biasing training data through augmentation or re-sampling, which are often prohibitive due to the data collection cost (e.g., collecting images of a snowmobile on a desert) and the difficulty of quantifying or expressing biases in the first place. In this work, we propose a novel framework to train a de-biased representation by encouraging it to be different from a set of representations that are biased by design. This tactic is feasible in many scenarios where it is much easier to define a set of biased representations than to define and quantify bias. We demonstrate the efficacy of our method across a variety of synthetic and real-world biases; our experiments show that the method discourages models from taking bias shortcuts, resulting in improved generalisation. Source code is available at https://github.com/clovaai/rebias.

Visual anagrams are images that change appearance upon transformation, like flipping or rotation. With the advent of diffusion models, generating such optical illusions can be achieved by averaging noise across multiple views during the reverse denoising process. However, we observe two critical failure modes in this approach: (i) concept segregation, where concepts in different views are independently generated, which can not be considered a true anagram, and (ii) concept domination, where certain concepts overpower others. In this work, we cast the visual anagram generation problem in a multi-task learning setting, where different viewpoint prompts are analogous to different tasks,and derive denoising trajectories that align well across tasks simultaneously. At the core of our designed framework are two newly introduced techniques, where (i) an anti-segregation optimization strategy that promotes overlap in cross-attention maps between different concepts, and (ii) a noise vector balancing method that adaptively adjusts the influence of different tasks. Additionally, we observe that directly averaging noise predictions yields suboptimal performance because statistical properties may not be preserved, prompting us to derive a noise variance rectification method. Extensive qualitative and quantitative experiments demonstrate our method's superior ability to generate visual anagrams spanning diverse concepts.

Many recent works have discussed the propensity, or lack thereof, for emergent languages to exhibit properties of natural languages. A favorite in the literature is learning compositionality. We note that most of those works have focused on communicative bandwidth as being of primary importance. While important, it is not the only contributing factor. In this paper, we investigate the learning biases that affect the efficacy and compositionality of emergent languages. Our foremost contribution is to explore how capacity of a neural network impacts its ability to learn a compositional language. We additionally introduce a set of evaluation metrics with which we analyze the learned languages. Our hypothesis is that there should be a specific range of model capacity and channel bandwidth that induces compositional structure in the resulting language and consequently encourages systematic generalization. While we empirically see evidence for the bottom of this range, we curiously do not find evidence for the top part of the range and believe that this is an open question for the community.

Recently, contrastive learning has found impressive success in advancing the state of the art in solving various machine learning tasks. However, the existing generalization analysis is very limited or even not meaningful. In particular, the existing generalization error bounds depend linearly on the number k of negative examples while it was widely shown in practice that choosing a large k is necessary to guarantee good generalization of contrastive learning in downstream tasks. In this paper, we establish novel generalization bounds for contrastive learning which do not depend on k, up to logarithmic terms. Our analysis uses structural results on empirical covering numbers and Rademacher complexities to exploit the Lipschitz continuity of loss functions. For self-bounding Lipschitz loss functions, we further improve our results by developing optimistic bounds which imply fast rates in a low noise condition. We apply our results to learning with both linear representation and nonlinear representation by deep neural networks, for both of which we derive Rademacher complexity bounds to get improved generalization bounds.

Diffusion-based generative models (DBGMs) perturb data to a target noise distribution and reverse this process to generate samples. The choice of noising process, or inference diffusion process, affects both likelihoods and sample quality. For example, extending the inference process with auxiliary variables leads to improved sample quality. While there are many such multivariate diffusions to explore, each new one requires significant model-specific analysis, hindering rapid prototyping and evaluation. In this work, we study Multivariate Diffusion Models (MDMs). For any number of auxiliary variables, we provide a recipe for maximizing a lower-bound on the MDMs likelihood without requiring any model-specific analysis. We then demonstrate how to parameterize the diffusion for a specified target noise distribution; these two points together enable optimizing the inference diffusion process. Optimizing the diffusion expands easy experimentation from just a few well-known processes to an automatic search over all linear diffusions. To demonstrate these ideas, we introduce two new specific diffusions as well as learn a diffusion process on the MNIST, CIFAR10, and ImageNet32 datasets. We show learned MDMs match or surpass bits-per-dims (BPDs) relative to fixed choices of diffusions for a given dataset and model architecture.

The lack of clean speech is a practical challenge to the development of speech enhancement systems, which means that there is an inevitable mismatch between their training criterion and evaluation metric. In response to this unfavorable situation, we propose a training and inference strategy that additionally uses enhanced speech as a target by improving the previously proposed noisy-target training (NyTT). Because homogeneity between in-domain noise and extraneous noise is the key to the effectiveness of NyTT, we train various student models by remixing 1) the teacher model's estimated speech and noise for enhanced-target training or 2) raw noisy speech and the teacher model's estimated noise for noisy-target training. Experimental results show that our proposed method outperforms several baselines, especially with the teacher/student inference, where predicted clean speech is derived successively through the teacher and final student models.

Instruction tuning (IT) achieves impressive zero-shot generalization results by training large language models (LLMs) on a massive amount of diverse tasks with instructions. However, how to select new tasks to improve the performance and generalizability of IT models remains an open question. Training on all existing tasks is impractical due to prohibiting computation requirements, and randomly selecting tasks can lead to suboptimal performance. In this work, we propose active instruction tuning based on prompt uncertainty, a novel framework to identify informative tasks, and then actively tune the models on the selected tasks. We represent the informativeness of new tasks with the disagreement of the current model outputs over perturbed prompts. Our experiments on NIV2 and Self-Instruct datasets demonstrate that our method consistently outperforms other baseline strategies for task selection, achieving better out-of-distribution generalization with fewer training tasks. Additionally, we introduce a task map that categorizes and diagnoses tasks based on prompt uncertainty and prediction probability. We discover that training on ambiguous (prompt-uncertain) tasks improves generalization while training on difficult (prompt-certain and low-probability) tasks offers no benefit, underscoring the importance of task selection for instruction tuning.

Learning features from data is one of the defining characteristics of deep learning, but our theoretical understanding of the role features play in deep learning is still rudimentary. To address this gap, we introduce a new tool, the interaction tensor, for empirically analyzing the interaction between data and model through features. With the interaction tensor, we make several key observations about how features are distributed in data and how models with different random seeds learn different features. Based on these observations, we propose a conceptual framework for feature learning. Under this framework, the expected accuracy for a single hypothesis and agreement for a pair of hypotheses can both be derived in closed-form. We demonstrate that the proposed framework can explain empirically observed phenomena, including the recently discovered Generalization Disagreement Equality (GDE) that allows for estimating the generalization error with only unlabeled data. Further, our theory also provides explicit construction of natural data distributions that break the GDE. Thus, we believe this work provides valuable new insight into our understanding of feature learning.

Much of recent progress in NLU was shown to be due to models' learning dataset-specific heuristics. We conduct a case study of generalization in NLI (from MNLI to the adversarially constructed HANS dataset) in a range of BERT-based architectures (adapters, Siamese Transformers, HEX debiasing), as well as with subsampling the data and increasing the model size. We report 2 successful and 3 unsuccessful strategies, all providing insights into how Transformer-based models learn to generalize.

Computer Vision (CV) has yet to fully achieve the zero-shot task generalization observed in Natural Language Processing (NLP), despite following many of the milestones established in NLP, such as large transformer models, extensive pre-training, and the auto-regression paradigm, among others. In this paper, we explore the idea that CV adopts discrete and terminological task definitions (\eg, ``image segmentation''), which may be a key barrier to zero-shot task generalization. Our hypothesis is that without truly understanding previously-seen tasks--due to these terminological definitions--deep models struggle to generalize to novel tasks. To verify this, we introduce Explanatory Instructions, which provide an intuitive way to define CV task objectives through detailed linguistic transformations from input images to outputs. We create a large-scale dataset comprising 12 million ``image input to explanatory instruction to output'' triplets, and train an auto-regressive-based vision-language model (AR-based VLM) that takes both images and explanatory instructions as input. By learning to follow these instructions, the AR-based VLM achieves instruction-level zero-shot capabilities for previously-seen tasks and demonstrates strong zero-shot generalization for unseen CV tasks. Code and dataset will be openly available on our GitHub repository.

Many complex tasks can be decomposed into simpler, independent parts. Discovering such underlying compositional structure has the potential to enable compositional generalization. Despite progress, our most powerful systems struggle to compose flexibly. It therefore seems natural to make models more modular to help capture the compositional nature of many tasks. However, it is unclear under which circumstances modular systems can discover hidden compositional structure. To shed light on this question, we study a teacher-student setting with a modular teacher where we have full control over the composition of ground truth modules. This allows us to relate the problem of compositional generalization to that of identification of the underlying modules. In particular we study modularity in hypernetworks representing a general class of multiplicative interactions. We show theoretically that identification up to linear transformation purely from demonstrations is possible without having to learn an exponential number of module combinations. We further demonstrate empirically that under the theoretically identified conditions, meta-learning from finite data can discover modular policies that generalize compositionally in a number of complex environments.

Large language models (LLMs) prompted with text and audio represent the state of the art in various auditory tasks, including speech, music, and general audio, showing emergent abilities on unseen tasks. However, these capabilities have yet to be fully demonstrated in bioacoustics tasks, such as detecting animal vocalizations in large recordings, classifying rare and endangered species, and labeling context and behavior - tasks that are crucial for conservation, biodiversity monitoring, and the study of animal behavior. In this work, we present NatureLM-audio, the first audio-language foundation model specifically designed for bioacoustics. Our carefully curated training dataset comprises text-audio pairs spanning a diverse range of bioacoustics, speech, and music data, designed to address the challenges posed by limited annotated datasets in the field. We demonstrate successful transfer of learned representations from music and speech to bioacoustics, and our model shows promising generalization to unseen taxa and tasks. Importantly, we test NatureLM-audio on a novel benchmark (BEANS-Zero) and it sets the new state of the art (SotA) on several bioacoustics tasks, including zero-shot classification of unseen species. To advance bioacoustics research, we also open-source the code for generating training and benchmark data, as well as for training the model.

Few-shot learning aims to transfer the knowledge acquired from training on a diverse set of tasks to unseen tasks from the same task distribution with a limited amount of labeled data. The underlying requirement for effective few-shot generalization is to learn a good representation of the task manifold. This becomes more difficult when only a limited number of tasks are available for training. In such a few-task few-shot setting, it is beneficial to explicitly preserve the local neighborhoods from the task manifold and exploit this to generate artificial tasks for training. To this end, we introduce the notion of interval bounds from the provably robust training literature to few-shot learning. The interval bounds are used to characterize neighborhoods around the training tasks. These neighborhoods can then be preserved by minimizing the distance between a task and its respective bounds. We then use a novel strategy to artificially form new tasks for training by interpolating between the available tasks and their respective interval bounds. We apply our framework to both model-agnostic meta-learning as well as prototype-based metric-learning paradigms. The efficacy of our proposed approach is evident from the improved performance on several datasets from diverse domains compared to current methods.

We propose that the grokking phenomenon, where the train loss of a neural network decreases much earlier than its test loss, can arise due to a neural network transitioning from lazy training dynamics to a rich, feature learning regime. To illustrate this mechanism, we study the simple setting of vanilla gradient descent on a polynomial regression problem with a two layer neural network which exhibits grokking without regularization in a way that cannot be explained by existing theories. We identify sufficient statistics for the test loss of such a network, and tracking these over training reveals that grokking arises in this setting when the network first attempts to fit a kernel regression solution with its initial features, followed by late-time feature learning where a generalizing solution is identified after train loss is already low. We provide an asymptotic theoretical description of the grokking dynamics in this model using dynamical mean field theory (DMFT) for high dimensional data. We find that the key determinants of grokking are the rate of feature learning -- which can be controlled precisely by parameters that scale the network output -- and the alignment of the initial features with the target function y(x). We argue this delayed generalization arises when (1) the top eigenvectors of the initial neural tangent kernel and the task labels y(x) are misaligned, but (2) the dataset size is large enough so that it is possible for the network to generalize eventually, but not so large that train loss perfectly tracks test loss at all epochs, and (3) the network begins training in the lazy regime so does not learn features immediately. We conclude with evidence that this transition from lazy (linear model) to rich training (feature learning) can control grokking in more general settings, like on MNIST, one-layer Transformers, and student-teacher networks.

Amid mounting concern about the reliability and credibility of machine learning research, we present a principled framework for making robust and generalizable claims: the multiverse analysis. Our framework builds upon the multiverse analysis (Steegen et al., 2016) introduced in response to psychology's own reproducibility crisis. To efficiently explore high-dimensional and often continuous ML search spaces, we model the multiverse with a Gaussian Process surrogate and apply Bayesian experimental design. Our framework is designed to facilitate drawing robust scientific conclusions about model performance, and thus our approach focuses on exploration rather than conventional optimization. In the first of two case studies, we investigate disputed claims about the relative merit of adaptive optimizers. Second, we synthesize conflicting research on the effect of learning rate on the large batch training generalization gap. For the machine learning community, the multiverse analysis is a simple and effective technique for identifying robust claims, for increasing transparency, and a step toward improved reproducibility.

In the classical transformer attention scheme, we are given three n times d size matrices Q, K, V (the query, key, and value tokens), and the goal is to compute a new n times d size matrix D^{-1} exp(QK^top) V where D = diag( exp(QK^top) {bf 1}_n ). In this work, we study a generalization of attention which captures triple-wise correlations. This generalization is able to solve problems about detecting triple-wise connections that were shown to be impossible for transformers. The potential downside of this generalization is that it appears as though computations are even more difficult, since the straightforward algorithm requires cubic time in n. However, we show that in the bounded-entry setting (which arises in practice, and which is well-studied in both theory and practice), there is actually a near-linear time algorithm. More precisely, we show that bounded entries are both necessary and sufficient for quickly performing generalized computations: bullet On the positive side, if all entries of the input matrices are bounded above by o(sqrt[3]{log n}) then we show how to approximate the ``tensor-type'' attention matrix in n^{1+o(1)} time. bullet On the negative side, we show that if the entries of the input matrices may be as large as Omega(sqrt[3]{log n}), then there is no algorithm that runs faster than n^{3-o(1)} (assuming the Strong Exponential Time Hypothesis from fine-grained complexity theory). We also show that our construction, algorithms, and lower bounds naturally generalize to higher-order tensors and correlations. Interestingly, the higher the order of the tensors, the lower the bound on the entries needs to be for an efficient algorithm. Our results thus yield a natural tradeoff between the boundedness of the entries, and order of the tensor one may use for more expressive, efficient attention computation.

Semantic segmentation usually suffers from a long-tail data distribution. Due to the imbalanced number of samples across categories, the features of those tail classes may get squeezed into a narrow area in the feature space. Towards a balanced feature distribution, we introduce category-wise variation into the network predictions in the training phase such that an instance is no longer projected to a feature point, but a small region instead. Such a perturbation is highly dependent on the category scale, which appears as assigning smaller variation to head classes and larger variation to tail classes. In this way, we manage to close the gap between the feature areas of different categories, resulting in a more balanced representation. It is noteworthy that the introduced variation is discarded at the inference stage to facilitate a confident prediction. Although with an embarrassingly simple implementation, our method manifests itself in strong generalizability to various datasets and task settings. Extensive experiments suggest that our plug-in design lends itself well to a range of state-of-the-art approaches and boosts the performance on top of them.

The goal of few-shot learning is to generalize and achieve high performance on new unseen learning tasks, where each task has only a limited number of examples available. Gradient-based meta-learning attempts to address this challenging task by learning how to learn new tasks by embedding inductive biases informed by prior learning experiences into the components of the learning algorithm. In this work, we build upon prior research and propose Neural Procedural Bias Meta-Learning (NPBML), a novel framework designed to meta-learn task-adaptive procedural biases. Our approach aims to consolidate recent advancements in meta-learned initializations, optimizers, and loss functions by learning them simultaneously and making them adapt to each individual task to maximize the strength of the learned inductive biases. This imbues each learning task with a unique set of procedural biases which is specifically designed and selected to attain strong learning performance in only a few gradient steps. The experimental results show that by meta-learning the procedural biases of a neural network, we can induce strong inductive biases towards a distribution of learning tasks, enabling robust learning performance across many well-established few-shot learning benchmarks.

Diffusion models have gained traction as powerful algorithms for synthesizing high-quality images. Central to these algorithms is the diffusion process, a set of equations which maps data to noise in a way that can significantly affect performance. In this paper, we explore whether the diffusion process can be learned from data. Our work is grounded in Bayesian inference and seeks to improve log-likelihood estimation by casting the learned diffusion process as an approximate variational posterior that yields a tighter lower bound (ELBO) on the likelihood. A widely held assumption is that the ELBO is invariant to the noise process: our work dispels this assumption and proposes multivariate learned adaptive noise (MULAN), a learned diffusion process that applies noise at different rates across an image. Specifically, our method relies on a multivariate noise schedule that is a function of the data to ensure that the ELBO is no longer invariant to the choice of the noise schedule as in previous works. Empirically, MULAN sets a new state-of-the-art in density estimation on CIFAR-10 and ImageNet and reduces the number of training steps by 50%. Code is available at https://github.com/s-sahoo/MuLAN

Autoregressive models are typically applied to sequences of discrete tokens, but recent research indicates that generating sequences of continuous embeddings in an autoregressive manner is also feasible. However, such Continuous Autoregressive Models (CAMs) can suffer from a decline in generation quality over extended sequences due to error accumulation during inference. We introduce a novel method to address this issue by injecting random noise into the input embeddings during training. This procedure makes the model robust against varying error levels at inference. We further reduce error accumulation through an inference procedure that introduces low-level noise. Experiments on musical audio generation show that CAM substantially outperforms existing autoregressive and non-autoregressive approaches while preserving audio quality over extended sequences. This work paves the way for generating continuous embeddings in a purely autoregressive setting, opening new possibilities for real-time and interactive generative applications.

Stepwise inference protocols, such as scratchpads and chain-of-thought, help language models solve complex problems by decomposing them into a sequence of simpler subproblems. Despite the significant gain in performance achieved via these protocols, the underlying mechanisms of stepwise inference have remained elusive. To address this, we propose to study autoregressive Transformer models on a synthetic task that embodies the multi-step nature of problems where stepwise inference is generally most useful. Specifically, we define a graph navigation problem wherein a model is tasked with traversing a path from a start to a goal node on the graph. Despite is simplicity, we find we can empirically reproduce and analyze several phenomena observed at scale: (i) the stepwise inference reasoning gap, the cause of which we find in the structure of the training data; (ii) a diversity-accuracy tradeoff in model generations as sampling temperature varies; (iii) a simplicity bias in the model's output; and (iv) compositional generalization and a primacy bias with in-context exemplars. Overall, our work introduces a grounded, synthetic framework for studying stepwise inference and offers mechanistic hypotheses that can lay the foundation for a deeper understanding of this phenomenon.

In this study, we examine the efficacy of post-hoc local attribution methods in identifying features with predictive power from irrelevant ones in domains characterized by a low signal-to-noise ratio (SNR), a common scenario in real-world machine learning applications. We developed synthetic datasets encompassing symbolic functional, image, and audio data, incorporating a benchmark on the {\it (Model \(\times\) Attribution\(\times\) Noise Condition)} triplet. By rigorously testing various classic models trained from scratch, we gained valuable insights into the performance of these attribution methods in multiple conditions. Based on these findings, we introduce a novel extension to the notable recursive feature elimination (RFE) algorithm, enhancing its applicability for neural networks. Our experiments highlight its strengths in prediction and feature selection, alongside limitations in scalability. Further details and additional minor findings are included in the appendix, with extensive discussions. The codes and resources are available at https://github.com/geshijoker/ChaosMining/{URL}.

End-to-end learning models have demonstrated a remarkable capability in performing speech segregation. Despite their wide-scope of real-world applications, little is known about the mechanisms they employ to group and consequently segregate individual speakers. Knowing that harmonicity is a critical cue for these networks to group sources, in this work, we perform a thorough investigation on ConvTasnet and DPT-Net to analyze how they perform a harmonic analysis of the input mixture. We perform ablation studies where we apply low-pass, high-pass, and band-stop filters of varying pass-bands to empirically analyze the harmonics most critical for segregation. We also investigate how these networks decide which output channel to assign to an estimated source by introducing discontinuities in synthetic mixtures. We find that end-to-end networks are highly unstable, and perform poorly when confronted with deformations which are imperceptible to humans. Replacing the encoder in these networks with a spectrogram leads to lower overall performance, but much higher stability. This work helps us to understand what information these network rely on for speech segregation, and exposes two sources of generalization-errors. It also pinpoints the encoder as the part of the network responsible for these errors, allowing for a redesign with expert knowledge or transfer learning.

Quantum machine learning models have shown successful generalization performance even when trained with few data. In this work, through systematic randomization experiments, we show that traditional approaches to understanding generalization fail to explain the behavior of such quantum models. Our experiments reveal that state-of-the-art quantum neural networks accurately fit random states and random labeling of training data. This ability to memorize random data defies current notions of small generalization error, problematizing approaches that build on complexity measures such as the VC dimension, the Rademacher complexity, and all their uniform relatives. We complement our empirical results with a theoretical construction showing that quantum neural networks can fit arbitrary labels to quantum states, hinting at their memorization ability. Our results do not preclude the possibility of good generalization with few training data but rather rule out any possible guarantees based only on the properties of the model family. These findings expose a fundamental challenge in the conventional understanding of generalization in quantum machine learning and highlight the need for a paradigm shift in the design of quantum models for machine learning tasks.

Despite significant advancements in multi-label text classification, the ability of existing models to generalize to novel and seldom-encountered complex concepts, which are compositions of elementary ones, remains underexplored. This research addresses this gap. By creating unique data splits across three benchmarks, we assess the compositional generalization ability of existing multi-label text classification models. Our results show that these models often fail to generalize to compositional concepts encountered infrequently during training, leading to inferior performance on tests with these new combinations. To address this, we introduce a data augmentation method that leverages two innovative text generation models designed to enhance the classification models' capacity for compositional generalization. Our experiments show that this data augmentation approach significantly improves the compositional generalization capabilities of classification models on our benchmarks, with both generation models surpassing other text generation baselines.

We carry out an information-theoretical analysis of a two-layer neural network trained from input-output pairs generated by a teacher network with matching architecture, in overparametrized regimes. Our results come in the form of bounds relating i) the mutual information between training data and network weights, or ii) the Bayes-optimal generalization error, to the same quantities but for a simpler (generalized) linear model for which explicit expressions are rigorously known. Our bounds, which are expressed in terms of the number of training samples, input dimension and number of hidden units, thus yield fundamental performance limits for any neural network (and actually any learning procedure) trained from limited data generated according to our two-layer teacher neural network model. The proof relies on rigorous tools from spin glasses and is guided by ``Gaussian equivalence principles'' lying at the core of numerous recent analyses of neural networks. With respect to the existing literature, which is either non-rigorous or restricted to the case of the learning of the readout weights only, our results are information-theoretic (i.e. are not specific to any learning algorithm) and, importantly, cover a setting where all the network parameters are trained.

Neural net classifiers trained on data with annotated class labels can also capture apparent visual similarity among categories without being directed to do so. We study whether this observation can be extended beyond the conventional domain of supervised learning: Can we learn a good feature representation that captures apparent similarity among instances, instead of classes, by merely asking the feature to be discriminative of individual instances? We formulate this intuition as a non-parametric classification problem at the instance-level, and use noise-contrastive estimation to tackle the computational challenges imposed by the large number of instance classes. Our experimental results demonstrate that, under unsupervised learning settings, our method surpasses the state-of-the-art on ImageNet classification by a large margin. Our method is also remarkable for consistently improving test performance with more training data and better network architectures. By fine-tuning the learned feature, we further obtain competitive results for semi-supervised learning and object detection tasks. Our non-parametric model is highly compact: With 128 features per image, our method requires only 600MB storage for a million images, enabling fast nearest neighbour retrieval at the run time.

Despite their recent successes, Transformer-based large language models show surprising failure modes. A well-known example of such failure modes is their inability to length-generalize: solving problem instances at inference time that are longer than those seen during training. In this work, we further explore the root cause of this failure by performing a detailed analysis of model behaviors on the simple parity task. Our analysis suggests that length generalization failures are intricately related to a model's inability to perform random memory accesses within its context window. We present supporting evidence for this hypothesis by demonstrating the effectiveness of methodologies that circumvent the need for indexing or that enable random token access indirectly, through content-based addressing. We further show where and how the failure to perform random memory access manifests through attention map visualizations.

Instruction tuning -- tuning large language models on instruction-output pairs -- is a promising technique for making models better adapted to the real world. Yet, the key factors driving the model's capability to understand and follow instructions not seen during training remain under-explored. Our investigation begins with a series of synthetic experiments within the theoretical framework of a Turing-complete algorithm called Markov algorithm, which allows fine-grained control over the instruction-tuning data. Generalization and robustness with respect to the training distribution emerge once a diverse enough set of tasks is provided, even though very few examples are provided for each task. We extend these initial results to a real-world application scenario of code generation and find that a more diverse instruction set, extending beyond code-related tasks, improves the performance of code generation. Our observations suggest that a more diverse semantic space for instruction-tuning sets greatly improves the model's ability to follow instructions and perform tasks.

Large language models have evolved data-efficient generalists, benefiting from the universal language interface and large-scale pre-training. However, constructing a data-efficient generalist for dense visual prediction presents a distinct challenge due to the variation in label structures across different tasks. Consequently, generalization to unseen dense prediction tasks in the low-data regime is not straightforward and has received less attention from previous vision generalists. In this study, we explore a universal model that can flexibly adapt to unseen dense label structures with a few examples, enabling it to serve as a data-efficient vision generalist in diverse real-world scenarios. To this end, we base our method on a powerful meta-learning framework and explore several axes to improve its performance and versatility for real-world problems, such as flexible adaptation mechanisms and scalability. We evaluate our model across a spectrum of unseen real-world scenarios where low-shot learning is desirable, including video, 3D, medical, biological, and user-interactive tasks. Equipped with a generic architecture and an effective adaptation mechanism, our model flexibly adapts to all of these tasks with at most 50 labeled images, showcasing a significant advancement over existing data-efficient generalist approaches. Codes are available at https://github.com/GitGyun/chameleon.

Neural Architecture Search (NAS) has been a source of dramatic improvements in neural network design, with recent results meeting or exceeding the performance of hand-tuned architectures. However, our understanding of how to represent the search space for neural net architectures and how to search that space efficiently are both still in their infancy. We have performed an in-depth analysis to identify limitations in a widely used search space and a recent architecture search method, Differentiable Architecture Search (DARTS). These findings led us to introduce novel network blocks with a more general, balanced, and consistent design; a better-optimized Cosine Power Annealing learning rate schedule; and other improvements. Our resulting sharpDARTS search is 50% faster with a 20-30% relative improvement in final model error on CIFAR-10 when compared to DARTS. Our best single model run has 1.93% (1.98+/-0.07) validation error on CIFAR-10 and 5.5% error (5.8+/-0.3) on the recently released CIFAR-10.1 test set. To our knowledge, both are state of the art for models of similar size. This model also generalizes competitively to ImageNet at 25.1% top-1 (7.8% top-5) error. We found improvements for existing search spaces but does DARTS generalize to new domains? We propose Differentiable Hyperparameter Grid Search and the HyperCuboid search space, which are representations designed to leverage DARTS for more general parameter optimization. Here we find that DARTS fails to generalize when compared against a human's one shot choice of models. We look back to the DARTS and sharpDARTS search spaces to understand why, and an ablation study reveals an unusual generalization gap. We finally propose Max-W regularization to solve this problem, which proves significantly better than the handmade design. Code will be made available.

Applications of deep learning for audio effects often focus on modeling analog effects or learning to control effects to emulate a trained audio engineer. However, deep learning approaches also have the potential to expand creativity through neural audio effects that enable new sound transformations. While recent work demonstrated that neural networks with random weights produce compelling audio effects, control of these effects is limited and unintuitive. To address this, we introduce a method for the steerable discovery of neural audio effects. This method enables the design of effects using example recordings provided by the user. We demonstrate how this method produces an effect similar to the target effect, along with interesting inaccuracies, while also providing perceptually relevant controls.

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

Web-crawled pretraining datasets underlie the impressive "zero-shot" evaluation performance of multimodal models, such as CLIP for classification/retrieval and Stable-Diffusion for image generation. However, it is unclear how meaningful the notion of "zero-shot" generalization is for such multimodal models, as it is not known to what extent their pretraining datasets encompass the downstream concepts targeted for during "zero-shot" evaluation. In this work, we ask: How is the performance of multimodal models on downstream concepts influenced by the frequency of these concepts in their pretraining datasets? We comprehensively investigate this question across 34 models and five standard pretraining datasets (CC-3M, CC-12M, YFCC-15M, LAION-400M, LAION-Aesthetics), generating over 300GB of data artifacts. We consistently find that, far from exhibiting "zero-shot" generalization, multimodal models require exponentially more data to achieve linear improvements in downstream "zero-shot" performance, following a sample inefficient log-linear scaling trend. This trend persists even when controlling for sample-level similarity between pretraining and downstream datasets, and testing on purely synthetic data distributions. Furthermore, upon benchmarking models on long-tailed data sampled based on our analysis, we demonstrate that multimodal models across the board perform poorly. We contribute this long-tail test set as the "Let it Wag!" benchmark to further research in this direction. Taken together, our study reveals an exponential need for training data which implies that the key to "zero-shot" generalization capabilities under large-scale training paradigms remains to be found.

How well can NLP models generalize to a variety of unseen tasks when provided with task instructions? To address this question, we first introduce Super-NaturalInstructions, a benchmark of 1,616 diverse NLP tasks and their expert-written instructions. Our collection covers 76 distinct task types, including but not limited to classification, extraction, infilling, sequence tagging, text rewriting, and text composition. This large and diverse collection of tasks enables rigorous benchmarking of cross-task generalization under instructions -- training models to follow instructions on a subset of tasks and evaluating them on the remaining unseen ones. Furthermore, we build Tk-Instruct, a transformer model trained to follow a variety of in-context instructions (plain language task definitions or k-shot examples). Our experiments show that Tk-Instruct outperforms existing instruction-following models such as InstructGPT by over 9% on our benchmark despite being an order of magnitude smaller. We further analyze generalization as a function of various scaling parameters, such as the number of observed tasks, the number of instances per task, and model sizes. We hope our dataset and model facilitate future progress towards more general-purpose NLP models.

Numerous deep learning algorithms have been inspired by and understood via the notion of information bottleneck, where unnecessary information is (often implicitly) minimized while task-relevant information is maximized. However, a rigorous argument for justifying why it is desirable to control information bottlenecks has been elusive. In this paper, we provide the first rigorous learning theory for justifying the benefit of information bottleneck in deep learning by mathematically relating information bottleneck to generalization errors. Our theory proves that controlling information bottleneck is one way to control generalization errors in deep learning, although it is not the only or necessary way. We investigate the merit of our new mathematical findings with experiments across a range of architectures and learning settings. In many cases, generalization errors are shown to correlate with the degree of information bottleneck: i.e., the amount of the unnecessary information at hidden layers. This paper provides a theoretical foundation for current and future methods through the lens of information bottleneck. Our new generalization bounds scale with the degree of information bottleneck, unlike the previous bounds that scale with the number of parameters, VC dimension, Rademacher complexity, stability or robustness. Our code is publicly available at: https://github.com/xu-ji/information-bottleneck

Program synthesis methods aim to automatically generate programs restricted to a language that can explain a given specification of input-output pairs. While purely symbolic approaches suffer from a combinatorial search space, recent methods leverage neural networks to learn distributions over program structures to narrow this search space significantly, enabling more efficient search. However, for challenging problems, it remains difficult to train models to perform program synthesis in one shot, making test-time search essential. Most neural methods lack structured search mechanisms during inference, relying instead on stochastic sampling or gradient updates, which can be inefficient. In this work, we propose the Latent Program Network (LPN), a general algorithm for program induction that learns a distribution over latent programs in a continuous space, enabling efficient search and test-time adaptation. We explore how to train these networks to optimize for test-time computation and demonstrate the use of gradient-based search both during training and at test time. We evaluate LPN on ARC-AGI, a program synthesis benchmark that evaluates performance by generalizing programs to new inputs rather than explaining the underlying specification. We show that LPN can generalize beyond its training distribution and adapt to unseen tasks by utilizing test-time computation, outperforming algorithms without test-time adaptation mechanisms.

We introduce a parametric nonlinear transformation that is well-suited for Gaussianizing data from natural images. The data are linearly transformed, and each component is then normalized by a pooled activity measure, computed by exponentiating a weighted sum of rectified and exponentiated components and a constant. We optimize the parameters of the full transformation (linear transform, exponents, weights, constant) over a database of natural images, directly minimizing the negentropy of the responses. The optimized transformation substantially Gaussianizes the data, achieving a significantly smaller mutual information between transformed components than alternative methods including ICA and radial Gaussianization. The transformation is differentiable and can be efficiently inverted, and thus induces a density model on images. We show that samples of this model are visually similar to samples of natural image patches. We demonstrate the use of the model as a prior probability density that can be used to remove additive noise. Finally, we show that the transformation can be cascaded, with each layer optimized using the same Gaussianization objective, thus offering an unsupervised method of optimizing a deep network architecture.