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 $\textit{the interplay between memorization and generalization}$, 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 $\textit{memorization-aware training}$ (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.

Tokenization imposes a fixed granularity on the input text, freezing how a language model operates on data and how far in the future it predicts. Byte Pair Encoding (BPE) and similar schemes split text once, build a static vocabulary, and leave the model stuck with that choice. We relax this rigidity by introducing an autoregressive U-Net that learns to embed its own tokens as it trains. The network reads raw bytes, pools them into words, then pairs of words, then up to 4 words, giving it a multi-scale view of the sequence. At deeper stages, the model must predict further into the future -- anticipating the next few words rather than the next byte -- so deeper stages focus on broader semantic patterns while earlier stages handle fine details. When carefully tuning and controlling pretraining compute, shallow hierarchies tie strong BPE baselines, and deeper hierarchies have a promising trend. Because tokenization now lives inside the model, the same system can handle character-level tasks and carry knowledge across low-resource languages.

Two lines of work are taking the central stage in AI research. On the one hand, the community is making increasing efforts to build models that discard spurious correlations and generalize better in novel test environments. Unfortunately, the hard lesson so far is that no proposal convincingly outperforms a simple empirical risk minimization baseline. On the other hand, large language models (LLMs) have erupted as algorithms able to learn in-context, generalizing on-the-fly to eclectic contextual circumstances that users enforce by means of prompting. In this paper, we argue that context is environment, and posit that in-context learning holds the key to better domain generalization. Via extensive theory and experiments, we show that paying attention to context$\unicode{x2013}\unicode{x2013}$unlabeled examples as they arrive$\unicode{x2013}\unicode{x2013}$allows our proposed In-Context Risk Minimization (ICRM) algorithm to zoom-in on the test environment risk minimizer, leading to significant out-of-distribution performance improvements. Furthermore, training with context helps the model learn a better featurizer. From all of this, two messages are worth taking home. Researchers in domain generalization should consider environment as context, and harness the adaptive power of in-context learning. Researchers in LLMs should consider context as environment, to better structure data towards generalization. Code is available at https://github.com/facebookresearch/ICRM.

Large language models such as GPT and Llama are trained with a next-token prediction loss. In this work, we suggest that training language models to predict multiple future tokens at once results in higher sample efficiency. More specifically, at each position in the training corpus, we ask the model to predict the following $n$ tokens using $n$ independent output heads, operating on top of a shared model trunk. Considering multi-token prediction as an auxiliary training task, we measure improved downstream capabilities with no overhead in training time for both code and natural language models. The method is increasingly useful for larger model sizes, and keeps its appeal when training for multiple epochs. Gains are especially pronounced on generative benchmarks like coding, where our models consistently outperform strong baselines by several percentage points. Our 13B parameter models solves 12% more problems on Human Eval and 17% more on MBPP than comparable next-token models. Experiments on small algorithmic tasks demonstrate that multi-token prediction is favorable for the development of induction heads and algorithmic reasoning capabilities. As an additional benefit, models trained with 4-token prediction are up to $3\times$ faster at inference, even with large batch sizes.

Environment annotations are essential for the success of many out-of-distribution (OOD) generalization methods. Unfortunately, these are costly to obtain and often limited by human annotators’ biases. To achieve robust generalization, it is essential to develop algorithms for automatic environment discovery within datasets. Current proposals, which divide examples based on their training error, suffer from one fundamental problem. These methods introduce hyper-parameters and early-stopping criteria, which require a validation set with human-annotated environments, the very information subject to discovery. In this paper, we propose Cross-Risk Minimization (XRM) to address this issue. XRM trains twin networks, each learning from one random half of the training data, while imitating confident held-out mistakes made by its sibling. XRM provides a recipe for hyper-parameter tuning, does not require early-stopping, and can discover environments for all training and validation data. Algorithms built on top of XRM environments achieve oracle worst-group-accuracy, addressing a long-standing challenge in OOD generalization.

When facing data with imbalanced classes or groups, practitioners follow an intriguing strategy to achieve best results. They throw away examples until the classes or groups are balanced in size, and then perform empirical risk minimization on the reduced training set. This opposes common wisdom in learning theory, where the expected error is supposed to decrease as the dataset grows in size. In this work, we leverage extreme value theory to address this apparent contradiction. Our results show that the tails of the data distribution play an important role in determining the worst-group-accuracy of linear classifiers. When learning on data with heavy tails, throwing away data restores the geometric symmetry of the resulting classifier, and therefore improves its worst-group generalization.

Foundation models are redefining how AI systems are built. Practitioners now follow a standard procedure to build their machine learning solutions: from a pre-trained foundation model, they fine-tune the weights on the target task of interest. So, the Internet is swarmed by a handful of foundation models fine-tuned on many diverse tasks: these individual fine-tunings exist in isolation without benefiting from each other. In our opinion, this is a missed opportunity, as these specialized models contain rich and diverse features. In this paper, we thus propose model ratatouille, a new strategy to recycle the multiple fine-tunings of the same foundation model on diverse auxiliary tasks. Specifically, we repurpose these auxiliary weights as initializations for multiple parallel fine-tunings on the target task; then, we average all fine-tuned weights to obtain the final model. This recycling strategy aims at maximizing the diversity in weights by leveraging the diversity in auxiliary tasks. Empirically, it improves the state of the art on the reference DomainBed benchmark for out-of-distribution generalization. Looking forward, this work contributes to the emerging paradigm of updatable machine learning where, akin to open-source software development, the community collaborates to reliably update machine learning models.

There often is a dilemma between ease of optimization and robust out-of-distribution (OoD) generalization. For instance, many OoD methods rely on penalty terms whose optimization is challenging. They are either too strong to optimize reliably or too weak to achieve their goals. We propose to initialize the networks with a rich representation containing a palette of potentially useful features, ready to be used by even simple models. On the one hand, a rich representation provides a good initialization for the optimizer. On the other hand, it also provides an inductive bias that helps OoD generalization. Such a representation is constructed with the Rich Feature Construction (RFC) algorithm, also called the Bonsai algorithm, which consists of a succession of training episodes. During discovery episodes, we craft a multi-objective optimization criterion and its associated datasets in a manner that prevents the network from using the features constructed in the previous iterations. During synthesis episodes, we use knowledge distillation to force the network to simultaneously represent all the previously discovered features. Initializing the networks with Bonsai representations consistently helps six OoD methods achieve top performance on ColoredMNIST benchmark. The same technique substantially outperforms comparable results on the Wilds Camelyon17 task, eliminates the high result variance that plagues other methods, and makes hyperparameter tuning and model selection more reliable.

A new causal discovery method, Structural Agnostic Modeling (SAM), is presented in this paper. Leveraging both conditional independencies and distributional asymmetries, SAM aims to find the underlying causal structure from observational data. The approach is based on a game between different players estimating each variable distribution conditionally to the others as a neural net, and an adversary aimed at discriminating the generated data against the original data. A learning criterion combining distribution estimation, sparsity and acyclicity constraints is used to enforce the optimization of the graph structure and parameters through stochastic gradient descent. SAM is extensively experimentally validated on synthetic and real data.

We introduce Interpolation Consistency Training (ICT), a simple and computation efficient algorithm for training Deep Neural Networks in the semi-supervised learning paradigm. ICT encourages the prediction at an interpolation of unlabeled points to be consistent with the interpolation of the predictions at those points. In classification problems, ICT moves the decision boundary to low-density regions of the data distribution. Our experiments show that ICT achieves state-of-the-art performance when applied to standard neural network architectures on the CIFAR-10 and SVHN benchmark datasets. Our theoretical analysis shows that ICT corresponds to a certain type of data-adaptive regularization with unlabeled points which reduces overfitting to labeled points under high confidence values.

In continual learning, the learner faces a stream of data whose distribution changes over time. Modern neural networks are known to suffer under this setting, as they quickly forget previously acquired knowledge. To address such catastrophic forgetting, many continual learning methods implement different types of experience replay, re-learning on past data stored in a small buffer known as episodic memory. In this work, we complement experience replay with a new objective that we call ``anchoring'', where the learner uses bilevel optimization to update its knowledge on the current task, while keeping intact the predictions on some anchor points of past tasks. These anchor points are learned using gradient-based optimization to maximize forgetting, which is approximated by fine-tuning the currently trained model on the episodic memory of past tasks. Experiments on several supervised learning benchmarks for continual learning demonstrate that our approach improves the standard experience replay in terms of both accuracy and forgetting metrics and for various sizes of episodic memory.

Recent work demonstrates that deep neural networks trained using Empirical Risk Minimization (ERM) can generalize under distribution shift, outperforming specialized training algorithms for domain generalization. The goal of this paper is to further understand this phenomenon. In particular, we study the extent to which the seminal domain adaptation theory of Ben-David et al. (2007) explains the performance of ERMs. Perhaps surprisingly, we find that this theory does not provide a tight explanation of the out-of-domain generalization observed across a large number of ERM models trained on three popular domain generalization datasets. This motivates us to investigate other possible measures—that, however, lack theory—which could explain generalization in this setting. Our investigation reveals that measures relating to the Fisher information, predictive entropy, and maximum mean discrepancy are good predictors of the out-of-distribution generalization of ERM models. We hope that our work helps galvanize the community towards building a better understanding of when deep networks trained with ERM generalize out-of-distribution.

Over the past few years, neural networks were proven vulnerable to adversarial images: targeted but imperceptible image perturbations lead to drastically different predictions. We show that adversarial vulnerability increases with the gradients of the training objective when viewed as a function of the inputs. Surprisingly, vulnerability does not depend on network topology: for many standard network architectures, we prove that at initialization, the L1-norm of these gradients grows as the square root of the input dimension, leaving the networks increasingly vulnerable with growing image size. We empirically show that this dimension-dependence persists after either usual or robust training, but gets attenuated with higher regularization.

Deep neural networks excel at learning the training data, but often provide incorrect and confident predictions when evaluated on slightly different test examples. This includes distribution shifts, outliers, and adversarial examples. To address these issues, we propose \manifoldmixup{}, a simple regularizer that encourages neural networks to predict less confidently on interpolations of hidden representations. \manifoldmixup{} leverages semantic interpolations as additional training signal, obtaining neural networks with smoother decision boundaries at multiple levels of representation. As a result, neural networks trained with \manifoldmixup{} learn flatter class-representations, that is, with fewer directions of variance. We prove theory on why this flattening happens under ideal conditions, validate it empirically on practical situations, and connect it to the previous works on information theory and generalization. In spite of incurring no significant computation and being implemented in a few lines of code, \manifoldmixup{} improves strong baselines in supervised learning, robustness to single-step adversarial attacks, and test log-likelihood.

We introduce the Neural Conditioner (NC), a self-supervised machine able to learn about all the conditional distributions of a random vector X. The NC is a function NC(x⋅a,a,r) that leverages adversarial training to match each conditional distribution P(Xr|Xa=xa). After training, the NC generalizes to sample from conditional distributions never seen, including the joint distribution. The NC is also able to auto-encode examples, providing data representations useful for downstream classification tasks. In sum, the NC integrates different self-supervised tasks (each being the estimation of a conditional distribution) and levels of supervision (partially observed data) seamlessly into a single learning experience.

We provide single-model estimates of aleatoric and epistemic uncertainty for deep neural networks. To estimate aleatoric uncertainty, we propose Simultaneous Quantile Regression (SQR), a loss function to learn all the conditional quantiles of a given target variable. These quantiles can be used to compute well-calibrated prediction intervals. To estimate epistemic uncertainty, we propose Orthonormal Certificates (OCs), a collection of diverse non-constant functions that map all training samples to zero. These certificates map out-of-distribution examples to non-zero values, signaling epistemic uncertainty. Our uncertainty estimators are computationally attractive, as they do not require ensembling or retraining deep models, and achieve state-of-the-art performance.

Generative Adversarial Networks (GANs) have achieved remarkable results in the task of generating realistic natural images. In most successful applications, GAN models share two common aspects: solving a challenging saddle point optimization problem, interpreted as an adversarial game between a generator and a discriminator functions; and parameterizing the generator and the discriminator as deep convolutional neural networks. The goal of this paper is to disentangle the contribution of these two factors to the success of GANs. In particular, we introduce Generative Latent Optimization (GLO), a framework to train deep convolutional generators using simple reconstruction losses. Throughout a variety of experiments, we show that GLO enjoys many of the desirable properties of GANs: synthesizing visually-appealing samples, interpolating meaningfully between samples, and performing linear arithmetic with noise vectors; all of this without the adversarial optimization scheme.

This paper establishes the existence of observable footprints that reveal the causal dispositions of the object categories appearing in collections of images. We achieve this goal in two steps. First, we take a learning approach to observational causal discovery, and build a classifier that achieves state-of-the-art performance on finding the causal direction between pairs of random variables, given samples from their joint distribution. Second, we use our causal direction classifier to effectively distinguish between features of objects and features of their contexts in collections of static images. Our experiments demonstrate the existence of a relation between the direction of causality and the difference between objects and their contexts, and by the same token, the existence of observable signals that reveal the causal dispositions of objects.

One major obstacle towards AI is the poor ability of models to solve new problems quicker, and without forgetting previously acquired knowledge. To better understand this issue, we study the problem of continual learning, where the model observes, once and one by one, examples concerning a sequence of tasks. First, we propose a set of metrics to evaluate models learning over a continuum of data. These metrics characterize models not only by their test accuracy, but also in terms of their ability to transfer knowledge across tasks. Second, we propose a model for continual learning, called Gradient Episodic Memory (GEM) that alleviates forgetting, while allowing beneficial transfer of knowledge to previous tasks. Our experiments on variants of the MNIST and CIFAR-100 datasets demonstrate the strong performance of GEM when compared to the state-of-the-art.

Algorithms for hyperparameter optimization abound, all of which work well under different and often unverifiable assumptions. Motivated by the general challenge of sequentially choosing which algorithm to use, we study the more specific task of choosing among distributions to use for random hyperparameter optimization. This work is naturally framed in the extreme bandit setting, which deals with sequentially choosing which distribution from a collection to sample in order to minimize (maximize) the single best cost (reward). Whereas the distributions in the standard bandit setting are primarily characterized by their means, a number of subtleties arise when we care about the minimal cost as opposed to the average cost. For example, there may not be a well-defined “best” distribution as there is in the standard bandit setting. The best distribution depends on the rewards that have been obtained and on the remaining time horizon. Whereas in the standard bandit setting, it is sensible to compare policies with an oracle which plays the single best arm, in the extreme bandit setting, there are multiple sensible oracle models. We define a sensible notion of “extreme regret” in the extreme bandit setting, which parallels the concept of regret in the standard bandit setting. We then prove that no policy can asymptotically achieve no extreme regret.

We provide theoretical and empirical evidence for a type of asymmetry between causes and effects that is present when these are related via linear models contaminated with additive non- Gaussian noise. Assuming that the causes and the effects have the same distribution, we show that the distribution of the residuals of a linear fit in the anti-causal direction is closer to a Gaussian than the distribution of the residuals in the causal direction. This Gaussianization effect is characterized by reduction of the magnitude of the high-order cumulants and by an increment of the differential entropy of the residuals. The problem of non-linear causal inference is addressed by performing an embedding in an expanded feature space, in which the relation between causes and effects can be assumed to be linear. The effectiveness of a method to discriminate between causes and effects based on this type of asymmetry is illustrated in a variety of experiments using different measures of Gaussianity. The proposed method is shown to be competitive with state-of-the-art techniques for causal inference.

We pose causal inference as the problem of learning to classify probability distributions. In particular, we assume access to a collection {(S_i,l_i)}_i=1^n, where each S_i is a sample drawn from the probability distribution of X_i \times Y_i, and l_i is a binary label indicating whether “X_i \to Y_i” or “X_i ←Y_i”. Given these data, we build a causal inference rule in two steps. First, we featurize each S_i using the kernel mean embedding associated with some characteristic kernel. Second, we train a binary classifier on such embeddings to distinguish between causal directions. We present generalization bounds showing the statistical consistency and learning rates of the proposed approach, and provide a simple implementation that achieves state-of-the-art cause-effect inference. Furthermore, we extend our ideas to infer causal relationships between more than two variables.

Classical methods such as Principal Component Analysis (PCA) and Canonical Correlation Analysis (CCA) are ubiquitous in statistics. However, these techniques are only able to reveal linear relationships in data. Although nonlinear variants of PCA and CCA have been proposed, these are computationally prohibitive in the large scale. In a separate strand of recent research, randomized methods have been proposed to construct features that help reveal nonlinear patterns in data. For basic tasks such as regression or classification, random features exhibit little or no loss in performance, while achieving drastic savings in computational requirements. In this paper we leverage randomness to design scalable new variants of nonlinear PCA and CCA; our ideas extend to key multivariate analysis tools such as spectral clustering or LDA. We demonstrate our algorithms through experiments on real-world data, on which we compare against the state-of-the-art. A simple R implementation of the presented algorithms is provided.

Copulas allow to learn marginal distributions separately from the multivariate dependence structure (copula) that links them together into a density function. Vine factorizations ease the learning of high-dimensional copulas by constructing a hierarchy of conditional bivariate copulas. However, to simplify inference, it is common to assume that each of these conditional bivariate copulas is independent from its conditioning variables. In this paper, we relax this assumption by discovering the latent functions that specify the shape of a conditional copula given its conditioning variables. We learn these functions by following a Bayesian approach based on sparse Gaussian processes with expectation propagation for scalable, approximate inference. Experiments on real-world datasets show that, when modeling all conditional dependencies, we obtain better estimates of the underlying copula of the data.

We introduce the Randomized Dependence Coefficient (RDC), a measure of non-linear dependence between random variables of arbitrary dimension based on the Hirschfeld-Gebelein-Rényi Maximum Correlation Coefficient. RDC is defined in terms of correlation of random non-linear copula projections; it is invariant with respect to marginal distribution transformations, has low computational cost and is easy to implement: just five lines of R code, included at the end of the paper.

A new framework based on the theory of copulas is proposed to address semi-supervised domain adaptation problems. The presented method factorizes any multivariate density into a product of marginal distributions and bivariate copula functions. Therefore, changes in each of these factors can be detected and corrected to adapt a density model across different learning domains. Importantly, we introduce a novel vine copula model, which allows for this factorization in a non-parametric manner. Experimental results on regression problems with real-world data illustrate the efficacy of the proposed approach when compared to state-of-the-art techniques.