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A major challenge to out-of-distribution generalization is reliance on spurious features -- patterns that are predictive of the class label in the training data distribution, but not causally related to the target. Standard methods for reducing the reliance on spurious features typically assume that we know what the spurious feature is, which is rarely true in the real world. Methods that attempt to alleviate this limitation are complex, hard to tune, and lead to a significant computational overhead compared to standard training. In this paper, we propose Automatic Feature Reweighting (AFR), an extremely simple and fast method for updating the model to reduce the reliance on spurious features. AFR retrains the last layer of a standard ERM-trained base model with a weighted loss that emphasizes the examples where the ERM model predicts poorly, automatically upweighting the minority group without group labels. With this simple procedure, we improve upon the best reported results among competing methods trained without spurious attributes on several vision and natural language classification benchmarks, using only a fraction of their compute., ICML 23. Code available at https://github.com/AndPotap/afr

A particularly successful class of approaches for few-shot learning combines language models with prompts -- hand-crafted task descriptions that complement data samples. However, designing prompts by hand for each task commonly requires domain knowledge and substantial guesswork. We observe, in the context of classification tasks, that instruction finetuned language models exhibit remarkable prompt robustness, and we subsequently propose a simple method to eliminate the need for handcrafted prompts, named AuT-Few. This approach consists of (i) a prompt retrieval module that selects suitable task instructions from the instruction-tuning knowledge base, and (ii) the generation of two distinct, semantically meaningful, class descriptions and a selection mechanism via cross-validation. Over $12$ datasets, spanning $8$ classification tasks, we show that AuT-Few outperforms current state-of-the-art few-shot learning methods. Moreover, AuT-Few is the best ranking method across datasets on the RAFT few-shot benchmark. Notably, these results are achieved without task-specific handcrafted prompts on unseen tasks.

Real-world data, such as administrative claims and electronic health records, are increasingly used for safety monitoring and to help guide regulatory decision-making. In these settings, it is important to document analytic decisions transparently and objectively to ensure that analyses meet their intended goals. The Causal Roadmap is an established framework that can guide and document analytic decisions through each step of the analytic pipeline, which will help investigators generate high-quality real-world evidence. In this paper, we illustrate the utility of the Causal Roadmap using two case studies previously led by workgroups sponsored by the Sentinel Initiative -- a program for actively monitoring the safety of regulated medical products. Each case example focuses on different aspects of the analytic pipeline for drug safety monitoring. The first case study shows how the Causal Roadmap encourages transparency, reproducibility, and objective decision-making for causal analyses. The second case study highlights how this framework can guide analytic decisions beyond inference on causal parameters, improving outcome ascertainment in clinical phenotyping. These examples provide a structured framework for implementing the Causal Roadmap in safety surveillance and guide transparent, reproducible, and objective analysis., 26 pages, 4 figures

Unlike conventional grid and mesh based methods for solving partial differential equations (PDEs), neural networks have the potential to break the curse of dimensionality, providing approximate solutions to problems where using classical solvers is difficult or impossible. While global minimization of the PDE residual over the network parameters works well for boundary value problems, catastrophic forgetting impairs the applicability of this approach to initial value problems (IVPs). In an alternative local-in-time approach, the optimization problem can be converted into an ordinary differential equation (ODE) on the network parameters and the solution propagated forward in time; however, we demonstrate that current methods based on this approach suffer from two key issues. First, following the ODE produces an uncontrolled growth in the conditioning of the problem, ultimately leading to unacceptably large numerical errors. Second, as the ODE methods scale cubically with the number of model parameters, they are restricted to small neural networks, significantly limiting their ability to represent intricate PDE initial conditions and solutions. Building on these insights, we develop Neural IVP, an ODE based IVP solver which prevents the network from getting ill-conditioned and runs in time linear in the number of parameters, enabling us to evolve the dynamics of challenging PDEs with neural networks., ICLR 2023. Code available at https://github.com/mfinzi/neural-ivp

Self-supervised learning, dubbed the dark matter of intelligence, is a promising path to advance machine learning. Yet, much like cooking, training SSL methods is a delicate art with a high barrier to entry. While many components are familiar, successfully training a SSL method involves a dizzying set of choices from the pretext tasks to training hyper-parameters. Our goal is to lower the barrier to entry into SSL research by laying the foundations and latest SSL recipes in the style of a cookbook. We hope to empower the curious researcher to navigate the terrain of methods, understand the role of the various knobs, and gain the know-how required to explore how delicious SSL can be.

We present Fortuna, an open-source library for uncertainty quantification in deep learning. Fortuna supports a range of calibration techniques, such as conformal prediction that can be applied to any trained neural network to generate reliable uncertainty estimates, and scalable Bayesian inference methods that can be applied to Flax-based deep neural networks trained from scratch for improved uncertainty quantification and accuracy. By providing a coherent framework for advanced uncertainty quantification methods, Fortuna simplifies the process of benchmarking and helps practitioners build robust AI systems.

A popular approach to protein design is to combine a generative model with a discriminative model for conditional sampling. The generative model samples plausible sequences while the discriminative model guides a search for sequences with high fitness. Given its broad success in conditional sampling, classifier-guided diffusion modeling is a promising foundation for protein design, leading many to develop guided diffusion models for structure with inverse folding to recover sequences. In this work, we propose diffusioN Optimized Sampling (NOS), a guidance method for discrete diffusion models that follows gradients in the hidden states of the denoising network. NOS makes it possible to perform design directly in sequence space, circumventing significant limitations of structure-based methods, including scarce data and challenging inverse design. Moreover, we use NOS to generalize LaMBO, a Bayesian optimization procedure for sequence design that facilitates multiple objectives and edit-based constraints. The resulting method, LaMBO-2, enables discrete diffusions and stronger performance with limited edits through a novel application of saliency maps. We apply LaMBO-2 to a real-world protein design task, optimizing antibodies for higher expression yield and binding affinity to a therapeutic target under locality and liability constraints, with 97% expression rate and 25% binding rate in exploratory in vitro experiments.

Bayesian optimization is a highly efficient approach to optimizing objective functions which are expensive to query. These objectives are typically represented by Gaussian process (GP) surrogate models which are easy to optimize and support exact inference. While standard GP surrogates have been well-established in Bayesian optimization, Bayesian neural networks (BNNs) have recently become practical function approximators, with many benefits over standard GPs such as the ability to naturally handle non-stationarity and learn representations for high-dimensional data. In this paper, we study BNNs as alternatives to standard GP surrogates for optimization. We consider a variety of approximate inference procedures for finite-width BNNs, including high-quality Hamiltonian Monte Carlo, low-cost stochastic MCMC, and heuristics such as deep ensembles. We also consider infinite-width BNNs and partially stochastic models such as deep kernel learning. We evaluate this collection of surrogate models on diverse problems with varying dimensionality, number of objectives, non-stationarity, and discrete and continuous inputs. We find: (i) the ranking of methods is highly problem dependent, suggesting the need for tailored inductive biases; (ii) HMC is the most successful approximate inference procedure for fully stochastic BNNs; (iii) full stochasticity may be unnecessary as deep kernel learning is relatively competitive; (iv) infinite-width BNNs are particularly promising, especially in high dimensions.

Diffusion models are a class of probabilistic generative models that have been widely used as a prior for image processing tasks like text conditional generation and inpainting. We demonstrate that these models can be adapted to make predictions and provide uncertainty quantification for chaotic dynamical systems. In these applications, diffusion models can implicitly represent knowledge about outliers and extreme events; however, querying that knowledge through conditional sampling or measuring probabilities is surprisingly difficult. Existing methods for conditional sampling at inference time seek mainly to enforce the constraints, which is insufficient to match the statistics of the distribution or compute the probability of the chosen events. To achieve these ends, optimally one would use the conditional score function, but its computation is typically intractable. In this work, we develop a probabilistic approximation scheme for the conditional score function which provably converges to the true distribution as the noise level decreases. With this scheme we are able to sample conditionally on nonlinear userdefined events at inference time, and matches data statistics even when sampling from the tails of the distribution., Comment: ICML 2023 Conference

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.

Vision transformers (ViTs) are quickly becoming the de-facto architecture for computer vision, yet we understand very little about why they work and what they learn. While existing studies visually analyze the mechanisms of convolutional neural networks, an analogous exploration of ViTs remains challenging. In this paper, we first address the obstacles to performing visualizations on ViTs. Assisted by these solutions, we observe that neurons in ViTs trained with language model supervision (e.g., CLIP) are activated by semantic concepts rather than visual features. We also explore the underlying differences between ViTs and CNNs, and we find that transformers detect image background features, just like their convolutional counterparts, but their predictions depend far less on high-frequency information. On the other hand, both architecture types behave similarly in the way features progress from abstract patterns in early layers to concrete objects in late layers. In addition, we show that ViTs maintain spatial information in all layers except the final layer. In contrast to previous works, we show that the last layer most likely discards the spatial information and behaves as a learned global pooling operation. Finally, we conduct large-scale visualizations on a wide range of ViT variants, including DeiT, CoaT, ConViT, PiT, Swin, and Twin, to validate the effectiveness of our method.

Deep neural networks are susceptible to shortcut learning, using simple features to achieve low training loss without discovering essential semantic structure. Contrary to prior belief, we show that generative models alone are not sufficient to prevent shortcut learning, despite an incentive to recover a more comprehensive representation of the data than discriminative approaches. However, we observe that shortcuts are preferentially encoded with minimal information, a fact that generative models can exploit to mitigate shortcut learning. In particular, we propose Chroma-VAE, a two-pronged approach where a VAE classifier is initially trained to isolate the shortcut in a small latent subspace, allowing a secondary classifier to be trained on the complementary, shortcut-free latent subspace. In addition to demonstrating the efficacy of Chroma-VAE on benchmark and real-world shortcut learning tasks, our work highlights the potential for manipulating the latent space of generative classifiers to isolate or interpret specific correlations., Presented at the 36th Conference on Neural Information Processing Systems (NeurIPS 2022)

While there has been progress in developing non-vacuous generalization bounds for deep neural networks, these bounds tend to be uninformative about why deep learning works. In this paper, we develop a compression approach based on quantizing neural network parameters in a linear subspace, profoundly improving on previous results to provide state-of-the-art generalization bounds on a variety of tasks, including transfer learning. We use these tight bounds to better understand the role of model size, equivariance, and the implicit biases of optimization, for generalization in deep learning. Notably, we find large models can be compressed to a much greater extent than previously known, encapsulating Occam's razor. We also argue for data-independent bounds in explaining generalization., NeurIPS 2022. Code is available at https://github.com/activatedgeek/tight-pac-bayes

Deep classifiers are known to rely on spurious features $\unicode{x2013}$ patterns which are correlated with the target on the training data but not inherently relevant to the learning problem, such as the image backgrounds when classifying the foregrounds. In this paper we evaluate the amount of information about the core (non-spurious) features that can be decoded from the representations learned by standard empirical risk minimization (ERM) and specialized group robustness training. Following recent work on Deep Feature Reweighting (DFR), we evaluate the feature representations by re-training the last layer of the model on a held-out set where the spurious correlation is broken. On multiple vision and NLP problems, we show that the features learned by simple ERM are highly competitive with the features learned by specialized group robustness methods targeted at reducing the effect of spurious correlations. Moreover, we show that the quality of learned feature representations is greatly affected by the design decisions beyond the training method, such as the model architecture and pre-training strategy. On the other hand, we find that strong regularization is not necessary for learning high quality feature representations. Finally, using insights from our analysis, we significantly improve upon the best results reported in the literature on the popular Waterbirds, CelebA hair color prediction and WILDS-FMOW problems, achieving 97%, 92% and 50% worst-group accuracies, respectively., NeurIPS 2022. Code available at https://github.com/izmailovpavel/spurious_feature_learning

Despite the clear performance benefits of data augmentations, little is known about why they are so effective. In this paper, we disentangle several key mechanisms through which data augmentations operate. Establishing an exchange rate between augmented and additional real data, we find that in out-of-distribution testing scenarios, augmentations which yield samples that are diverse, but inconsistent with the data distribution can be even more valuable than additional training data. Moreover, we find that data augmentations which encourage invariances can be more valuable than invariance alone, especially on small and medium sized training sets. Following this observation, we show that augmentations induce additional stochasticity during training, effectively flattening the loss landscape., 31 pages, 29 figures. To be presented at ICLR 2023. Code at https://github.com/JonasGeiping/dataaugs

A broad class of stochastic volatility models are defined by systems of stochastic differential equations. While these models have seen widespread success in domains such as finance and statistical climatology, they typically lack an ability to condition on historical data to produce a true posterior distribution. To address this fundamental limitation, we show how to re-cast a class of stochastic volatility models as a hierarchical Gaussian process (GP) model with specialized covariance functions. This GP model retains the inductive biases of the stochastic volatility model while providing the posterior predictive distribution given by GP inference. Within this framework, we take inspiration from well studied domains to introduce a new class of models, Volt and Magpie, that significantly outperform baselines in stock and wind speed forecasting, and naturally extend to the multitask setting., ICML 2022. Code available at https://github.com/g-benton/Volt

Recent work on deep learning for tabular data demonstrates the strong performance of deep tabular models, often bridging the gap between gradient boosted decision trees and neural networks. Accuracy aside, a major advantage of neural models is that they learn reusable features and are easily fine-tuned in new domains. This property is often exploited in computer vision and natural language applications, where transfer learning is indispensable when task-specific training data is scarce. In this work, we demonstrate that upstream data gives tabular neural networks a decisive advantage over widely used GBDT models. We propose a realistic medical diagnosis benchmark for tabular transfer learning, and we present a how-to guide for using upstream data to boost performance with a variety of tabular neural network architectures. Finally, we propose a pseudo-feature method for cases where the upstream and downstream feature sets differ, a tabular-specific problem widespread in real-world applications. Our code is available at https://github.com/LevinRoman/tabular-transfer-learning .

While low-precision optimization has been widely used to accelerate deep learning, low-precision sampling remains largely unexplored. As a consequence, sampling is simply infeasible in many large-scale scenarios, despite providing remarkable benefits to generalization and uncertainty estimation for neural networks. In this paper, we provide the first study of low-precision Stochastic Gradient Langevin Dynamics (SGLD), showing that its costs can be significantly reduced without sacrificing performance, due to its intrinsic ability to handle system noise. We prove that the convergence of low-precision SGLD with full-precision gradient accumulators is less affected by the quantization error than its SGD counterpart in the strongly convex setting. To further enable low-precision gradient accumulators, we develop a new quantization function for SGLD that preserves the variance in each update step. We demonstrate that low-precision SGLD achieves comparable performance to full-precision SGLD with only 8 bits on a variety of deep learning tasks., Published at ICML 2022

Deep learning is increasingly moving towards a transfer learning paradigm whereby large foundation models are fine-tuned on downstream tasks, starting from an initialization learned on the source task. But an initialization contains relatively little information about the source task. Instead, we show that we can learn highly informative posteriors from the source task, through supervised or self-supervised approaches, which then serve as the basis for priors that modify the whole loss surface on the downstream task. This simple modular approach enables significant performance gains and more data-efficient learning on a variety of downstream classification and segmentation tasks, serving as a drop-in replacement for standard pre-training strategies. These highly informative priors also can be saved for future use, similar to pre-trained weights, and stand in contrast to the zero-mean isotropic uninformative priors that are typically used in Bayesian deep learning., Code available at https://github.com/hsouri/BayesianTransferLearning

Neural network classifiers can largely rely on simple spurious features, such as backgrounds, to make predictions. However, even in these cases, we show that they still often learn core features associated with the desired attributes of the data, contrary to recent findings. Inspired by this insight, we demonstrate that simple last layer retraining can match or outperform state-of-the-art approaches on spurious correlation benchmarks, but with profoundly lower complexity and computational expenses. Moreover, we show that last layer retraining on large ImageNet-trained models can also significantly reduce reliance on background and texture information, improving robustness to covariate shift, after only minutes of training on a single GPU., ICLR 2023. Code is available at https://github.com/PolinaKirichenko/deep_feature_reweighting

Aleatoric uncertainty captures the inherent randomness of the data, such as measurement noise. In Bayesian regression, we often use a Gaussian observation model, where we control the level of aleatoric uncertainty with a noise variance parameter. By contrast, for Bayesian classification we use a categorical distribution with no mechanism to represent our beliefs about aleatoric uncertainty. Our work shows that explicitly accounting for aleatoric uncertainty significantly improves the performance of Bayesian neural networks. We note that many standard benchmarks, such as CIFAR, have essentially no aleatoric uncertainty. Moreover, we show data augmentation in approximate inference has the effect of softening the likelihood, leading to underconfidence and profoundly misrepresenting our honest beliefs about aleatoric uncertainty. Accordingly, we find that a cold posterior, tempered by a power greater than one, often more honestly reflects our beliefs about aleatoric uncertainty than no tempering -- providing an explicit link between data augmentation and cold posteriors. We show that we can match or exceed the performance of posterior tempering by using a Dirichlet observation model, where we explicitly control the level of aleatoric uncertainty, without any need for tempering.

Bayesian optimization (BayesOpt) is a gold standard for query-efficient continuous optimization. However, its adoption for drug design has been hindered by the discrete, high-dimensional nature of the decision variables. We develop a new approach (LaMBO) which jointly trains a denoising autoencoder with a discriminative multi-task Gaussian process head, allowing gradient-based optimization of multi-objective acquisition functions in the latent space of the autoencoder. These acquisition functions allow LaMBO to balance the explore-exploit tradeoff over multiple design rounds, and to balance objective tradeoffs by optimizing sequences at many different points on the Pareto frontier. We evaluate LaMBO on two small-molecule design tasks, and introduce new tasks optimizing \emph{in silico} and \emph{in vitro} properties of large-molecule fluorescent proteins. In our experiments LaMBO outperforms genetic optimizers and does not require a large pretraining corpus, demonstrating that BayesOpt is practical and effective for biological sequence design., ICML 2022. Code available at https://github.com/samuelstanton/lambo

How do we compare between hypotheses that are entirely consistent with observations? The marginal likelihood (aka Bayesian evidence), which represents the probability of generating our observations from a prior, provides a distinctive approach to this foundational question, automatically encoding Occam's razor. Although it has been observed that the marginal likelihood can overfit and is sensitive to prior assumptions, its limitations for hyperparameter learning and discrete model comparison have not been thoroughly investigated. We first revisit the appealing properties of the marginal likelihood for learning constraints and hypothesis testing. We then highlight the conceptual and practical issues in using the marginal likelihood as a proxy for generalization. Namely, we show how marginal likelihood can be negatively correlated with generalization, with implications for neural architecture search, and can lead to both underfitting and overfitting in hyperparameter learning. We also re-examine the connection between the marginal likelihood and PAC-Bayes bounds and use this connection to further elucidate the shortcomings of the marginal likelihood for model selection. We provide a partial remedy through a conditional marginal likelihood, which we show is more aligned with generalization, and practically valuable for large-scale hyperparameter learning, such as in deep kernel learning., Extended version. Shorter ICML version available at arXiv:2202.11678v2

Bayesian optimization is a coherent, ubiquitous approach to decision-making under uncertainty, with applications including multi-arm bandits, active learning, and black-box optimization. Bayesian optimization selects decisions (i.e. objective function queries) with maximal expected utility with respect to the posterior distribution of a Bayesian model, which quantifies reducible, epistemic uncertainty about query outcomes. In practice, subjectively implausible outcomes can occur regularly for two reasons: 1) model misspecification and 2) covariate shift. Conformal prediction is an uncertainty quantification method with coverage guarantees even for misspecified models and a simple mechanism to correct for covariate shift. We propose conformal Bayesian optimization, which directs queries towards regions of search space where the model predictions have guaranteed validity, and investigate its behavior on a suite of black-box optimization tasks and tabular ranking tasks. In many cases we find that query coverage can be significantly improved without harming sample-efficiency., Comment: For code, see https://www.github.com/samuelstanton/conformal-bayesopt.git

As we move away from the data, the predictive uncertainty should increase, since a great variety of explanations are consistent with the little available information. We introduce Distance-Aware Prior (DAP) calibration, a method to correct overconfidence of Bayesian deep learning models outside of the training domain. We define DAPs as prior distributions over the model parameters that depend on the inputs through a measure of their distance from the training set. DAP calibration is agnostic to the posterior inference method, and it can be performed as a post-processing step. We demonstrate its effectiveness against several baselines in a variety of classification and regression problems, including benchmarks designed to test the quality of predictive distributions away from the data.

Sharpness-Aware Minimization (SAM) has recently emerged as a robust technique for improving the accuracy of deep neural networks. However, SAM incurs a high computational cost in practice, requiring up to twice as much computation as vanilla SGD. The computational challenge posed by SAM arises because each iteration requires both ascent and descent steps and thus double the gradient computations. To address this challenge, we propose to compute gradients in both stages of SAM on only the top-k samples with highest loss. K-SAM is simple and extremely easy-to-implement while providing significant generalization boosts over vanilla SGD at little to no additional cost., Comment: 13 pages, 2 figures

Low-precision arithmetic has had a transformative effect on the training of neural networks, reducing computation, memory and energy requirements. However, despite its promise, low-precision arithmetic has received little attention for Gaussian processes (GPs), largely because GPs require sophisticated linear algebra routines that are unstable in low-precision. We study the different failure modes that can occur when training GPs in half precision. To circumvent these failure modes, we propose a multi-faceted approach involving conjugate gradients with re-orthogonalization, mixed precision, and preconditioning. Our approach significantly improves the numerical stability and practical performance of conjugate gradients in low-precision over a wide range of settings, enabling GPs to train on $1.8$ million data points in $10$ hours on a single GPU, without any sparse approximations., Comment: UAI 2022. Code available at https://github.com/AndPotap/halfpres_gps

The ability to jointly learn from multiple modalities, such as text, audio, and visual data, is a defining feature of intelligent systems. While there have been promising advances in designing neural networks to harness multimodal data, the enormous success of data augmentation currently remains limited to single-modality tasks like image classification. Indeed, it is particularly difficult to augment each modality while preserving the overall semantic structure of the data; for example, a caption may no longer be a good description of an image after standard augmentations have been applied, such as translation. Moreover, it is challenging to specify reasonable transformations that are not tailored to a particular modality. In this paper, we introduce LeMDA, Learning Multimodal Data Augmentation, an easy-to-use method that automatically learns to jointly augment multimodal data in feature space, with no constraints on the identities of the modalities or the relationship between modalities. We show that LeMDA can (1) profoundly improve the performance of multimodal deep learning architectures, (2) apply to combinations of modalities that have not been previously considered, and (3) achieve state-of-the-art results on a wide range of applications comprised of image, text, and tabular data., Comment: ICLR 2023. Code available at https://github.com/lzcemma/LeMDA/

Equivariance guarantees that a model's predictions capture key symmetries in data. When an image is translated or rotated, an equivariant model's representation of that image will translate or rotate accordingly. The success of convolutional neural networks has historically been tied to translation equivariance directly encoded in their architecture. The rising success of vision transformers, which have no explicit architectural bias towards equivariance, challenges this narrative and suggests that augmentations and training data might also play a significant role in their performance. In order to better understand the role of equivariance in recent vision models, we introduce the Lie derivative, a method for measuring equivariance with strong mathematical foundations and minimal hyperparameters. Using the Lie derivative, we study the equivariance properties of hundreds of pretrained models, spanning CNNs, transformers, and Mixer architectures. The scale of our analysis allows us to separate the impact of architecture from other factors like model size or training method. Surprisingly, we find that many violations of equivariance can be linked to spatial aliasing in ubiquitous network layers, such as pointwise non-linearities, and that as models get larger and more accurate they tend to display more equivariance, regardless of architecture. For example, transformers can be more equivariant than convolutional neural networks after training.

While recent work on conjugate gradient methods and Lanczos decompositions have achieved scalable Gaussian process inference with highly accurate point predictions, in several implementations these iterative methods appear to struggle with numerical instabilities in learning kernel hyperparameters, and poor test likelihoods. By investigating CG tolerance, preconditioner rank, and Lanczos decomposition rank, we provide a particularly simple prescription to correct these issues: we recommend that one should use a small CG tolerance ($\epsilon \leq 0.01$) and a large root decomposition size ($r \geq 5000$). Moreover, we show that L-BFGS-B is a compelling optimizer for Iterative GPs, achieving convergence with fewer gradient updates., Comment: ICML 2021 OPTML Workshop

Learning new tasks continuously without forgetting on a constantly changing data distribution is essential for real-world problems but extremely challenging for modern deep learning. In this work we propose HCL, a Hybrid generative-discriminative approach to Continual Learning for classification. We model the distribution of each task and each class with a normalizing flow. The flow is used to learn the data distribution, perform classification, identify task changes, and avoid forgetting, all leveraging the invertibility and exact likelihood which are uniquely enabled by the normalizing flow model. We use the generative capabilities of the flow to avoid catastrophic forgetting through generative replay and a novel functional regularization technique. For task identification, we use state-of-the-art anomaly detection techniques based on measuring the typicality of the model's statistics. We demonstrate the strong performance of HCL on a range of continual learning benchmarks such as split-MNIST, split-CIFAR, and SVHN-MNIST.

Approximate Bayesian inference for neural networks is considered a robust alternative to standard training, often providing good performance on out-of-distribution data. However, Bayesian neural networks (BNNs) with high-fidelity approximate inference via full-batch Hamiltonian Monte Carlo achieve poor generalization under covariate shift, even underperforming classical estimation. We explain this surprising result, showing how a Bayesian model average can in fact be problematic under covariate shift, particularly in cases where linear dependencies in the input features cause a lack of posterior contraction. We additionally show why the same issue does not affect many approximate inference procedures, or classical maximum a-posteriori (MAP) training. Finally, we propose novel priors that improve the robustness of BNNs to many sources of covariate shift., NeurIPS 2021. Code is available at https://github.com/izmailovpavel/bnn_covariate_shift

State-of-the-art methods for scalable Gaussian processes use iterative algorithms, requiring fast matrix vector multiplies (MVMs) with the covariance kernel. The Structured Kernel Interpolation (SKI) framework accelerates these MVMs by performing efficient MVMs on a grid and interpolating back to the original space. In this work, we develop a connection between SKI and the permutohedral lattice used for high-dimensional fast bilateral filtering. Using a sparse simplicial grid instead of a dense rectangular one, we can perform GP inference exponentially faster in the dimension than SKI. Our approach, Simplex-GP, enables scaling SKI to high dimensions, while maintaining strong predictive performance. We additionally provide a CUDA implementation of Simplex-GP, which enables significant GPU acceleration of MVM based inference., International Conference on Machine Learning (ICML), 2021

With a better understanding of the loss surfaces for multilayer networks, we can build more robust and accurate training procedures. Recently it was discovered that independently trained SGD solutions can be connected along one-dimensional paths of near-constant training loss. In this paper, we show that there are mode-connecting simplicial complexes that form multi-dimensional manifolds of low loss, connecting many independently trained models. Inspired by this discovery, we show how to efficiently build simplicial complexes for fast ensembling, outperforming independently trained deep ensembles in accuracy, calibration, and robustness to dataset shift. Notably, our approach only requires a few training epochs to discover a low-loss simplex, starting from a pre-trained solution. Code is available at https://github.com/g-benton/loss-surface-simplexes., ICML 2021

There is often a trade-off between building deep learning systems that are expressive enough to capture the nuances of the reality, and having the right inductive biases for efficient learning. We introduce Residual Pathway Priors (RPPs) as a method for converting hard architectural constraints into soft priors, guiding models towards structured solutions, while retaining the ability to capture additional complexity. Using RPPs, we construct neural network priors with inductive biases for equivariances, but without limiting flexibility. We show that RPPs are resilient to approximate or misspecified symmetries, and are as effective as fully constrained models even when symmetries are exact. We showcase the broad applicability of RPPs with dynamical systems, tabular data, and reinforcement learning. In Mujoco locomotion tasks, where contact forces and directional rewards violate strict equivariance assumptions, the RPP outperforms baseline model-free RL agents, and also improves the learned transition models for model-based RL., Comment: NeurIPS 2021. Code available at https://github.com/mfinzi/residual-pathway-priors

We introduce a new scalable variational Gaussian process approximation which provides a high fidelity approximation while retaining general applicability. We propose the harmonic kernel decomposition (HKD), which uses Fourier series to decompose a kernel as a sum of orthogonal kernels. Our variational approximation exploits this orthogonality to enable a large number of inducing points at a low computational cost. We demonstrate that, on a range of regression and classification problems, our approach can exploit input space symmetries such as translations and reflections, and it significantly outperforms standard variational methods in scalability and accuracy. Notably, our approach achieves state-of-the-art results on CIFAR-10 among pure GP models., Comment: ICML2021, 21 pages

The inductive biases of trained neural networks are difficult to understand and, consequently, to adapt to new settings. We study the inductive biases of linearizations of neural networks, which we show to be surprisingly good summaries of the full network functions. Inspired by this finding, we propose a technique for embedding these inductive biases into Gaussian processes through a kernel designed from the Jacobian of the network. In this setting, domain adaptation takes the form of interpretable posterior inference, with accompanying uncertainty estimation. This inference is analytic and free of local optima issues found in standard techniques such as fine-tuning neural network weights to a new task. We develop significant computational speed-ups based on matrix multiplies, including a novel implementation for scalable Fisher vector products. Our experiments on both image classification and regression demonstrate the promise and convenience of this framework for transfer learning, compared to neural network fine-tuning. Code is available at https://github.com/amzn/xfer/tree/master/finite_ntk., Comment: AISTATS 2021

With a principled representation of uncertainty and closed form posterior updates, Gaussian processes (GPs) are a natural choice for online decision making. However, Gaussian processes typically require at least $\mathcal{O}(n^2)$ computations for $n$ training points, limiting their general applicability. Stochastic variational Gaussian processes (SVGPs) can provide scalable inference for a dataset of fixed size, but are difficult to efficiently condition on new data. We propose online variational conditioning (OVC), a procedure for efficiently conditioning SVGPs in an online setting that does not require re-training through the evidence lower bound with the addition of new data. OVC enables the pairing of SVGPs with advanced look-ahead acquisition functions for black-box optimization, even with non-Gaussian likelihoods. We show OVC provides compelling performance in a range of applications including active learning of malaria incidence, and reinforcement learning on MuJoCo simulated robotic control tasks., Comment: NeurIPS 2021

Existing methods in estimating the mean outcome under a given dynamic treatment regime rely on intention-to-treat analyses which estimate the effect of following a certain dynamic treatment regime regardless of compliance behavior of patients. There are two major concerns with intention-to-treat analyses: (1) the estimated effects are often biased toward the null effect; (2) the results are not generalizable and reproducible due to the potential differential compliance behavior. These are particularly problematic in settings with high level of non-compliance such as substance use disorder treatments. Our work is motivated by the Adaptive Treatment for Alcohol and Cocaine Dependence study (ENGAGE), which is a multi-stage trial that aimed to construct optimal treatment strategies to engage patients in therapy. Due to the relatively low level of compliance in this trial, intention-to-treat analyses essentially estimate the effect of being randomized to a certain treatment sequence which is not of interest. We fill this important gap by defining the target parameter as the mean outcome under a dynamic treatment regime given potential compliance strata. We propose a flexible non-parametric Bayesian approach, which consists of a Gaussian copula model for the potential compliances, and a Dirichlet process mixture model for the potential outcomes. Our simulations highlight the need for and usefulness of this approach in practice and illustrate the robustness of our estimator in non-linear and non-Gaussian settings.

The posterior over Bayesian neural network (BNN) parameters is extremely high-dimensional and non-convex. For computational reasons, researchers approximate this posterior using inexpensive mini-batch methods such as mean-field variational inference or stochastic-gradient Markov chain Monte Carlo (SGMCMC). To investigate foundational questions in Bayesian deep learning, we instead use full-batch Hamiltonian Monte Carlo (HMC) on modern architectures. We show that (1) BNNs can achieve significant performance gains over standard training and deep ensembles; (2) a single long HMC chain can provide a comparable representation of the posterior to multiple shorter chains; (3) in contrast to recent studies, we find posterior tempering is not needed for near-optimal performance, with little evidence for a "cold posterior" effect, which we show is largely an artifact of data augmentation; (4) BMA performance is robust to the choice of prior scale, and relatively similar for diagonal Gaussian, mixture of Gaussian, and logistic priors; (5) Bayesian neural networks show surprisingly poor generalization under domain shift; (6) while cheaper alternatives such as deep ensembles and SGMCMC methods can provide good generalization, they provide distinct predictive distributions from HMC. Notably, deep ensemble predictive distributions are similarly close to HMC as standard SGLD, and closer than standard variational inference.

Knowledge distillation is a popular technique for training a small student network to emulate a larger teacher model, such as an ensemble of networks. We show that while knowledge distillation can improve student generalization, it does not typically work as it is commonly understood: there often remains a surprisingly large discrepancy between the predictive distributions of the teacher and the student, even in cases when the student has the capacity to perfectly match the teacher. We identify difficulties in optimization as a key reason for why the student is unable to match the teacher. We also show how the details of the dataset used for distillation play a role in how closely the student matches the teacher -- and that more closely matching the teacher paradoxically does not always lead to better student generalization., Comment: NeurIPS 2021. Code available at https://github.com/samuelstanton/gnosis

Reasoning about the physical world requires models that are endowed with the right inductive biases to learn the underlying dynamics. Recent works improve generalization for predicting trajectories by learning the Hamiltonian or Lagrangian of a system rather than the differential equations directly. While these methods encode the constraints of the systems using generalized coordinates, we show that embedding the system into Cartesian coordinates and enforcing the constraints explicitly with Lagrange multipliers dramatically simplifies the learning problem. We introduce a series of challenging chaotic and extended-body systems, including systems with N-pendulums, spring coupling, magnetic fields, rigid rotors, and gyroscopes, to push the limits of current approaches. Our experiments show that Cartesian coordinates with explicit constraints lead to a 100x improvement in accuracy and data efficiency., NeurIPS 2020. Code available at https://github.com/mfinzi/constrained-hamiltonian-neural-networks

Invariances to translations have imbued convolutional neural networks with powerful generalization properties. However, we often do not know a priori what invariances are present in the data, or to what extent a model should be invariant to a given symmetry group. We show how to \emph{learn} invariances and equivariances by parameterizing a distribution over augmentations and optimizing the training loss simultaneously with respect to the network parameters and augmentation parameters. With this simple procedure we can recover the correct set and extent of invariances on image classification, regression, segmentation, and molecular property prediction from a large space of augmentations, on training data alone., NeurIPS 2020. Code available at https://github.com/g-benton/learning-invariances

Detecting out-of-distribution (OOD) data is crucial for robust machine learning systems. Normalizing flows are flexible deep generative models that often surprisingly fail to distinguish between in- and out-of-distribution data: a flow trained on pictures of clothing assigns higher likelihood to handwritten digits. We investigate why normalizing flows perform poorly for OOD detection. We demonstrate that flows learn local pixel correlations and generic image-to-latent-space transformations which are not specific to the target image dataset. We show that by modifying the architecture of flow coupling layers we can bias the flow towards learning the semantic structure of the target data, improving OOD detection. Our investigation reveals that properties that enable flows to generate high-fidelity images can have a detrimental effect on OOD detection., Code is available at https://github.com/PolinaKirichenko/flows_ood

Neural networks appear to have mysterious generalization properties when using parameter counting as a proxy for complexity. Indeed, neural networks often have many more parameters than there are data points, yet still provide good generalization performance. Moreover, when we measure generalization as a function of parameters, we see double descent behaviour, where the test error decreases, increases, and then again decreases. We show that many of these properties become understandable when viewed through the lens of effective dimensionality, which measures the dimensionality of the parameter space determined by the data. We relate effective dimensionality to posterior contraction in Bayesian deep learning, model selection, width-depth tradeoffs, double descent, and functional diversity in loss surfaces, leading to a richer understanding of the interplay between parameters and functions in deep models. We also show that effective dimensionality compares favourably to alternative norm- and flatness- based generalization measures.

The key distinguishing property of a Bayesian approach is marginalization, rather than using a single setting of weights. Bayesian marginalization can particularly improve the accuracy and calibration of modern deep neural networks, which are typically underspecified by the data, and can represent many compelling but different solutions. We show that deep ensembles provide an effective mechanism for approximate Bayesian marginalization, and propose a related approach that further improves the predictive distribution by marginalizing within basins of attraction, without significant overhead. We also investigate the prior over functions implied by a vague distribution over neural network weights, explaining the generalization properties of such models from a probabilistic perspective. From this perspective, we explain results that have been presented as mysterious and distinct to neural network generalization, such as the ability to fit images with random labels, and show that these results can be reproduced with Gaussian processes. We also show that Bayesian model averaging alleviates double descent, resulting in monotonic performance improvements with increased flexibility. Finally, we provide a Bayesian perspective on tempering for calibrating predictive distributions., 31 pages, 19 figures

For over a decade, model-based reinforcement learning has been seen as a way to leverage control-based domain knowledge to improve the sample-efficiency of reinforcement learning agents. While model-based agents are conceptually appealing, their policies tend to lag behind those of model-free agents in terms of final reward, especially in non-trivial environments. In response, researchers have proposed model-based agents with increasingly complex components, from ensembles of probabilistic dynamics models, to heuristics for mitigating model error. In a reversal of this trend, we show that simple model-based agents can be derived from existing ideas that not only match, but outperform state-of-the-art model-free agents in terms of both sample-efficiency and final reward. We find that a model-free soft value estimate for policy evaluation and a model-based stochastic value gradient for policy improvement is an effective combination, achieving state-of-the-art results on a high-dimensional humanoid control task, which most model-based agents are unable to solve. Our findings suggest that model-based policy evaluation deserves closer attention., Comment: L4DC 2021

The translation equivariance of convolutional layers enables convolutional neural networks to generalize well on image problems. While translation equivariance provides a powerful inductive bias for images, we often additionally desire equivariance to other transformations, such as rotations, especially for non-image data. We propose a general method to construct a convolutional layer that is equivariant to transformations from any specified Lie group with a surjective exponential map. Incorporating equivariance to a new group requires implementing only the group exponential and logarithm maps, enabling rapid prototyping. Showcasing the simplicity and generality of our method, we apply the same model architecture to images, ball-and-stick molecular data, and Hamiltonian dynamical systems. For Hamiltonian systems, the equivariance of our models is especially impactful, leading to exact conservation of linear and angular momentum., Comment: ICML 2020. Code available at https://github.com/mfinzi/LieConv

The key distinguishing property of a Bayesian approach is marginalization instead of optimization, not the prior, or Bayes rule. Bayesian inference is especially compelling for deep neural networks. (1) Neural networks are typically underspecified by the data, and can represent many different but high performing models corresponding to different settings of parameters, which is exactly when marginalization will make the biggest difference for both calibration and accuracy. (2) Deep ensembles have been mistaken as competing approaches to Bayesian methods, but can be seen as approximate Bayesian marginalization. (3) The structure of neural networks gives rise to a structured prior in function space, which reflects the inductive biases of neural networks that help them generalize. (4) The observed correlation between parameters in flat regions of the loss and a diversity of solutions that provide good generalization is further conducive to Bayesian marginalization, as flat regions occupy a large volume in a high dimensional space, and each different solution will make a good contribution to a Bayesian model average. (5) Recent practical advances for Bayesian deep learning provide improvements in accuracy and calibration compared to standard training, while retaining scalability.

Despite success on a wide range of problems related to vision, generative adversarial networks (GANs) often suffer from inferior performance due to unstable training, especially for text generation. To solve this issue, we propose a new variational GAN training framework which enjoys superior training stability. Our approach is inspired by a connection of GANs and reinforcement learning under a variational perspective. The connection leads to (1) probability ratio clipping that regularizes generator training to prevent excessively large updates, and (2) a sample re-weighting mechanism that improves discriminator training by downplaying bad-quality fake samples. Moreover, our variational GAN framework can provably overcome the training issue in many GANs that an optimal discriminator cannot provide any informative gradient to training generator. By plugging the training approach in diverse state-of-the-art GAN architectures, we obtain significantly improved performance over a range of tasks, including text generation, text style transfer, and image generation., Comment: NeurIPS 2020 camera ready version (citations updated)