A Generative Model of Symmetry Transformations

Correctly capturing the symmetry transformations of data can lead to efficient models with strong generalization capabilities, though methods incorporating symmetries often require prior knowledge. While recent advancements have been made in learning those symmetries directly from the dataset, most of this work has focused on the discriminative setting. In this paper, we construct a generative model that explicitly aims to capture symmetries in the data, resulting in a model that learns which symmetries are present in an interpretable way. We provide a simple algorithm for efficiently learning our generative model and demonstrate its ability to capture symmetries under affine and color transformations. Combining our symmetry model with existing generative models results in higher marginal test-log-likelihoods and robustness to data sparsification.

Stochastic Gradient Descent for Gaussian Processes Done Right

We study the optimisation problem associated with Gaussian process regression using squared loss. The most common approach to this problem is to apply an exact solver, such as conjugate gradient descent, either directly, or to a reduced-order version of the problem. Recently, driven by successes in deep learning, stochastic gradient descent has gained traction as an alternative. In this paper, we show that when done right$\unicode{x2014}$by which we mean using specific insights from the optimisation and kernel communities$\unicode{x2014}$this approach is highly effective. We thus introduce a particular stochastic dual gradient descent algorithm, that may be implemented with a few lines of code using any deep learning framework. We explain our design decisions by illustrating their advantage against alternatives with ablation studies and show that the new method is highly competitive. Our evaluations on standard regression benchmarks and a Bayesian optimisation task set our approach apart from preconditioned conjugate gradients, variational Gaussian process approximations, and a previous version of stochastic gradient descent for Gaussian processes. On a molecular binding affinity prediction task, our method places Gaussian process regression on par in terms of performance with state-of-the-art graph neural networks.

Sampling from Gaussian Process Posteriors using Stochastic Gradient Descent

Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to conditioning. We explore stochastic gradient algorithms as a computationally efficient method of approximately solving these linear systems: we develop low-variance optimization objectives for sampling from the posterior and extend these to inducing points. Counterintuitively, stochastic gradient descent often produces accurate predictions, even in cases where it does not converge quickly to the optimum. We explain this through a spectral characterization of the implicit bias from non-convergence. We show that stochastic gradient descent produces predictive distributions close to the true posterior both in regions with sufficient data coverage, and in regions sufficiently far away from the data. Experimentally, stochastic gradient descent achieves state-of-the-art performance on sufficiently large-scale or ill-conditioned regression tasks. Its uncertainty estimates match the performance of significantly more expensive baselines on a large-scale Bayesian~optimization~task.

Kernel Regression with Infinite-Width Neural Networks on Millions of Examples

Neural kernels have drastically increased performance on diverse and nonstandard data modalities but require significantly more compute, which previously limited their application to smaller datasets. In this work, we address this by massively parallelizing their computation across many GPUs. We combine this with a distributed, preconditioned conjugate gradients algorithm to enable kernel regression at a large scale (i.e. up to five million examples). Using this approach, we study scaling laws of several neural kernels across many orders of magnitude for the CIFAR-5m dataset. Using data augmentation to expand the original CIFAR-10 training dataset by a factor of 20, we obtain a test accuracy of 91.2\% (SotA for a pure kernel method). Moreover, we explore neural kernels on other data modalities, obtaining results on protein and small molecule prediction tasks that are competitive with SotA methods.

Sampling-based inference for large linear models, with application to linearised Laplace

Large-scale linear models are ubiquitous throughout machine learning, with contemporary application as surrogate models for neural network uncertainty quantification; that is, the linearised Laplace method. Alas, the computational cost associated with Bayesian linear models constrains this method's application to small networks, small output spaces and small datasets. We address this limitation by introducing a scalable sample-based Bayesian inference method for conjugate Gaussian multi-output linear models, together with a matching method for hyperparameter (regularisation) selection. Furthermore, we use a classic feature normalisation method (the g-prior) to resolve a previously highlighted pathology of the linearised Laplace method. Together, these contributions allow us to perform linearised neural network inference with ResNet-18 on CIFAR100 (11M parameters, 100 output dimensions x 50k datapoints) and with a U-Net on a high-resolution tomographic reconstruction task (2M parameters, 251k output dimensions).

A Simple Approach to Improve Single-Model Deep Uncertainty via Distance-Awareness

Accurate uncertainty quantification is a major challenge in deep learning, as neural networks can make overconfident errors and assign high confidence predictions to out-of-distribution (OOD) inputs. The most popular approaches to estimate predictive uncertainty in deep learning are methods that combine predictions from multiple neural networks, such as Bayesian neural networks (BNNs) and deep ensembles. However their practicality in real-time, industrial-scale applications are limited due to the high memory and computational cost. Furthermore, ensembles and BNNs do not necessarily fix all the issues with the underlying member networks. In this work, we study principled approaches to improve uncertainty property of a single network, based on a single, deterministic representation. By formalizing the uncertainty quantification as a minimax learning problem, we first identify distance awareness, i.e., the model's ability to quantify the distance of a testing example from the training data, as a necessary condition for a DNN to achieve high-quality (i.e., minimax optimal) uncertainty estimation. We then propose Spectral-normalized Neural Gaussian Process (SNGP), a simple method that improves the distance-awareness ability of modern DNNs with two simple changes: (1) applying spectral normalization to hidden weights to enforce bi-Lipschitz smoothness in representations and (2) replacing the last output layer with a Gaussian process layer. On a suite of vision and language understanding benchmarks, SNGP outperforms other single-model approaches in prediction, calibration and out-of-domain detection. Furthermore, SNGP provides complementary benefits to popular techniques such as deep ensembles and data augmentation, making it a simple and scalable building block for probabilistic deep learning. Code is open-sourced at https://github.com/google/uncertainty-baselines

A Simple Fix to Mahalanobis Distance for Improving Near-OOD Detection

Mahalanobis distance (MD) is a simple and popular post-processing method for detecting out-of-distribution (OOD) inputs in neural networks. We analyze its failure modes for near-OOD detection and propose a simple fix called relative Mahalanobis distance (RMD) which improves performance and is more robust to hyperparameter choice. On a wide selection of challenging vision, language, and biology OOD benchmarks (CIFAR-100 vs CIFAR-10, CLINC OOD intent detection, Genomics OOD), we show that RMD meaningfully improves upon MD performance (by up to 15% AUROC on genomics OOD).

Uncertainty Baselines: Benchmarks for Uncertainty & Robustness in Deep Learning

High-quality estimates of uncertainty and robustness are crucial for numerous real-world applications, especially for deep learning which underlies many deployed ML systems. The ability to compare techniques for improving these estimates is therefore very important for research and practice alike. Yet, competitive comparisons of methods are often lacking due to a range of reasons, including: compute availability for extensive tuning, incorporation of sufficiently many baselines, and concrete documentation for reproducibility. In this paper we introduce Uncertainty Baselines: high-quality implementations of standard and state-of-the-art deep learning methods on a variety of tasks. As of this writing, the collection spans 19 methods across 9 tasks, each with at least 5 metrics. Each baseline is a self-contained experiment pipeline with easily reusable and extendable components. Our goal is to provide immediate starting points for experimentation with new methods or applications. Additionally we provide model checkpoints, experiment outputs as Python notebooks, and leaderboards for comparing results. Code available at https://github.com/google/uncertainty-baselines.

Evaluating Prediction-Time Batch Normalization for Robustness under Covariate Shift

Covariate shift has been shown to sharply degrade both predictive accuracy and the calibration of uncertainty estimates for deep learning models. This is worrying, because covariate shift is prevalent in a wide range of real world deployment settings. However, in this paper, we note that frequently there exists the potential to access small unlabeled batches of the shifted data just before prediction time. This interesting observation enables a simple but surprisingly effective method which we call prediction-time batch normalization, which significantly improves model accuracy and calibration under covariate shift. Using this one line code change, we achieve state-of-the-art on recent covariate shift benchmarks and an mCE of 60.28\% on the challenging ImageNet-C dataset; to our knowledge, this is the best result for any model that does not incorporate additional data augmentation or modification of the training pipeline. We show that prediction-time batch normalization provides complementary benefits to existing state-of-the-art approaches for improving robustness (e.g. deep ensembles) and combining the two further improves performance. Our findings are supported by detailed measurements of the effect of this strategy on model behavior across rigorous ablations on various dataset modalities. However, the method has mixed results when used alongside pre-training, and does not seem to perform as well under more natural types of dataset shift, and is therefore worthy of additional study. We include links to the data in our figures to improve reproducibility, including a Python notebooks that can be run to easily modify our analysis at https://colab.research.google.com/drive/11N0wDZnMQQuLrRwRoumDCrhSaIhkqjof.

Revisiting One-vs-All Classifiers for Predictive Uncertainty and Out-of-Distribution Detection in Neural Networks

Accurate estimation of predictive uncertainty in modern neural networks is critical to achieve well calibrated predictions and detect out-of-distribution (OOD) inputs. The most promising approaches have been predominantly focused on improving model uncertainty (e.g. deep ensembles and Bayesian neural networks) and post-processing techniques for OOD detection (e.g. ODIN and Mahalanobis distance). However, there has been relatively little investigation into how the parametrization of the probabilities in discriminative classifiers affects the uncertainty estimates, and the dominant method, softmax cross-entropy, results in misleadingly high confidences on OOD data and under covariate shift. We investigate alternative ways of formulating probabilities using (1) a one-vs-all formulation to capture the notion of "none of the above", and (2) a distance-based logit representation to encode uncertainty as a function of distance to the training manifold. We show that one-vs-all formulations can improve calibration on image classification tasks, while matching the predictive performance of softmax without incurring any additional training or test-time complexity.