Partial differential equations (PDEs) play a central role in the mathematical analysis and modeling of complex dynamic processes across all corners of science and engineering. Their solution often requires laborious analytical or computational tools, associated with a cost that is markedly amplified when different scenarios need to be investigated, for example, corresponding to different initial …

In this paper, we introduce the \textit{Layer-Peeled Model}, a nonconvex yet analytically tractable optimization program, in a quest to better understand deep neural networks that are trained for a sufficiently long time. As the name suggests, this new model is derived by isolating the topmost layer from the remainder of the neural network, followed by imposing certain constraints separately on …

Time series anomaly detection has been a perennially important topic in data science, with papers dating back to the 1950s. However, in recent years there has been an explosion of interest in this topic, much of it driven by the success of deep learning in other domains and for other time series tasks. Most of these papers test on one or more of a handful of popular benchmark datasets, created by …

Real world decision making problems often involve both discrete and continuous variables and require a combination of probabilistic and deterministic knowledge. Stimulated by recent advances in automated reasoning technology, hybrid (discrete+continuous) probabilistic reasoning with constraints has emerged as a lively and fast growing research field. In this paper we provide a survey of existing …

While improving prediction accuracy has been the focus of machine learning in recent years, this alone does not suffice for reliable decision-making. Deploying learning systems in consequential settings also requires calibrating and communicating the uncertainty of predictions. To convey instance-wise uncertainty for prediction tasks, we show how to generate set-valued predictions from a black-box …

A learning algorithm A trained on a dataset D is revealed to have poor performance on some subpopulation at test time. Where should the responsibility for this lay? It can be argued that the data is responsible, if for example training A on a more representative dataset D' would have improved the performance. But it can similarly be argued that A itself is at fault, if training a different variant …

The Bayesian paradigm has the potential to solve core issues of deep neural networks such as poor calibration and data inefficiency. Alas, scaling Bayesian inference to large weight spaces often requires restrictive approximations. In this work, we show that it suffices to perform inference over a small subset of model weights in order to obtain accurate predictive posteriors. The other weights …

State-of-the-art computer vision systems are trained to predict a fixed set of predetermined object categories. This restricted form of supervision limits their generality and usability since additional labeled data is needed to specify any other visual concept. Learning directly from raw text about images is a promising alternative which leverages a much broader source of supervision. We …

Self-supervised learning (SSL) is rapidly closing the gap with supervised methods on large computer vision benchmarks. A successful approach to SSL is to learn embeddings which are invariant to distortions of the input sample. However, a recurring issue with this approach is the existence of trivial constant solutions. Most current methods avoid such solutions by careful implementation details. We …

Deep generative models (DGMs) seem a natural fit for detecting out-of-distribution (OOD) inputs, but such models have been shown to assign higher probabilities or densities to OOD images than images from the training distribution. In this work, we explain why this behavior should be attributed to model misestimation. We first prove that no method can guarantee performance beyond random chance …

We present Brax, an open source library for rigid body simulation with a focus on performance and parallelism on accelerators, written in JAX. We present results on a suite of tasks inspired by the existing reinforcement learning literature, but remade in our engine. Additionally, we provide reimplementations of PPO, SAC, ES, and direct policy optimization in JAX that compile alongside our …

Deep neural networks that yield human interpretable decisions by architectural design have lately become an increasingly popular alternative to post hoc interpretation of traditional black-box models. Among these networks, the arguably most widespread approach is so-called prototype learning, where similarities to learned latent prototypes serve as the basis of classifying an unseen data point. In …

There has been a recent resurgence of interest in explainable artificial intelligence (XAI) that aims to reduce the opaqueness of AI-based decision-making systems, allowing humans to scrutinize and trust them. Prior work in this context has focused on the attribution of responsibility for an algorithm's decisions to its inputs wherein responsibility is typically approached as a purely …

It is well-known that standard neural networks, even with a high classification accuracy, are vulnerable to small $\ell_\infty$-norm bounded adversarial perturbations. Although many attempts have been made, most previous works either can only provide empirical verification of the defense to a particular attack method, or can only develop a certified guarantee of the model robustness in limited …

Many of the recent triumphs in machine learning are dependent on well-tuned hyperparameters. This is particularly prominent in reinforcement learning (RL) where a small change in the configuration can lead to failure. Despite the importance of tuning hyperparameters, it remains expensive and is often done in a naive and laborious way. A recent solution to this problem is Population Based Training …

Kyle is a python library that contains utilities for measuring and visualizing calibration of probabilistic classifiers as well as for recalibrating them. Kyle is model agnostic. It also offers support for developing and testing custom calibration metrics and algorithms via custom samplers based on fake classifiers. These samplers can also be fit on an arbitrary data set (the outputs of a …

Despite great progress in simulating multiphysics problems using the numerical discretization of partial differential equations (PDEs), one still cannot seamlessly incorporate noisy data into existing algorithms, mesh generation remains complex, and high-dimensional problems governed by parameterized PDEs cannot be tackled. Moreover, solving inverse problems with hidden physics is often …

The prevalent approach to problems of credit assignment in machine learning — such as feature and data valuation— is to model the problem at hand as a cooperative game and apply the Shapley value. But cooperative game theory offers a rich menu of alternative solution concepts, which famously includes the core and its variants. Our goal is to challenge the machine learning community’s current …

With machine learning models being increasingly used to aid decision making even in high-stakes domains, there has been a growing interest in developing interpretable models. Although many supposedly interpretable models have been proposed, there have been relatively few experimental studies investigating whether these models achieve their intended effects, such as making people more closely …

Reinforcement learning (RL) provides an appealing formalism for learning control policies from experience. However, the classic active formulation of RL necessitates a lengthy active exploration process for each behavior, making it difficult to apply in real-world settings such as robotic control. If we can instead allow RL algorithms to effectively use previously collected data to aid the online …

Adversarial training is one of the most effective approaches defending against adversarial examples for deep learning models. Unlike other defense strategies, adversarial training aims to promote the robustness of models intrinsically. During the last few years, adversarial training has been studied and discussed from various aspects. A variety of improvements and developments of adversarial …

Density estimation is among the most fundamental problems in statistics. It is notoriously difficult to estimate the density of high-dimensional data due to the “curse of dimensionality.” Here, we introduce a new general-purpose density estimator based on deep generative neural networks. By modeling data normally distributed around a manifold of reduced dimension, we show how the power of …

Recent advances in probabilistic modelling have led to a large number of simulation-based inference algorithms which do not require numerical evaluation of likelihoods. However, a public benchmark with appropriate performance metrics for such 'likelihood-free' algorithms has been lacking. This has made it difficult to compare algorithms and identify their strengths and weaknesses. We set out to …

We consider the problem of estimating an object's physical properties such as mass, friction, and elasticity directly from video sequences. Such a system identification problem is fundamentally ill-posed due to the loss of information during image formation. Current solutions require precise 3D labels which are labor-intensive to gather, and infeasible to create for many systems such as deformable …

Cross-validation is a widely-used technique to estimate prediction error, but its behavior is complex and not fully understood. Ideally, one would like to think that cross-validation estimates the prediction error for the model at hand, fit to the training data. We prove that this is not the case for the linear model fit by ordinary least squares; rather it estimates the average prediction error …

The reliability of machine learning models can be compromised when trained on low quality data. Many large-scale medical imaging datasets contain low quality labels extracted from sources such as medical reports. Moreover, images within a dataset may have heterogeneous quality due to artifacts and biases arising from equipment or measurement errors. Therefore, algorithms that can automatically …

The generalized Gauss-Newton (GGN) approximation is often used to make practical Bayesian deep learning approaches scalable by replacing a second order derivative with a product of first order derivatives. In this paper we argue that the GGN approximation should be understood as a local linearization of the underlying Bayesian neural network (BNN), which turns the BNN into a generalized linear …

Distributional data Shapley value (DShapley) has recently been proposed as a principled framework to quantify the contribution of individual datum in machine learning. DShapley develops the founda...

We revisit g-modeling empirical Bayes in the absence of a tractable likelihood function, as is typical in scientific domains relying on computer simulations. We investigate how the empirical Bayesian can make use of neural density estimators first to use all noise-corrupted observations to estimate a prior or source distribution over uncorrupted samples, and then to perform single-observation …

Deep neural networks (DNNs) have achieved state-of-the-art performance in many important domains, including medical diagnosis, security, and autonomous driving. In domains where safety is highly critical, an erroneous decision can result in serious consequences. While a perfect prediction accuracy is not always achievable, recent work on Bayesian deep networks shows that it is possible to know …