We introduce a gradient-based learning method to automatically adapt Markov chain Monte Carlo (MCMC) proposal distributions to intractable targets. We define a maximum entropy regularised objective function, referred to as generalised speed measure, which can be robustly optimised over the parameters of the proposal distribution by applying stochastic gradient optimisation. An advantage of our method compared to traditional adaptive MCMC methods is that the adaptation occurs even when candidate state values are rejected. This is a highly desirable property of any adaptation strategy because the adaptation starts in early iterations even if the initial proposal distribution is far from optimum. We apply the framework for learning multivariate random walk Metropolis and Metropolis-adjusted Langevin proposals with full covariance matrices, and provide empirical evidence that our method can outperform other MCMC algorithms, including Hamiltonian Monte Carlo schemes.

Multiple Instance Learning (MIL) is widely used in medical imaging classification to reduce the labeling effort. While only bag labels are available for training, one typically seeks predictions at both bag and instance levels (classification and localization tasks, respectively). Early MIL methods treated the instances in a bag independently. Recent methods account for global and local dependencies among instances. Although they have yielded excellent results in classification, their performance in terms of localization is comparatively limited.

Wide neural networks with random weights and biases are Gaussian processes, as originally observed by Neal (1995) and more recently by Lee et al. (2018) and Matthews et al. (2018) for deep fully-connected networks, as well as by Novak et al. (2019) and Garriga-Alonso et al. (2019) for deep convolutional networks. We show that this Neural Network-Gaussian Process correspondence surprisingly extends to all modern feedforward or recurrent neural networks composed of multilayer perceptron, RNNs (e.g. LSTMs, GRUs), (nD or graph) convolution, pooling, skip connection, attention, batch normalization, and/or layer normalization. More generally, we introduce a language for expressing neural network computations, and our result encompasses all such expressible neural networks. This work serves as a tutorial on the tensor programs technique formulated in Yang (2019) and elucidates the Gaussian Process results obtained there.

We investigate the mathematical capabilities of two versions of ChatGPT (released 9-January-2023 and 30-January-2023) and of GPT-4 by testing them on publicly available datasets, as well as hand-crafted ones, using a novel evaluation scheme. In contrast to formal mathematics, where large databases of formal proofs are available (e.g., mathlib, the Lean Mathematical Library), current datasets of natural-language mathematics used to benchmark language models either cover only elementary mathematics or are very small. We address this by publicly releasing two new datasets: GHOSTS and miniGHOSTS. These are the first natural-language datasets curated by working researchers in mathematics that (1) aim to cover graduate-level mathematics, (2) provide a holistic overview of the mathematical capabilities of language models, and (3) distinguish multiple dimensions of mathematical reasoning. These datasets test, by using 1636 human expert evaluations, whether ChatGPT and GPT-4 can be helpful assistants to professional mathematicians by emulating use cases that arise in the daily professional activities of mathematicians.

Models for student reading performance can empower educators and institutions to proactively identify at-risk students, thereby enabling early and tailored instructional interventions. However, there are no suitable publicly available educational datasets for modeling and predicting future reading performance. In this work, we introduce the Enhanced Core Reading Instruction (ECRI) dataset, a novel largescale longitudinal tabular dataset collected across 44 schools with 6,916 students and 172 teachers. We leverage the dataset to empirically evaluate the ability of state-of-the-art machine learning models to recognize early childhood educational patterns in multivariate and partial measurements. Specifically, we demonstrate a simple self-supervised strategy in which a Multi-Layer Perception (MLP) network is pre-trained over masked inputs to outperform several strong baselines while generalizing over diverse educational settings. To facilitate future developments in precise modeling and responsible use of models for individualized and early intervention strategies, our data and code are available at https://ecri-data.github.io/.

All prior results suffer from at least one of the two obstacles: the curse of multiple agents and the barrier of long horizon, regardless of the sampling protocol in use. We take a step towards settling this problem, assuming access to a flexible sampling mechanism: the generative model. Focusing on non-stationary finite-horizon Markov games, we develop a fast learning algorithm called Q-FTRL and an adaptive sampling scheme that leverage the optimism principle in online adversarial learning (particularly the Follow-the-Regularized-Leader (FTRL) method).

Energy based models (EBMs) are appealing due to their generality and simplicity in likelihood modeling, but have been traditionally difficult to train. We present techniques to scale MCMC based EBM training on continuous neural networks, and we show its success on the high-dimensional data domains of ImageNet32x32, ImageNet128x128, CIFAR-10, and robotic hand trajectories, achieving better samples than other likelihood models and nearing the performance of contemporary GAN approaches, while covering all modes of the data. We highlight some unique capabilities of implicit generation such as compositionality and corrupt image reconstruction and inpainting. Finally, we show that EBMs are useful models across a wide variety of tasks, achieving state-of-the-art out-of-distribution classification, adversarially robust classification, state-of-the-art continual online class learning, and coherent long term predicted trajectory rollouts.

Neural Information Processing Systems http://nips.cc/