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Hamiltonian Monte Carlo is a widely used algorithm for sampling from posterior distributions of complex Bayesian models. It can efficiently explore high-dimensional parameter spaces guided by simulated Hamiltonian flows. However, the…

Recently, purpose-built analog hardware that can efficiently minimize the Ising energy and thereby solve a variety of combinatorial optimization problems has been receiving widespread attention. In this work, we show how multidimensional,…

Despite achieving remarkable success in various domains, recent studies have uncovered the vulnerability of deep neural networks to adversarial perturbations, creating concerns on model generalizability and new threats such as…

Recursive neural networks (RNN) and their recently proposed extension recursive long short term memory networks (RLSTM) are models that compute representations for sentences, by recursively combining word embeddings according to an…

To understand how neural networks process information, it is important to investigate how neural network dynamics varies with respect to different stimuli. One challenging task is to design efficient statistical approaches to analyze…

A number of recent papers have provided evidence that practical design questions about neural networks may be tackled theoretically by studying the behavior of random networks. However, until now the tools available for analyzing random…

Classical or quantum physical systems can simulate the Ising Hamiltonian for large-scale optimization and machine learning. However, devices such as quantum annealers and coherent Ising machines suffer an exponential drop in the probability…

Efficient sampling and approximation of Boltzmann distributions involving large sets of binary variables, or spins, are pivotal in diverse scientific fields even beyond physics. Recent advances in generative neural networks have…

Modern applications have made ubiquitous high-dimensional data, especially time-dependent data, with more and more complicated structures, and it also has become more frequent to encounter the scenario of hierarchical relationships among…

Modeling quantum many-body systems is enormously challenging due to the exponential scaling of Hilbert dimension with system size. Finding efficient compressions of the wavefunction is key to building scalable models. Here, we introduce…

Social networks as a representation of relational data, often possess multiple types of dependency structures at the same time. There could be clustering (beyond homophily) at a macro level as well as transitivity (a friend's friend is more…

Random projections are able to perform dimension reduction efficiently for datasets with nonlinear low-dimensional structures. One well-known example is that random matrices embed sparse vectors into a low-dimensional subspace nearly…

We develop deep autoregressive networks with multi channels to compute many-body systems with \emph{continuous} spin degrees of freedom directly. As a concrete example, we embed the two-dimensional XY model into the continuous-mixture…

Tensor network methods provide a scalable solution to represent high-dimensional data. However, their efficacy is often limited by static, expert-defined structures that fail to adapt to evolving data correlations. We address this…

Deep reinforcement learning has achieved many impressive results in recent years. However, tasks with sparse rewards or long horizons continue to pose significant challenges. To tackle these important problems, we propose a general…

We extend recurrent neural networks to include several flexible timescales for each dimension of their output, which mechanically improves their abilities to account for processes with long memory or with highly disparate time scales. We…

Neural networks, a central tool in machine learning, have demonstrated remarkable, high fidelity performance on image recognition and classification tasks. These successes evince an ability to accurately represent high dimensional…

Neural networks have seen limited use in prediction for high-dimensional data with small sample sizes, because they tend to overfit and require tuning many more hyperparameters than existing off-the-shelf machine learning methods. With…

Variational tensor network optimization has become a powerful tool for studying classical statistical models in two dimensions. However, its application to three-dimensional systems remains limited, primarily due to the high computational…

The field of neuroscience and the development of artificial neural networks (ANNs) have mutually influenced each other, drawing from and contributing to many concepts initially developed in statistical mechanics. Notably, Hopfield networks…