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We propose a method to construct a tensor network representation of partition functions without singular value decompositions nor series expansions. The approach is demonstrated for one- and two-dimensional Ising models and we study the…
In the study of condensed matter physics, spectral information plays an important role for understand the mechanism of materials. However, it is difficult to obtain the spectrum directly through experiments or simulation. For example, the…
Spectral methods are widely used in geometry processing of 3D models. They rely on the projection of the mesh geometry on the basis defined by the eigenvectors of the graph Laplacian operator, becoming computationally prohibitive as the…
Trajectory optimization using a learned model of the environment is one of the core elements of model-based reinforcement learning. This procedure often suffers from exploiting inaccuracies of the learned model. We propose to regularize…
We study identifiability of stochastic differential equations (SDE) under multiple interventions. Our results give the first provable bounds for unique recovery of SDE parameters given samples from their stationary distributions. We give…
Interest in higher-order tensors has recently surged in data-intensive fields, with a wide range of applications including image processing, blind source separation, community detection, and feature extraction. A common paradigm in…
In this paper, we consider a compressed sensing problem of reconstructing a sparse signal from an undersampled set of noisy linear measurements. The regularized least squares or least absolute shrinkage and selection operator (LASSO)…
This work considers a computationally and statistically efficient parameter estimation method for a wide class of latent variable models---including Gaussian mixture models, hidden Markov models, and latent Dirichlet allocation---which…
This paper provides a unified framework for analyzing tensor estimation problems that allow for nonlinear observations, heteroskedastic noise, and covariate information. We study a general class of high-dimensional models where each…
Deep equilibrium networks (DEQs) are a promising way to construct models which trade off memory for compute. However, theoretical understanding of these models is still lacking compared to traditional networks, in part because of the…
The continuous improvements on image compression with variational autoencoders have lead to learned codecs competitive with conventional approaches in terms of rate-distortion efficiency. Nonetheless, taking the quantization into account…
We study model-based end-to-end learning in the context of integrated sensing and communication (ISAC) under hardware impairments. Hardware impairments are usually addressed by means of array calibration with a focus on communication…
Factorized layers--operations parameterized by products of two or more matrices--occur in a variety of deep learning contexts, including compressed model training, certain types of knowledge distillation, and multi-head self-attention…
Many idealized problems in signal processing, machine learning and statistics can be reduced to the problem of finding the symmetric canonical decomposition of an underlying symmetric and orthogonally decomposable (SOD) tensor. Drawing…
Several key questions remain unanswered regarding overparameterized learning models. It is unclear how (stochastic) gradient descent finds solutions that generalize well, and in particular the role of small random initializations. Matrix…
Incorporating geometric inductive biases into models can aid interpretability and generalization, but encoding to a specific geometric structure can be challenging due to the imposed topological constraints. In this paper, we theoretically…
Unforeseen particle accelerator interruptions, also known as interlocks, lead to abrupt operational changes despite being necessary safety measures. These may result in substantial loss of beam time and perhaps even equipment damage. We…
Most of machine learning deals with vector parameters. Ideally we would like to take higher order information into account and make use of matrix or even tensor parameters. However the resulting algorithms are usually inefficient. Here we…
We initiate a formal study of reproducibility in optimization. We define a quantitative measure of reproducibility of optimization procedures in the face of noisy or error-prone operations such as inexact or stochastic gradient computations…
Signal recovery from nonlinear measurements involves solving an iterative optimization problem. In this paper, we present a framework to optimize the sensing parameters to improve the quality of the signal recovered by the given iterative…