Related papers: AMP-Inspired Deep Networks for Sparse Linear Inver…

Compressed sensing (CS) deals with the problem of reconstructing a sparse vector from an under-determined set of observations. Approximate message passing (AMP) is a technique used in CS based on iterative thresholding and inspired by…

Approximate Message Passing (AMP) is an efficient iterative parameter-estimation technique for certain high-dimensional linear systems with non-Gaussian distributions, such as sparse systems. In AMP, a so-called Onsager term is added to…

Deep neural networks have been applied successfully to a wide variety of inverse problems arising in computational imaging. These networks are typically trained using a forward model that describes the measurement process to be inverted,…

We show how fitting sparse linear models over learned deep feature representations can lead to more debuggable neural networks. These networks remain highly accurate while also being more amenable to human interpretation, as we demonstrate…

In this paper, we focus on the matching recovery problem between a pair of correlated Gaussian Wigner matrices with a latent vertex correspondence. We are particularly interested in a robust version of this problem such that our observation…

Recently, Approximate Message Passing (AMP) has been integrated with stochastic localization (diffusion model) by providing a computationally efficient estimator of the posterior mean. Existing (rigorous) analysis typically proves the…

We propose a tensor generalized approximate message passing (TeG-AMP) algorithm for low-rank tensor inference, which can be used to solve tensor completion and decomposition problems. We derive TeG-AMP algorithm as an approximation of the…

This paper addresses the reconstruction of an unknown signal vector with sublinear sparsity from generalized linear measurements. Generalized approximate message-passing (GAMP) is proposed via state evolution in the sublinear sparsity…

Neuromorphic hardware tends to pose limits on the connectivity of deep networks that one can run on them. But also generic hardware and software implementations of deep learning run more efficiently for sparse networks. Several methods…

We consider the estimation of an i.i.d.\ random vector observed through a linear transform followed by a componentwise, probabilistic (possibly nonlinear) measurement channel. A novel algorithm, called generalized approximate message…

Gaussian and quadratic approximations of message passing algorithms on graphs have attracted considerable recent attention due to their computational simplicity, analytic tractability, and wide applicability in optimization and statistical…

We study the problem of regression in a generalized linear model (GLM) with multiple signals and latent variables. This model, which we call a matrix GLM, covers many widely studied problems in statistical learning, including mixed linear…

This work proposes a general learned proximal alternating minimization algorithm, LPAM, for solving learnable two-block nonsmooth and nonconvex optimization problems. We tackle the nonsmoothness by an appropriate smoothing technique with…

Recently, there have been increasing demands to construct compact deep architectures to remove unnecessary redundancy and to improve the inference speed. While many recent works focus on reducing the redundancy by eliminating unneeded…

Recovering a sparse signal from an undersampled set of random linear measurements is the main problem of interest in compressed sensing. In this paper, we consider the case where both the signal and the measurements are complex. We study…

We consider the problem of estimating a signal from measurements obtained via a generalized linear model. We focus on estimators based on approximate message passing (AMP), a family of iterative algorithms with many appealing features: the…

A recent line of work shows that a deep neural network with ReLU nonlinearities arises from a finite sequence of cascaded sparse coding models, the outputs of which, except for the last element in the cascade, are sparse and unobservable.…

Deep neural networks (DNNs) have emerged as key enablers of machine learning. Applying larger DNNs to more diverse applications is an important challenge. The computations performed during DNN training and inference are dominated by…

In this work, we propose an algorithm for solving exact sparse linear regression problems over a network in a distributed manner. Particularly, we consider the problem where data is stored among different computers or agents that seek to…

In cosparse analysis compressive sensing (CS), one seeks to estimate a non-sparse signal vector from noisy sub-Nyquist linear measurements by exploiting the knowledge that a given linear transform of the signal is cosparse, i.e., has…