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Many communications and sensing applications hinge on the detection of a signal in a noisy, interference-heavy environment. Signal processing theory yields techniques such as the generalized likelihood ratio test (GLRT) to perform detection…

We introduce the first neural optimization framework to solve a classical instance of the tiling problem. Namely, we seek a non-periodic tiling of an arbitrary 2D shape using one or more types of tiles: the tiles maximally fill the shape's…

We prove that stochastic gradient descent efficiently converges to the global optimizer of the maximum likelihood objective of an unknown linear time-invariant dynamical system from a sequence of noisy observations generated by the system.…

The graph neural network (GNN) has demonstrated its superior performance in various applications. The working mechanism behind it, however, remains mysterious. GNN models are designed to learn effective representations for graph-structured…

In recent works, both sparsity-based methods as well as learning-based methods have proven to be successful in solving several challenging linear inverse problems. However, sparsity priors for natural signals and images suffer from poor…

Stochastic gradient descent (SGD) is a premium optimization method for training neural networks, especially for learning objectively defined labels such as image objects and events. When a neural network is instead faced with subjectively…

Innovations in neural architectures have fostered significant breakthroughs in language modeling and computer vision. Unfortunately, novel architectures often result in challenging hyper-parameter choices and training instability if the…

We study a class of generalized linear programs (GLP) in a large-scale setting, which includes simple, possibly nonsmooth convex regularizer and simple convex set constraints. By reformulating (GLP) as an equivalent convex-concave min-max…

Recent research in neural networks and machine learning suggests that using many more parameters than strictly required by the initial complexity of a regression problem can result in more accurate or faster-converging models -- contrary to…

This paper develops expansive gradient dynamics in deep neural network-induced mapping spaces. Specifically, we generate tools and concepts for minimizing a class of energy functionals in an abstract Hilbert space setting covering a wide…

Neural networks trained with standard objectives exhibit behaviors characteristic of probabilistic inference: soft clustering, prototype specialization, and Bayesian uncertainty tracking. These phenomena appear across architectures -- in…

$\ell_1$ regularization has been used for logistic regression to circumvent the overfitting and use the estimated sparse coefficient for feature selection. However, the challenge of such a regularization is that the $\ell_1$ norm is not…

Graphical models are widely used in science to represent joint probability distributions with an underlying conditional dependence structure. The inverse problem of learning a discrete graphical model given i.i.d samples from its joint…

Neural networks are trained primarily based on their inputs and outputs, without regard for their internal mechanisms. These neglected mechanisms determine properties that are critical for safety, like (i) transparency; (ii) the absence of…

Tree-based models are widely recognized for their interpretability and have proven effective in various application domains, particularly in high-stakes domains. However, learning decision trees (DTs) poses a significant challenge due to…

We present a general variational framework for the training of freeform nonlinearities in layered computational architectures subject to some slope constraints. The regularization that we add to the traditional training loss penalizes the…

We propose a gradient-based method for quadratic programming problems with a single linear constraint and bounds on the variables. Inspired by the GPCG algorithm for bound-constrained convex quadratic programming [J.J. Mor\'e and G.…

This paper considers convex optimization problems where nodes of a network have access to summands of a global objective. Each of these local objectives is further assumed to be an average of a finite set of functions. The motivation for…

We study the problem of training deep neural networks with Rectified Linear Unit (ReLU) activation function using gradient descent and stochastic gradient descent. In particular, we study the binary classification problem and show that for…

Generative Adversarial Networks (GANs) have achieved remarkable results in the task of generating realistic natural images. In most successful applications, GAN models share two common aspects: solving a challenging saddle point…