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Transfer learning allows us to train deep architectures requiring a large number of learned parameters, even if the amount of available data is limited, by leveraging existing models previously trained for another task. Here we explore the…

Estimation of physical quantities is at the core of most scientific research and the use of quantum devices promises to enhance its performances. In real scenarios, it is fundamental to consider that the resources are limited and Bayesian…

We study the problem of learning an unknown function using random feature models. Our main contribution is an exact asymptotic analysis of such learning problems with Gaussian data. Under mild regularity conditions for the feature matrix,…

Choice modeling has been a central topic in the study of individual preference or utility across many fields including economics, marketing, operations research, and psychology. While the vast majority of the literature on choice models has…

This paper aims to handle the joint transmitter and noncoherent receiver design for multiuser multiple-input multiple-output (MU-MIMO) systems through deep learning. Given the deep neural network (DNN) based noncoherent receiver, the…

In this paper, a review of model-free reinforcement learning for learning of dynamical systems in uncertain environments has discussed. For this purpose, the Markov Decision Process (MDP) will be reviewed. Furthermore, some learning…

The recent literature on deep learning offers new tools to learn a rich probability distribution over high dimensional data such as images or sounds. In this work we investigate the possibility of learning the prior distribution over neural…

We develop a simple and computationally efficient significance test for the features of a machine learning model. Our forward-selection approach applies to any model specification, learning task and variable type. The test is…

We propose a novel objective function for learning robust deep representations of data based on information theory. Data is projected into a feature-vector space such that the mutual information of all subsets of features relative to the…

In several physical systems, important properties characterizing the system itself are theoretically related with specific degrees of freedom. Although standard Monte Carlo simulations provide an effective tool to accurately reconstruct the…

Shortcut learning, i.e., a model's reliance on undesired features not directly relevant to the task, is a major challenge that severely limits the applications of machine learning algorithms, particularly when deploying them to assist in…

Estimating nonlinear functionals of probability distributions from samples is a fundamental statistical problem. The "plug-in" estimator obtained by applying the target functional to the empirical distribution of samples is biased.…

To benefit from the modeling capacity of deep models in system identification, without worrying about inference time, this study presents a novel training strategy that uses deep models only at the training stage. For this purpose two…

We consider the problem of exactly learning an $s$-sparse real-valued Boolean polynomial of degree $d$ of the form $f:\{ 0,1\}^n \rightarrow \mathbb{R}$. This problem corresponds to decomposing functions in the AND basis and is known as…

We prove an implicit function theorem and an inverse function theorem for free noncommutative functions over operator spaces and on the set of nilpotent matrices. We apply these results to study dependence of the solution of the initial…

In this paper, we present a statistical-mechanical analysis of deep learning. We elucidate some of the essential components of deep learning---pre-training by unsupervised learning and fine tuning by supervised learning. We formulate the…

Despite the tremendous successes of deep neural networks (DNNs) in various applications, many fundamental aspects of deep learning remain incompletely understood, including DNN trainability. In a trainability study, one aims to discern what…

We investigate Sarnak's conjecture on the M\"obius function in the special case when the test function is the indicator of the set of integers for which a real additive function assumes a given value.

Traditional NMF-based signal decomposition relies on the factorization of spectral data, which is typically computed by means of short-time frequency transform. In this paper we propose to relax the choice of a pre-fixed transform and learn…

Deep learning applies hierarchical layers of hidden variables to construct nonlinear high dimensional predictors. Our goal is to develop and train deep learning architectures for spatio-temporal modeling. Training a deep architecture is…