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This work investigates the application of the Newton's method for the numerical solution of a nonlinear boundary value problem formulated through an ordinary differential equation (ODE). Nonlinear ODEs arise in various mathematical modeling…

This paper models the dynamics of a large set of interacting neurons within the framework of statistical field theory. We use a method initially developed in the context of statistical field theory [44] and later adapted to complex systems…

In this paper we explore a relevant aspect of the interplay between two core elements of global optimization algorithms for nonconvex nonlinear programming problems, which we believe has been overlooked by past literature. The first one is…

Imbalanced problems can arise in different real-world situations, and to address this, certain strategies in the form of resampling or balancing algorithms are proposed. This issue has largely been studied in the context of classification,…

This paper introduces a fast and numerically stable algorithm for the solution of fourth-order linear boundary value problems on an interval. This type of equation arises in a variety of settings in physics and signal processing. Our method…

The interference channel models a wireless network where several source-destination pairs compete for the same resources. When nodes transmit simultaneously the destinations experience interference. This paper considers a 4-node network,…

In conventional deep learning, the number of neurons typically remains fixed during training. However, insights from biology suggest that the human hippocampus undergoes continuous neuron generation and pruning of neurons over the course of…

We present NNrepair, a constraint-based technique for repairing neural network classifiers. The technique aims to fix the logic of the network at an intermediate layer or at the last layer. NNrepair first uses fault localization to find…

Over the past two decades, an increasing array of control-theoretic methods have been used to study the brain as a complex dynamical system and better understand its structure-function relationship. This article provides an overview on one…

This research introduces an extended application of neural networks for solving nonlinear partial differential equations (PDEs). A neural network, combined with a pseudo-arclength continuation, is proposed to construct bifurcation diagrams…

Transseries expansions build upon ordinary power series methods by including additional basis elements such as exponentials and logarithms. Alternative summation methods can then be used to "resum" series to obtain more efficient…

We consider distributed stochastic optimization problems that are solved with master/workers computation architecture. Statistical arguments allow to exploit statistical similarity and approximate this problem by a finite-sum problem, for…

A residual-networks family with hundreds or even thousands of layers dominates major image recognition tasks, but building a network by simply stacking residual blocks inevitably limits its optimization ability. This paper proposes a novel…

Network pruning reduces the size of neural networks by removing (pruning) neurons such that the performance drop is minimal. Traditional pruning approaches focus on designing metrics to quantify the usefulness of a neuron which is often…

The training of neural networks is a complex, high-dimensional, non-convex and noisy optimization problem whose theoretical understanding is interesting both from an applicative perspective and for fundamental reasons. A core challenge is…

Recent interest has developed around the problem of dynamic compressed sensing, or the recovery of time-varying, sparse signals from limited observations. In this paper, we study how the dynamics of recurrent networks, formulated as general…

Mounting evidence in neuroscience suggests the possibility of neuronal representations that individual neurons serve as the substrates of different mental representations in a point-to-point way. Combined with associationism, it can…