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The minimization of a data-fidelity term and an additive regularization functional gives rise to a powerful framework for supervised learning. In this paper, we present a unifying regularization functional that depends on an operator L\documentclass[12pt]{ ...
In the past few years, Machine Learning (ML) techniques have ushered in a paradigm shift, allowing the harnessing of ever more abundant sources of data to automate complex tasks. The technical workhorse behind these important breakthroughs arguably lies in ...
Neural network approaches to approximate the ground state of quantum hamiltonians require the numerical solution of a highly nonlinear optimization problem. We introduce a statistical learning approach that makes the optimization trivial by using kernel me ...
Deep Neural Networks (DNNs) training can be difficult due to vanishing and exploding gradients during weight optimization through backpropagation. To address this problem, we propose a general class of Hamiltonian DNNs (H-DNNs) that stem from the discretiz ...
Deep neural networks have become ubiquitous in today's technological landscape, finding their way in a vast array of applications. Deep supervised learning, which relies on large labeled datasets, has been particularly successful in areas such as image cla ...
The way biological brains carry out advanced yet extremely energy efficient signal processing remains both fascinating and unintelligible. It is known however that at least some areas of the brain perform fast and low-cost processing relying only on a smal ...
The variational approach is a cornerstone of computational physics, considering both conventional and quantum computing computational platforms. The variational quantum eigensolver algorithm aims to prepare the ground state of a Hamiltonian exploiting para ...
The monumental progress in the development of machine learning models has led to a plethora of applications with transformative effects in engineering and science. This has also turned the attention of the research community towards the pursuit of construc ...
Diagonal linear networks (DLNs) are a toy simplification of artificial neural networks; they consist in a quadratic reparametrization of linear regression inducing a sparse implicit regularization. In this paper, we describe the trajectory of the gradient ...
Adaptive first-order methods in optimization are prominent in machine learning and data science owing to their ability to automatically adapt to the landscape of the function being optimized. However, their convergence guarantees are typically stated in te ...