Publication

Sharp asymptotics on the compression of two-layer neural networks

Related publications (59)

Graph Chatbot

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

Safe Deep Neural Networks

Kyle Michael Matoba

				The capabilities of deep learning systems have advanced much faster than our ability to understand them. Whilst the gains from deep neural networks (DNNs) are significant, they are accompanied by a growing risk and gravity of a bad outcome. This is tr ...

EPFL2024

On the number of regions of piecewise linear neural networks

Michaël Unser, Alexis Marie Frederic Goujon

Many feedforward neural networks (NNs) generate continuous and piecewise-linear (CPWL) mappings. Specifically, they partition the input domain into regions on which the mapping is affine. The number of these so-called linear regions offers a natural metric ...

2024

Benign Overfitting in Deep Neural Networks under Lazy Training

Volkan Cevher, Grigorios Chrysos, Fanghui Liu, Zhenyu Zhu

This paper focuses on over-parameterized deep neural networks (DNNs) with ReLU activation functions and proves that when the data distribution is well-separated, DNNs can achieve Bayesoptimal test error for classification while obtaining (nearly) zero-trai ...

2023

An exact mapping from ReLU networks to spiking neural networks

Wulfram Gerstner, Stanislaw Andrzej Wozniak, Ana Stanojevic, Giovanni Cherubini, Angeliki Pantazi

Deep spiking neural networks (SNNs) offer the promise of low-power artificial intelligence. However, training deep SNNs from scratch or converting deep artificial neural networks to SNNs without loss of performance has been a challenge. Here we propose an ...

2023

From Kernel Methods to Neural Networks: A Unifying Variational Formulation

Michaël Unser

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]{ ...

New York2023

A Theory of Finite-Width Neural Networks: Generalization, Scaling Laws, and the Loss Landscape

Berfin Simsek

Deep learning has achieved remarkable success in various challenging tasks such as generating images from natural language or engaging in lengthy conversations with humans.The success in practice stems from the ability to successfully train massive neural ...

EPFL2023

ReLU Neural Network Galerkin BEM

Fernando José Henriquez Barraza

We introduce Neural Network (NN for short) approximation architectures for the numerical solution of Boundary Integral Equations (BIEs for short). We exemplify the proposed NN approach for the boundary reduction of the potential problem in two spatial dime ...

SPRINGER/PLENUM PUBLISHERS2023

How deep convolutional neural networks lose spatial information with training

Matthieu Wyart, Leonardo Petrini, Umberto Maria Tomasini, Francesco Cagnetta

A central question of machine learning is how deep nets manage to learn tasks in high dimensions. An appealing hypothesis is that they achieve this feat by building a representation of the data where information irrelevant to the task is lost. For image da ...

Bristol2023

Expectation consistency for calibration of neural networks

Florent Gérard Krzakala, Lenka Zdeborová, Lucas Andry Clarte, Bruno Loureiro

Despite their incredible performance, it is well reported that deep neural networks tend to be overoptimistic about their prediction confidence. Finding effective and efficient calibration methods for neural networks is therefore an important endeavour tow ...

2023

Penalising the biases in norm regularisation enforces sparsity

Nicolas Henri Bernard Flammarion, Etienne Patrice Boursier

Controlling the parameters' norm often yields good generalisation when training neural networks. Beyond simple intuitions, the relation between parameters' norm and obtained estimators theoretically remains misunderstood. For one hidden ReLU layer networks ...

2023