We show that discrete synaptic weights can be efficiently used for learning in large scale
neural systems, and lead to unanticipated computational performance. We focus on the …

We prove, under an assumption on the critical points of a real-valued function, that the
symmetric Ising perceptron exhibits thefrozen 1-RSB'structure conjectured by Krauth and …

The binary (or Ising) perceptron is a toy model of a single-layer neural network and can be
viewed as a random constraint satisfaction problem with a high degree of connectivity. The …

This paper first describes, from a high-level viewpoint, the main challenges that had to be
solved in order to develop a theory of spin glasses in the last fifty years. It then explains how …

It was recently shown that almost all solutions in the symmetric binary perceptron are
isolated, even at low constraint densities, suggesting that finding typical solutions is hard. In …

We consider the symmetric binary perceptron model, a simple model of neural networks that
has gathered significant attention in the statistical physics, information theory and probability …

We study the problem of determining the capacity of the binary perceptron for two variants of
the problem where the corresponding constraint is symmetric. We call these variants the …

Abstract Machine learning algorithms relying on deep neural networks recently allowed a
great leap forward in artificial intelligence. Despite the popularity of their applications, the …

Algorithmic obstructions in the random number partitioning problem Page 1 The Annals of
Applied Probability 2023, Vol. 33, No. 6B, 5497–5563 https://doi.org/10.1214/23-AAP1953 …

We study the binary and continuous negative-margin perceptrons as simple nonconvex
neural network models learning random rules and associations. We analyze the geometry of …