The problem of optimizing over random structures emerges in many areas of science and
engineering, ranging from statistical physics to machine learning and artificial intelligence …

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 …

Current deep neural networks are highly overparameterized (up to billions of connection
weights) and nonlinear. Yet they can fit data almost perfectly through variants of gradient …

The dreaming Hopfield model constitutes a generalization of the Hebbian paradigm for
neural networks, that is able to perform on-line learning when “awake” and also to account …

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 …

For many computational problems involving randomness, intricate geometric features of the
solution space have been used to rigorously rule out powerful classes of algorithms. This is …

We study the random binary symmetric perceptron problem, focusing on the behavior of rare
high-margin solutions. While most solutions are isolated, we demonstrate that these rare …

The symmetric binary perceptron (SBP) is a random constraint satisfaction problem (CSP)
and a single-layer neural network; it exhibits intriguing features, most notably a sharp phase …

Linear separability, a core concept in supervised machine learning, refers to whether the
labels of a data set can be captured by the simplest possible machine: a linear classifier. In …