Publications de Matthieu Wyart

A phase transition in diffusion models reveals the hierarchical nature of data

Matthieu Wyart, Alessandro Favero, Antonio Sclocchi

Understanding the structure of real data is paramount in advancing modern deep-learning methodologies. Natural data such as images are believed to be composed of features organized in a hierarchical and combinatorial manner, which neural networks capture d ...

National Academy of Sciences2025

Dynamical heterogeneities of thermal creep in pinned interfaces

Matthieu Wyart, Thomas Willem Jan de Geus

Disordered systems under applied loading display slow creep flows at finite temperature. Renormalization group arguments predicted that creep proceeds via thermal avalanches of activated events. Recently, thermal avalanches were argued to control the dynam ...

2025

The role of excitations in supercooled liquids: Density, geometry, and relaxation dynamics

Matthieu Wyart

Low-energy excitations play a key role in all condensed-matter systems, yet there is limited understanding of their nature in glasses, where they correspond to local rearrangements of groups of particles. Here, we introduce an algorithm to systematically u ...

2025

How Deep Neural Networks Learn Compositional Data: The Random Hierarchy Model

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

Deep learning algorithms demonstrate a surprising ability to learn high-dimensional tasks from limited examples. This is commonly attributed to the depth of neural networks, enabling them to build a hierarchy of abstract, low-dimensional data representatio ...

American Physical Society2024

On the different regimes of stochastic gradient descent

Matthieu Wyart, Antonio Sclocchi

Modern deep networks are trained with stochastic gradient descent (SGD) whose key hyperparameters are the number of data considered at each step or batch size B, and the step size or learning rate n. For small B and large n, SGD corresponds to a stochastic ...

National Academy of Sciences2024

Armouring of a Frictional Interface by Mechanical Noise

Matthieu Wyart, Thomas Willem Jan de Geus

A dry frictional interface loaded in shear often displays stick–slip. The amplitude of this cycle depends on the probability that a microscopic event nucleates a rupture and on the rate at which microscopic events are triggered. The latter is determined by ...

2024

Local vs. cooperative: Unraveling glass transition mechanisms with SEER

Matthieu Wyart, Wencheng Ji

Which phenomenon slows down the dynamics in supercooled liquids and turns them into glasses is a long-standing question of condensed matter. Most popular theories posit that as the temperature decreases, many events must occur in a coordinated fashion on a ...

National Academy of Sciences2024

What can be learnt with wide convolutional neural networks?

Matthieu Wyart, Francesco Cagnetta, Alessandro Favero

Understanding how convolutional neural networks (CNNs) can efficiently learn high-dimensional functions remains a fundamental challenge. A popular belief is that these models harness the local and hierarchical structure of natural data such as images. Yet, ...

2024

Testing Theories of the Glass Transition with the Same Liquid but Many Kinetic Rules

Matthieu Wyart, Carolina Brito Carvalho dos Santos

We study the glass transition by exploring a broad class of kinetic rules that can significantly modify the normal dynamics of supercooled liquids while maintaining thermal equilibrium. Beyond the usual dynamics of liquids, this class includes dynamics in ...

Amer Physical Soc2024

Scaling Description of Dynamical Heterogeneity and Avalanches of Relaxation in Glass-Forming Liquids

Matthieu Wyart, Ali Tahaei

We provide a theoretical description of dynamical heterogeneities in glass-forming liquids, based on the premise that relaxation occurs via local rearrangements coupled by elasticity. In our framework, the growth of the dynamical correlation length e and o ...

American Physical Society2023