Publications by 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, Leonardo Petrini, Alessandro Favero, Umberto Maria Tomasini, Francesco Cagnetta

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, Alessandro Favero, Francesco Cagnetta

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

Ali Tahaei, Matthieu Wyart

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

Learning sparse features can lead to overfitting in neural networks

Matthieu Wyart, Leonardo Petrini, Francesco Cagnetta

It is widely believed that the success of deep networks lies in their ability to learn a meaningful representation of the features of the data. Yet, understanding when and how this feature learning improves performance remains a challenge. For example, it ...

Iop Publishing Ltd2023

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 ...

Iop Publishing Ltd2023

Failure and success of the spectral bias prediction for Laplace Kernel Ridge Regression: the case of low-dimensional data

Matthieu Wyart, Umberto Maria Tomasini, Antonio Sclocchi

Recently, several theories including the replica method made predictions for the generalization error of Kernel Ridge Regression. In some regimes, they predict that the method has a 'spectral bias': decomposing the true function f* on the eigenbasis of the ...

JMLR-JOURNAL MACHINE LEARNING RESEARCH2022

Scaling theory for the statistics of slip at frictional interfaces

Matthieu Wyart, Thomas Willem Jan de Geus

Slip at a frictional interface occurs via intermittent events. Understanding how these events are nucleated, can propagate, or stop spontaneously remains a challenge, central to earthquake science and tribology. In the absence of disorder, rate-and-state a ...

AMER PHYSICAL SOC2022

Relative stability toward diffeomorphisms indicates performance in deep nets

Mario Geiger, Matthieu Wyart, Leonardo Petrini, Alessandro Favero

Understanding why deep nets can classify data in large dimensions remains a challenge. It has been proposed that they do so by becoming stable to diffeomorphisms, yet existing empirical measurements support that it is often not the case. We revisit this qu ...

IOP Publishing Ltd2022

Locality defeats the curse of dimensionality in convolutional teacher-student scenarios*

Matthieu Wyart, Alessandro Favero, Francesco Cagnetta

Convolutional neural networks perform a local and translationally-invariant treatment of the data: quantifying which of these two aspects is central to their success remains a challenge. We study this problem within a teacher-student framework for kernel r ...

IOP Publishing Ltd2022

Scaling Description of Creep Flow in Amorphous Solids

Marko Popovic, Matthieu Wyart, Wencheng Ji, Thomas Willem Jan de Geus

Amorphous solids such as coffee foam, toothpaste, or mayonnaise display a transient creep flow when a stress E is suddenly imposed. The associated strain rate is commonly found to decay in time as gamma_ -t-nu, followed either by arrest or by a sudden flui ...

AMER PHYSICAL SOC2022

Mean-field description for the architecture of low-energy excitations in glasses

Matthieu Wyart, Wencheng Ji, Thomas Willem Jan de Geus, Elisabeth Agoritsas

In amorphous materials, groups of particles can rearrange locally into a new stable configuration. Such elementary excitations are key as they determine the response to external stresses, as well as to thermal and quantum fluctuations. Yet, understanding w ...

2022

Nonlocal Effects Reflect the Jamming Criticality in Frictionless Granular Flows Down Inclines

Matthieu Wyart, Hugo Robin Louis Perrin

The jamming transition is accompanied by a rich phenomenology such as hysteresis or nonlocal effects that is still not well understood. Here, we experimentally investigate a model frictionless granular layer flowing down an inclined plane as a way to disen ...

AMER PHYSICAL SOC2021

Thermally activated flow in models of amorphous solids

Marko Popovic, Matthieu Wyart, Wencheng Ji, Thomas Willem Jan de Geus

Amorphous solids yield at a critical value Sigma(c) of the imposed stress Sigma through a dynamical phase transition. While sharp in athermal systems, the presence of thermal fluctuations leads to the rounding of the transition and thermally activated flow ...

AMER PHYSICAL SOC2021