Publications de Matthieu Wyart

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The response of amorphous materials to an applied strain can be continuous or instead discontinuous if the initial configuration is very stable. We study theoretically how such a stress drop emerges as the system's initial stability is increased. We show t ...

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 ...

How many training data are needed to learn a supervised task? It is often observed that the generalization error decreases as n(-beta) where n is the number of training examples and beta is an exponent that depends on both data and algorithm. In this work ...

Quasilocalized modes appear in the vibrational spectrum of amorphous solids at low frequency. Though never formalized, these modes are believed to have a close relationship with other important local excitations, including shear transformations and two-lev ...

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, ...

We investigate how the training curve of isotropic kernel methods depends on the symmetry of the task to be learned, in several settings. (i) We consider a regression task, where the target function is a Gaussian random field that depends only on d(paralle ...

Allosteric regulation plays an important role in many biological processes, such as signal transduction, transcriptional regulation, andmetabolism. Allostery is rooted in the fundamental physical properties of macromolecular systems, but its underlying mec ...

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 ...

We study the role of hydrodynamic instabilities in the morphogenesis of some typical karst draperies structures encountered in limestone caves. The problem is tackled using the long wave approximation for the fluid film that flows under an inclined substra ...

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 ...

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 ...

Key aspects of glasses are controlled by the presence of excitations in which a group of particles can rearrange. Surprisingly, recent observations indicate that their density is dramatically reduced and their size decreases as the temperature of the super ...

Deep learning has been immensely successful at a variety of tasks, ranging from classification to artificial intelligence. Learning corresponds to fitting training data, which is implemented by descending a very high-dimensional loss function. Understandin ...

We present a model and protocol that enable the generation of extremely stable computer glasses at minimal computational cost. The protocol consists of an instantaneous quench in an augmented potential energy landscape, with particle radii as additional de ...

Deep learning algorithms are responsible for a technological revolution in a variety oftasks including image recognition or Go playing. Yet, why they work is not understood.Ultimately, they manage to classify data lying in high dimension – a feat generical ...

The thermodynamics and dynamics of supercooled liquids correlate with their elasticity. In particular for covalent networks, the jump of specific heat is small and the liquid is strong near the threshold valence where the network acquires rigidity. By cont ...

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 ...

In allosteric proteins, the binding of a ligand modifies function at a distant active site. Such allosteric pathways can be used as target for drug design, generating considerable interest in inferring them from sequence alignment data. Currently, differen ...

In this paper we first recall the recent result that in deep networks a phase transition, analogous to the jamming transition of granular media, delimits the over- and under-parametrized regimes where fitting can or cannot be achieved. The analysis leading ...

Two distinct limits for deep learning have been derived as the network width h -> infinity, depending on how the weights of the last layer scale with h. In the neural tangent Kernel (NTK) limit, the dynamics becomes linear in the weights and is described b ...

Matthieu Wyart

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Elastoplastic description of sudden failure in athermal amorphous materials during quasistatic loading

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

Asymptotic learning curves of kernel methods: empirical data versus teacher-student paradigm

Theory for the density of interacting quasilocalized modes in amorphous solids

What can be learnt with wide convolutional neural networks?

How isotropic kernels perform on simple invariants

Allostery in Its Many Disguises: From Theory to Applications

Scaling Description of Creep Flow in Amorphous Solids

Hydrodynamic-driven morphogenesis of karst draperies: spatio-temporal analysis of the two-dimensional impulse response

Relative stability toward diffeomorphisms indicates performance in deep nets

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

Thermal origin of quasilocalized excitations in glasses

Jamming transition as a paradigm to understand the loss landscape of deep neural networks

Fast generation of ultrastable computer glasses by minimization of an augmented potential energy

Landscape and training regimes in deep learning

Adaptive elastic networks as models of supercooled liquids

Scaling theory for the statistics of slip at frictional interfaces

Direct coupling analysis of epistasis in allosteric materials

A jamming transition from under- to over-parametrization affects generalization in deep learning

Disentangling feature and lazy training in deep neural networks