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Matthieu Wyart

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Publications associées (66)

Inferring the flow properties of epithelial tissues from their geometry

Marko Popovic, Valentin Camille Druelle, Matthieu Wyart

Amorphous materials exhibit complex material properties with strongly nonlinear behaviors. Below a yield stress they behave as plastic solids, while they start to yield above a critical stress sigma(c). A key quantity controlling plasticity which is, howev ...

2021

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

Gioele Mariano Nicolò Balestra, François Gallaire, Matthieu Wyart, Gaëtan Pierre Clément Lerisson, Pier Giuseppe Ledda

Cambridge University Press2021

Geometric compression of invariant manifolds in neural networks

Mario Geiger, Matthieu Wyart, Leonardo Petrini

We study how neural networks compress uninformative input space in models where data lie in d dimensions, but the labels of which only vary within a linear manifold of dimension d(parallel to) < d. We show that for a one-hidden-layer network initialized wi ...

IOP PUBLISHING LTD2021

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 ...

2021

Landscape and training regimes in deep learning

Mario Geiger, Matthieu Wyart, Leonardo Petrini

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 ...

2021

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

François Gallaire, Matthieu Wyart, Gaëtan Pierre Clément Lerisson, Pier Giuseppe Ledda

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 ...

Cambridge University Press2021

How isotropic kernels perform on simple invariants

Matthieu Wyart, Stefano Spigler

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 ...

IOP PUBLISHING LTD2021

Thermal origin of quasilocalized excitations in glasses

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

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 ...

2020

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

Mario Geiger, Matthieu Wyart, Stefano Spigler

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 ...

IOP PUBLISHING LTD2020

Infinitesimal asphericity changes the universality of the jamming transition

Matthieu Wyart, Carolina Brito Carvalho dos Santos

The jamming transition of non-spherical particles is fundamentally different from the spherical case. Non-spherical particles are hypostatic at their jamming points, while isostaticity is ensured in the case of the jamming of spherical particles. This stru ...

IOP PUBLISHING LTD2020

Direct coupling analysis of epistasis in allosteric materials

Matthieu Wyart, Riccardo Ravasio, Barbara Bravi, Carolina Brito Carvalho dos Santos

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 ...

2020

Disentangling feature and lazy training in deep neural networks

Mario Geiger, Arthur Ulysse Jacot-Guillarmod, Matthieu Wyart, Stefano Spigler, Arthur Jacot

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 ...

IOP PUBLISHING LTD2020

Jamming with Tunable Roughness

Matthieu Wyart, Carolina Brito Carvalho dos Santos

We introduce a new model to study the effect of surface roughness on the jamming transition. By performing numerical simulations, we show that for a smooth surface, the jamming transition density and the contact number at the transition point both increase ...

AMER PHYSICAL SOC2020

Scaling description of generalization with number of parameters in deep learning

Clément Hongler, Mario Geiger, Arthur Ulysse Jacot-Guillarmod, Matthieu Wyart, Franck Raymond Gabriel, Stefano Spigler, Levent Dogus Sagun, Arthur Jacot

Supervised deep learning involves the training of neural networks with a large number N of parameters. For large enough N, in the so-called over-parametrized regime, one can essentially fit the training data points. Sparsitybased arguments would suggest th ...

IOP PUBLISHING LTD2020

How collective asperity detachments nucleate slip at frictional interfaces

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

Sliding at a quasi-statically loaded frictional interface can occur via macroscopic slip events, which nucleate locally before propagating as rupture fronts very similar to fracture. We introduce a microscopic model of a frictional interface that includes ...

National Academy of Sciences2019

Interparticle Friction Leads to Nonmonotonic Flow Curves and Hysteresis in Viscous Suspensions

Matthieu Wyart, Hugo Robin Louis Perrin

Hysteresis is a major feature of the solid-liquid transition in granular materials. This property, by allowing metastable states, can potentially yield catastrophic phenomena such as earthquakes or aerial landslides. The origin of hysteresis in granular fl ...

American Physical Society2019

Comparing dynamics: deep neural networks versus glassy systems

Mario Geiger, Matthieu Wyart, Stefano Spigler, Levent Dogus Sagun, Marco Baity-Jesi

We analyze numerically the training dynamics of deep neural networks (DNN) by using methods developed in statistical physics of glassy systems. The two main issues we address are (1) the complexity of the loss landscape and of the dynamics within it, and ( ...

IOP PUBLISHING LTD2019

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

Matthieu Wyart, Wencheng Ji, Carolina Brito Carvalho dos Santos

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 ...

AMER PHYSICAL SOC2019

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

Mario Geiger, Matthieu Wyart, Stefano Spigler, Levent Dogus Sagun, Marco Baity-Jesi

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 ...

AMER PHYSICAL SOC2019

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

Matthieu Wyart, Stefano Spigler, Levent Dogus Sagun

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 ...

IOP PUBLISHING LTD2019

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