Person

Mario Geiger

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Related publications (16)

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A long-standing goal of science is to accurately simulate large molecular systems using quantum mechanics. The poor scaling of current quantum chemistry algorithms on classical computers, however, imposes an effective limit of about a few dozen atoms on tr ...

IOP Publishing Ltd2023

Relative stability toward diffeomorphisms indicates performance in deep nets

Matthieu Wyart, Mario Geiger, 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

Loss landscape and symmetries in Neural Networks

Mario Geiger

Neural networks (NNs) have been very successful in a variety of tasks ranging from machine translation to image classification. Despite their success, the reasons for their performance are still not well-understood. This thesis explores two main themes: lo ...

EPFL2021

Landscape and training regimes in deep learning

Matthieu Wyart, Mario Geiger, 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

Finding symmetry breaking order parameters with Euclidean neural networks

Mario Geiger

Curie's principle states that "when effects show certain asymmetry, this asymmetry must be found in the causes that gave rise to them." We demonstrate that symmetry equivariant neural networks uphold Curie's principle and can be used to articulate many sym ...

AMER PHYSICAL SOC2021

Disentangling feature and lazy training in deep neural networks

Matthieu Wyart, Mario Geiger, 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

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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

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

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

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

Comparing dynamics: deep neural networks versus glassy systems

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

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

A General Theory of Equivariant CNNs on Homogeneous Spaces

Mario Geiger

We present a general theory of Group equivariant Convolutional Neural Networks (G-CNNs) on homogeneous spaces such as Euclidean space and the sphere. Feature maps in these networks represent fields on a homogeneous base space, and layers are equivariant ma ...

NEURAL INFORMATION PROCESSING SYSTEMS (NIPS)2019