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no code implementations • ICML 2020 • Stéphane d'Ascoli, Maria Refinetti, Giulio Biroli, Florent Krzakala

We demonstrate that the latter two contributions are the crux of the double descent: they lead to the overfitting peak at the interpolation threshold and to the decay of the test error upon overparametrization.

no code implementations • 11 Jul 2022 • Tanguy Marchand, Misaki Ozawa, Giulio Biroli, Stéphane Mallat

We develop a multiscale approach to estimate high-dimensional probability distributions from a dataset of physical fields or configurations observed in experiments or simulations.

no code implementations • 9 Feb 2022 • Stéphane d'Ascoli, Maria Refinetti, Giulio Biroli

In this case, it is optimal to keep a large learning rate during the exploration phase to escape the non-convex region as quickly as possible, then use the convex criterion $\beta=1$ to converge rapidly to the solution.

no code implementations • 13 Dec 2021 • Jules Fraboul, Giulio Biroli, Silvia De Monte

Species-rich communities, such as the microbiota or microbial ecosystems, provide key functions for human health and climatic resilience.

no code implementations • 10 Jun 2021 • Stéphane d'Ascoli, Levent Sagun, Giulio Biroli, Ari Morcos

Finally, we experiment initializing the T-CNN from a partially trained CNN, and find that it reaches better performance than the corresponding hybrid model trained from scratch, while reducing training time.

1 code implementation • 27 Apr 2021 • Franco Pellegrini, Giulio Biroli

Our results show that the winning lottery tickets of FCNs display the key features of CNNs.

4 code implementations • 19 Mar 2021 • Stéphane d'Ascoli, Hugo Touvron, Matthew Leavitt, Ari Morcos, Giulio Biroli, Levent Sagun

We initialise the GPSA layers to mimic the locality of convolutional layers, then give each attention head the freedom to escape locality by adjusting a gating parameter regulating the attention paid to position versus content information.

Ranked #314 on Image Classification on ImageNet

1 code implementation • NeurIPS 2021 • Stéphane d'Ascoli, Marylou Gabrié, Levent Sagun, Giulio Biroli

One of the central puzzles in modern machine learning is the ability of heavily overparametrized models to generalize well.

1 code implementation • 2 Mar 2021 • Rahul N. Chacko François P. Landes, Giulio Biroli, Olivier Dauchot, Andrea J. Liu, David R. Reichman

As liquids approach the glass transition temperature, dynamical heterogeneity emerges as a crucial universal feature of their behavior.

Soft Condensed Matter Statistical Mechanics Chemical Physics

no code implementations • 11 Feb 2021 • Misaki Ozawa, Ludovic Berthier, Giulio Biroli, Gilles Tarjus

We use atomistic computer simulations to provide a microscopic description of the brittle failure of amorphous materials, and we assess the role of rare events and quenched disorder.

Soft Condensed Matter Disordered Systems and Neural Networks Materials Science

no code implementations • 11 Jan 2021 • Giulio Biroli, Jean-Philippe Bouchaud, Francois Ladieu

We review 15 years of theoretical and experimental work on the non-linear response of glassy systems.

Disordered Systems and Neural Networks Soft Condensed Matter Statistical Mechanics

no code implementations • 23 Dec 2020 • Giulio Biroli, Marco Tarzia

The idea is that the energy spreading of the mini-bands can be determined self-consistently by requiring that the maximum of the matrix elements between a site $i$ and the other $N^{D_1}$ sites of the support set is of the same order of the Thouless energy itself $N^{D_1 - 1}$.

Disordered Systems and Neural Networks Quantum Gases Statistical Mechanics

1 code implementation • NeurIPS 2020 • Franco Pellegrini, Giulio Biroli

Neural networks have been shown to perform incredibly well in classification tasks over structured high-dimensional datasets.

no code implementations • NeurIPS 2020 • Stefano Sarao Mannelli, Giulio Biroli, Chiara Cammarota, Florent Krzakala, Pierfrancesco Urbani, Lenka Zdeborová

Despite the widespread use of gradient-based algorithms for optimizing high-dimensional non-convex functions, understanding their ability of finding good minima instead of being trapped in spurious ones remains to a large extent an open problem.

1 code implementation • NeurIPS 2020 • Stéphane d'Ascoli, Levent Sagun, Giulio Biroli

We show that this peak is implicitly regularized by the nonlinearity, which is why it only becomes salient at high noise and is weakly affected by explicit regularization.

2 code implementations • 2 Mar 2020 • Stéphane d'Ascoli, Maria Refinetti, Giulio Biroli, Florent Krzakala

We obtain a precise asymptotic expression for the bias-variance decomposition of the test error, and show that the bias displays a phase transition at the interpolation threshold, beyond which it remains constant.

no code implementations • 4 Dec 2019 • Antoine Maillard, Gérard Ben Arous, Giulio Biroli

We obtain a rigorous explicit variational formula for the annealed complexity, which is the logarithm of the average number of critical points at fixed value of the empirical risk.

1 code implementation • NeurIPS 2019 • Stefano Sarao Mannelli, Giulio Biroli, Chiara Cammarota, Florent Krzakala, Lenka Zdeborová

Gradient-based algorithms are effective for many machine learning tasks, but despite ample recent effort and some progress, it often remains unclear why they work in practice in optimising high-dimensional non-convex functions and why they find good minima instead of being trapped in spurious ones. Here we present a quantitative theory explaining this behaviour in a spiked matrix-tensor model. Our framework is based on the Kac-Rice analysis of stationary points and a closed-form analysis of gradient-flow originating from statistical physics.

no code implementations • 18 Jul 2019 • Stefano Sarao Mannelli, Giulio Biroli, Chiara Cammarota, Florent Krzakala, Lenka Zdeborová

Gradient-based algorithms are effective for many machine learning tasks, but despite ample recent effort and some progress, it often remains unclear why they work in practice in optimising high-dimensional non-convex functions and why they find good minima instead of being trapped in spurious ones.

1 code implementation • NeurIPS 2019 • Stéphane d'Ascoli, Levent Sagun, Joan Bruna, Giulio Biroli

The aim of this work is to understand this fact through the lens of dynamics in the loss landscape.

no code implementations • 3 Jun 2019 • François P. Landes, Giulio Biroli, Olivier Dauchot, Andrea J. Liu, David R. Reichman

We compare glassy dynamics in two liquids that differ in the form of their interaction potentials.

no code implementations • 29 May 2019 • Giulio Biroli, Chiara Cammarota, Federico Ricci-Tersenghi

In many high-dimensional estimation problems the main task consists in minimizing a cost function, which is often strongly non-convex when scanned in the space of parameters to be estimated.

1 code implementation • 6 Jan 2019 • Mario Geiger, Arthur Jacot, Stefano Spigler, Franck Gabriel, Levent Sagun, Stéphane d'Ascoli, Giulio Biroli, Clément Hongler, Matthieu Wyart

At this threshold, we argue that $\|f_{N}\|$ diverges.

no code implementations • 21 Dec 2018 • Stefano Sarao Mannelli, Giulio Biroli, Chiara Cammarota, Florent Krzakala, Pierfrancesco Urbani, Lenka Zdeborová

Gradient-descent-based algorithms and their stochastic versions have widespread applications in machine learning and statistical inference.

no code implementations • 22 Oct 2018 • Stefano Spigler, Mario Geiger, Stéphane d'Ascoli, Levent Sagun, Giulio Biroli, Matthieu Wyart

We argue that in fully-connected networks a phase transition delimits the over- and under-parametrized regimes where fitting can or cannot be achieved.

2 code implementations • 25 Sep 2018 • Mario Geiger, Stefano Spigler, Stéphane d'Ascoli, Levent Sagun, Marco Baity-Jesi, Giulio Biroli, Matthieu Wyart

In the vicinity of this transition, properties of the curvature of the minima of the loss are critical.

no code implementations • ICML 2018 • Marco Baity-Jesi, Levent Sagun, Mario Geiger, Stefano Spigler, Gerard Ben Arous, Chiara Cammarota, Yann Lecun, Matthieu Wyart, Giulio Biroli

We analyze numerically the training dynamics of deep neural networks (DNN) by using methods developed in statistical physics of glassy systems.

no code implementations • 8 Apr 2018 • Valentina Ros, Gerard Ben Arous, Giulio Biroli, Chiara Cammarota

We study rough high-dimensional landscapes in which an increasingly stronger preference for a given configuration emerges.

1 code implementation • 15 Mar 2012 • Ludovic Berthier, Giulio Biroli, Daniele Coslovich, Walter Kob, Cristina Toninelli

We present a comprehensive theoretical study of finite size effects in the relaxation dynamics of glass-forming liquids.

Statistical Mechanics

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