Search Results for author: Giulio Biroli

Found 29 papers, 12 papers with code

Double Trouble in Double Descent: Bias and Variance(s) in the Lazy Regime

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.

Wavelet Conditional Renormalization Group

no code implementations11 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.

Optimal learning rate schedules in high-dimensional non-convex optimization problems

no code implementations9 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.

Artificial selection of communities drives the emergence of structured interactions

no code implementations13 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.

Transformed CNNs: recasting pre-trained convolutional layers with self-attention

no code implementations10 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.

ConViT: Improving Vision Transformers with Soft Convolutional Inductive Biases

4 code implementations19 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.

Image Classification Inductive Bias

On the interplay between data structure and loss function in classification problems

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.

Elastoplasticity Mediates Dynamical Heterogeneity Below the Mode-Coupling Temperature

1 code implementation2 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

Rare events and disorder control the brittle yielding of well-annealed amorphous solids

no code implementations11 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

Amorphous Order & Non-linear Susceptibilities in Glassy Materials

no code implementations11 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

The Lévy-Rosenzweig-Porter random matrix ensemble

no code implementations23 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

An analytic theory of shallow networks dynamics for hinge loss classification

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.

General Classification

Complex Dynamics in Simple Neural Networks: Understanding Gradient Flow in Phase Retrieval

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.

Triple descent and the two kinds of overfitting: Where & why do they appear?

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.

Double Trouble in Double Descent : Bias and Variance(s) in the Lazy Regime

2 code implementations2 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.

Landscape Complexity for the Empirical Risk of Generalized Linear Models

no code implementations4 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.

Who is Afraid of Big Bad Minima? Analysis of gradient-flow in spiked matrix-tensor models

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.

Who is Afraid of Big Bad Minima? Analysis of Gradient-Flow in a Spiked Matrix-Tensor Model

no code implementations18 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.

How to iron out rough landscapes and get optimal performances: Averaged Gradient Descent and its application to tensor PCA

no code implementations29 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.

Marvels and Pitfalls of the Langevin Algorithm in Noisy High-dimensional Inference

no code implementations21 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.

A jamming transition from under- to over-parametrization affects loss landscape and generalization

no code implementations22 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.

Comparing Dynamics: Deep Neural Networks versus Glassy Systems

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.

Finite size effects in the dynamics of glass-forming liquids

1 code implementation15 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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