Search Results for author: Chiara Cammarota

Found 8 papers, 1 papers with code

Dynamical systems on large networks with predator-prey interactions are stable and exhibit oscillations

no code implementations23 Sep 2020 Andrea Marcello Mambuca, Chiara Cammarota, Izaak Neri

We show that, in general, linear dynamical systems defined on random graphs with a prescribed degree distribution of unbounded support are unstable if they are large enough, implying a tradeoff between stability and diversity.

Statistical Mechanics Disordered Systems and Neural Networks Populations and Evolution

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.

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.

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.

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