486 citations · 2.8k across the 59 of their papers we have counts for
61 papers
Learning limit cycles via Hebbian synaptic plasticity
Samantha J. Fournier, Luca Vincenzo Spallanzani, Pierfrancesco Urbani
We investigate high-dimensional, non-linear dynamical systems when exposed to incoherent periodic inputs and Hebbian-like synaptic plasticity. Our findings reveal a striking phenom…
Theory of learning of high-dimensional controlled non-linear dynamical systems (I): models and methods
Pierfrancesco Urbani
Neural ordinary differential equations (neural ODEs) have rapidly gained prominence as a powerful and unifying framework for conceptualizing artificial neural networks, elegantly c…
Chaos in high-dimensional dynamical systems with tunable non-reciprocity
Samantha Fournier, Pierfrancesco Urbani
High-dimensional dynamical systems of interacting degrees of freedom are ubiquitous in the study of complex systems. When the directed interactions are totally uncorrelated, suffic…
High-dimensional dynamical systems: co-existence of attractors, phase transitions, maximal Lyapunov exponent and response to periodic drive
Samantha J. Fournier, Pierfrancesco Urbani
We study the dynamical properties of a broad class of high-dimensional random dynamical systems exhibiting chaotic as well as fixed point and periodic attractors. We consider cases…
Non-reciprocal interactions and high-dimensional chaos: comparing dynamics and statistics of equilibria in a solvable class of models
Samantha J. Fournier, Alessandro Pacco, Valentina Ros +1
We investigate a model of high-dimensional dynamical variables with all-to-all interactions that are random and non-reciprocal. We characterize its phase diagram and show that the…
Dynamical Decoupling of Generalization and Overfitting in Large Two-Layer Networks
Andrea Montanari, Pierfrancesco Urbani
Understanding the inductive bias and generalization properties of large overparametrized machine learning models requires to characterize the dynamics of the training algorithm. We…
Statistical physics of complex systems: glasses, spin glasses, continuous constraint satisfaction problems, high-dimensional inference and neural networks
Pierfrancesco Urbani
The purpose of this manuscript is to review my recent activity on three main research topics. The first concerns the nature of low temperature amorphous solids and their relation w…
Generative modeling through internal high-dimensional chaotic activity
Samantha J. Fournier, Pierfrancesco Urbani
Generative modeling aims at producing new datapoints whose statistical properties resemble the ones in a training dataset. In recent years, there has been a burst of machine learni…
Stochastic Gradient Descent outperforms Gradient Descent in recovering a high-dimensional signal in a glassy energy landscape
Persia Jana Kamali, Pierfrancesco Urbani
Stochastic Gradient Descent (SGD) is an out-of-equilibrium algorithm used extensively to train artificial neural networks. However very little is known on to what extent SGD is cru…
Dynamical mean field theory for models of confluent tissues and beyond
Persia Jana Kamali, Pierfrancesco Urbani
We consider a recently proposed model to understand the rigidity transition in confluent tissues and we derive the dynamical mean field theory (DMFT) equations that describes sever…
Statistical physics of learning in high-dimensional chaotic systems
Samantha J. Fournier, Pierfrancesco Urbani
In many complex systems, elementary units live in a chaotic environment and need to adapt their strategies to perform a task, by extracting information from the environment and con…
Quantum exploration of high-dimensional canyon landscapes
Pierfrancesco Urbani
Canyon landscapes in high dimension can be described as manifolds of small, but extensive dimension, immersed in a higher dimensional ambient space and characterized by a zero pote…
Low temperature amorphous solids: mean field theory and beyond
Pierfrancesco Urbani
Amorphous solids at low temperature display unusual features which have been escaped a clear and unified comprehension. In recent years a mean field theory of amorphous solids cons…
A continuous constraint satisfaction problem for the rigidity transition in confluent tissues
Pierfrancesco Urbani
Models of confluent tissues are built out of tessellations of the space (both in two and three dimensions) in which the cost function is constructed in such a way that individual c…
Field theory for zero temperature soft anharmonic spin glasses in a field
Pierfrancesco Urbani
We introduce a finite dimensional anharmonic soft spin glass in a field and show how it allows the construction a field theory at zero temperature and the corresponding loop expans…
The effective noise of Stochastic Gradient Descent
Francesca Mignacco, Pierfrancesco Urbani
Stochastic Gradient Descent (SGD) is the workhorse algorithm of deep learning technology. At each step of the training phase, a mini batch of samples is drawn from the training dat…
Marginal stability of soft anharmonic mean field spin glasses
Giampaolo Folena, Pierfrancesco Urbani
We investigate the properties of the glass phase of a recently introduced spin glass model of soft spins subjected to an anharmonic quartic local potential, which serves as a model…
High dimensional optimization under non-convex excluded volume constraints
Antonio Sclocchi, Pierfrancesco Urbani
We consider high dimensional random optimization problems where the dynamical variables are subjected to non-convex excluded volume constraints. We focus on the case in which the c…
Stochasticity helps to navigate rough landscapes: comparing gradient-descent-based algorithms in the phase retrieval problem
Francesca Mignacco, Pierfrancesco Urbani, Lenka Zdeborová
In this paper we investigate how gradient-based algorithms such as gradient descent, (multi-pass) stochastic gradient descent, its persistent variant, and the Langevin algorithm na…
Analytical Study of Momentum-Based Acceleration Methods in Paradigmatic High-Dimensional Non-Convex Problems
Stefano Sarao Mannelli, Pierfrancesco Urbani
The optimization step in many machine learning problems rarely relies on vanilla gradient descent but it is common practice to use momentum-based accelerated methods. Despite these…
Disordered high-dimensional optimal control
Pierfrancesco Urbani
Mean field optimal control problems are a class of optimization problems that arise from optimal control when applied to the many body setting. In the noisy case one has a set of c…
Low-frequency vibrational spectrum of mean-field disordered systems
Eran Bouchbinder, Edan Lerner, Corrado Rainone +2
We study a recently introduced and exactly solvable mean-field model for the density of vibrational states of a structurally disordered system. The model is formul…
Mean-field model of interacting quasilocalized excitations in glasses
Corrado Rainone, Pierfrancesco Urbani, Francesco Zamponi +2
Structural glasses feature quasilocalized excitations whose frequencies follow a universal density of states . Yet, the underlying physics behind this u…
Proliferation of non-linear excitations in the piecewise-linear perceptron
Antonio Sclocchi, Pierfrancesco Urbani
We investigate the properties of local minima of the energy landscape of a continuous non-convex optimization problem, the spherical perceptron with piecewise linear cost function…