35 citations · 360 across the 36 of their papers we have counts for
37 papers
Microscopic and collective signatures of feature learning in neural networks
Andrea Corti, Rosalba Pacelli, Pietro Rotondo +1
Feature extraction - the ability to identify relevant properties of data - is a key factor underlying the success of deep learning. Yet, it has proved difficult to elucidate its na…
Learning to flock in open space by avoiding collisions and staying together
Martino Brambati, Antonio Celani, Marco Gherardi +1
We investigate the emergence of cohesive flocking in open, boundless space using a multi-agent reinforcement learning framework. Agents integrate positional and orientational infor…
Feature learning in finite-width Bayesian deep linear networks with multiple outputs and convolutional layers
Federico Bassetti, Marco Gherardi, Alessandro Ingrosso +2
Deep linear networks have been extensively studied, as they provide simplified models of deep learning. However, little is known in the case of finite-width architectures with mult…
Resolution of similar patterns in a solvable model of unsupervised deep learning with structured data
Andrea Baroffio, Pietro Rotondo, Marco Gherardi
Empirical data, on which deep learning relies, has substantial internal structure, yet prevailing theories often disregard this aspect. Recent research has led to the definition of…
Inversion dynamics of class manifolds in deep learning reveals tradeoffs underlying generalisation
Simone Ciceri, Lorenzo Cassani, Matteo Osella +3
To achieve near-zero training error in a classification problem, the layers of a feed-forward network have to disentangle the manifolds of data points with different labels, to fac…
A statistical mechanics framework for Bayesian deep neural networks beyond the infinite-width limit
R. Pacelli, S. Ariosto, M. Pastore +3
Despite the practical success of deep neural networks, a comprehensive theoretical framework that can predict practically relevant scores, such as the test accuracy, from knowledge…
Universal mean field upper bound for the generalisation gap of deep neural networks
S. Ariosto, R. Pacelli, F. Ginelli +2
Modern deep neural networks (DNNs) represent a formidable challenge for theorists: according to the commonly accepted probabilistic framework that describes their performance, thes…
Remote teaching data-driven physical modeling through a COVID-19 open ended data challenge
Marco Cosentino Lagomarsino, Guglielmo Pacifico, Valerio Firmano +7
Physics can be seen as a conceptual approach to scientific problems, a method for discovery, but teaching this aspect of our discipline can be a challenge. We report on a first-tim…
Criticality and conformality in the random dimer model
Sergio Caracciolo, Riccardo Fabbricatore, Marco Gherardi +3
In critical systems, the effect of a localized perturbation affects points that are arbitrarily far from the perturbation location. In this paper, we study the effect of localized…
Statistical learning theory of structured data
Mauro Pastore, Pietro Rotondo, Vittorio Erba +1
The traditional approach of statistical physics to supervised learning routinely assumes unrealistic generative models for the data: usually inputs are independent random variables…
Beyond the storage capacity: data driven satisfiability transition
Pietro Rotondo, Mauro Pastore, Marco Gherardi
Data structure has a dramatic impact on the properties of neural networks, yet its significance in the established theoretical frameworks is poorly understood. Here we compute the…
Random geometric graphs in high dimension
Vittorio Erba, Sebastiano Ariosto, Marco Gherardi +1
Many machine learning algorithms used for dimensional reduction and manifold learning leverage on the computation of the nearest neighbours to each point of a dataset to perform th…
Intrinsic dimension estimation for locally undersampled data
Vittorio Erba, Marco Gherardi, Pietro Rotondo
High-dimensional data are ubiquitous in contemporary science and finding methods to compress them is one of the primary goals of machine learning. Given a dataset lying in a high-d…
Counting the learnable functions of structured data
Pietro Rotondo, Marco Cosentino Lagomarsino, Marco Gherardi
Cover's function counting theorem is a milestone in the theory of artificial neural networks. It provides an answer to the fundamental question of determining how many binary assig…
Generalization from correlated sets of patterns in the perceptron
Francesco Borra, Marco Cosentino Lagomarsino, Pietro Rotondo +1
Generalization is a central aspect of learning theory. Here, we propose a framework that explores an auxiliary task-dependent notion of generalization, and attempts to quantitative…
Efficiency and shrinking in evolving networks
Arianna Bottinelli, Marco Gherardi, Marc Barthelemy
Characterizing the spatio-temporal evolution of networks is a central topic in many disciplines. While network expansion has been studied thoroughly, less is known about how empiri…
A network model of conviction-driven social segregation
Gianluca Teza, Samir Suweis, Marco Gherardi +2
In order to measure, predict, and prevent social segregation, it is necessary to understand the factors that cause it. While in most available descriptions space plays an essential…
Spontaneous domain formation in disordered copolymers as a mechanism for chromosome structuring
Matteo Negri, Marco Gherardi, Guido Tiana +1
Motivated by the problem of domain formation in chromosomes, we studied a co--polymer model where only a subset of the monomers feel attractive interactions. These monomers are dis…
Solution for a bipartite Euclidean traveling-salesman problem in one dimension
Sergio Caracciolo, Andrea Di Gioacchino, Marco Gherardi +1
The traveling salesman problem is one of the most studied combinatorial optimization problems, because of the simplicity in its statement and the difficulty in its solution. We cha…
Zipf and Heaps laws from dependency structures in component systems
Andrea Mazzolini, Jacopo Grilli, Eleonora De Lazzari +3
Complex natural and technological systems can be considered, on a coarse-grained level, as assemblies of elementary components: for example, genomes as sets of genes, or texts as s…
Jack on a Devil's staircase
Andrea Di Gioacchino, Marco Gherardi, Luca Guido Molinari +1
We review a simple mechanism for the formation of plateaux in the fractional quantum Hall effect. It arises from a map of the microscopic Hamiltonian in the thin torus limit to a l…
Current quantization and fractal hierarchy in a driven repulsive lattice gas
Pietro Rotondo, Alessandro Luigi Sellerio, Pietro Glorioso +3
Driven lattice gases are widely regarded as the paradigm of collective phenomena out of equilibrium. While such models are usually studied with nearest-neighbor interactions, many…
Statistics of shared components in complex component systems
Andrea Mazzolini, Marco Gherardi, Michele Caselle +2
Many complex systems are modular. Such systems can be represented as "component systems", i.e., sets of elementary components, such as LEGO bricks in LEGO sets. The bricks found in…
Intermittent transport of bacterial chromosomal loci
Marco Gherardi, Ludovico Calabrese, Mikhail Tamm +1
The short-time dynamics of bacterial chromosomal loci is a mixture of subdiffusive and active motion, in the form of rapid relocations with near-ballistic dynamics. While previous…