60 citations · 235 across the 23 of their papers we have counts for
16 papers · 1 filter
Generalization performance of narrow one-hidden layer networks in the teacher-student setting
Rodrigo Pérez Ortiz, Gibbs Nwemadji, Jean Barbier +4
Understanding the generalization properties of neural networks on simple input-output distributions is key to explaining their performance on real datasets. The classical teacher-s…
Random Features Hopfield Networks generalize retrieval to previously unseen examples
Silvio Kalaj, Clarissa Lauditi, Gabriele Perugini +3
It has been recently shown that a learning transition happens when a Hopfield Network stores examples generated as superpositions of random features, where new attractors correspon…
The star-shaped space of solutions of the spherical negative perceptron
Brandon Livio Annesi, Clarissa Lauditi, Carlo Lucibello +4
Empirical studies on the landscape of neural networks have shown that low-energy configurations are often found in complex connected structures, where zero-energy paths between pai…
Storage and Learning phase transitions in the Random-Features Hopfield Model
Matteo Negri, Clarissa Lauditi, Gabriele Perugini +2
The Hopfield model is a paradigmatic model of neural networks that has been analyzed for many decades in the statistical physics, neuroscience, and machine learning communities. In…
Typical and atypical solutions in non-convex neural networks with discrete and continuous weights
Carlo Baldassi, Enrico M. Malatesta, Gabriele Perugini +1
We study the binary and continuous negative-margin perceptrons as simple non-convex neural network models learning random rules and associations. We analyze the geometry of the lan…
Unveiling the structure of wide flat minima in neural networks
Carlo Baldassi, Clarissa Lauditi, Enrico M. Malatesta +2
The success of deep learning has revealed the application potential of neural networks across the sciences and opened up fundamental theoretical problems. In particular, the fact t…
Properties of the geometry of solutions and capacity of multi-layer neural networks with Rectified Linear Units activations
Carlo Baldassi, Enrico M. Malatesta, Riccardo Zecchina
Rectified Linear Units (ReLU) have become the main model for the neural units in current deep learning systems. This choice has been originally suggested as a way to compensate for…
Fluctuations in the random-link matching problem
Enrico M. Malatesta, Giorgio Parisi, Gabriele Sicuro
Using the replica approach and the cavity method, we study the fluctuations of the optimal cost in the random-link matching problem. By means of replica arguments, we derive the ex…
Random Combinatorial Optimization Problems: Mean Field and Finite-Dimensional Results
Enrico M. Malatesta
This PhD thesis is organized as follows. In the first two chapters I will review some basic notions of statistical physics of disordered systems, such as random graph theory, the m…
Average optimal cost for the Euclidean TSP in one dimension
Sergio Caracciolo, Andrea Di Gioacchino, Enrico M. Malatesta +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 stu…
Selberg integrals in 1D random Euclidean optimization problems
Sergio Caracciolo, Andrea Di Gioacchino, Enrico M. Malatesta +1
We consider a set of Euclidean optimization problems in one dimension, where the cost function associated to the couple of points and is the Euclidean distance between them…
Exact value for the average optimal cost of bipartite traveling-salesman and 2-factor problems in two dimensions
Riccardo Capelli, Sergio Caracciolo, Andrea Di Gioacchino +1
We show that the average cost for the traveling-salesman problem in two dimensions, which is the archetypal problem in combinatorial optimization, in the bipartite case, is simply…
Plastic number and possible optimal solutions for an Euclidean 2-matching in one dimension
Sergio Caracciolo, Andrea Di Gioacchino, Enrico M. Malatesta
In this work we consider the problem of finding the minimum-weight loop cover of an undirected graph. This combinatorial optimization problem is called 2-matching and can be seen a…
The Random Fractional Matching Problem
Carlo Lucibello, Enrico M. Malatesta, Giorgio Parisi +1
We consider two formulations of the random-link fractional matching problem, a relaxed version of the more standard random-link (integer) matching problem. In one formulation, we a…
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…
Finite-size corrections in the random assignment problem
Sergio Caracciolo, Matteo P. D'Achille, Enrico M. Malatesta +1
We analytically derive, in the context of the replica formalism, the first finite size corrections to the average optimal cost in the random assignment problem for a quite generic…