35 citations · 115 across the 10 of their papers we have counts for
10 papers
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…
Deep Networks on Toroids: Removing Symmetries Reveals the Structure of Flat Regions in the Landscape Geometry
Fabrizio Pittorino, Antonio Ferraro, Gabriele Perugini +3
We systematize the approach to the investigation of deep neural network landscapes by basing it on the geometry of the space of implemented functions rather than the space of param…
Deep learning via message passing algorithms based on belief propagation
Carlo Lucibello, Fabrizio Pittorino, Gabriele Perugini +1
Message-passing algorithms based on the Belief Propagation (BP) equations constitute a well-known distributed computational scheme. It is exact on tree-like graphical models and ha…
Learning through atypical "phase transitions" in overparameterized neural networks
Carlo Baldassi, Clarissa Lauditi, Enrico M. Malatesta +3
Current deep neural networks are highly overparameterized (up to billions of connection weights) and nonlinear. Yet they can fit data almost perfectly through variants of gradient…
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…
Entropic gradient descent algorithms and wide flat minima
Fabrizio Pittorino, Carlo Lucibello, Christoph Feinauer +4
The properties of flat minima in the empirical risk landscape of neural networks have been debated for some time. Increasing evidence suggests they possess better generalization ca…
An improved Belief Propagation algorithm finds many Bethe states in the random field Ising model on random graphs
Gabriele Perugini, Federico Ricci-Tersenghi
We first present an empirical study of the Belief Propagation (BP) algorithm, when run on the random field Ising model defined on random regular graphs in the zero temperature limi…