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Marvels and Pitfalls of the Langevin Algorithm in Noisy High-dimensional Inference
Stefano Sarao Mannelli, Giulio Biroli, Chiara Cammarota +3
Gradient-descent-based algorithms and their stochastic versions have widespread applications in machine learning and statistical inference. In this work we perform an analytic stud…
Dynamics around the Site Percolation Threshold on High-Dimensional Hypercubic Lattices
Giulio Biroli, Patrick Charbonneau, Yi Hu
Recent advances on the glass problem motivate reexamining classical models of percolation. Here, we consider the displacement of an ant in a labyrinth near the percolation threshol…
Delocalization and ergodicity of the Anderson model on Bethe lattices
Giulio Biroli, Marco Tarzia
We review the state of the art on the delocalized non-ergodic regime of the Anderson model on Bethe lattices. We also present new results using Belief Propagation, which consists i…
A jamming transition from under- to over-parametrization affects loss landscape and generalization
Stefano Spigler, Mario Geiger, Stéphane d'Ascoli +3
We argue that in fully-connected networks a phase transition delimits the over- and under-parametrized regimes where fitting can or cannot be achieved. Under some general condition…
Complexity of energy barriers in mean-field glassy systems
Valentina Ros, Giulio Biroli, Chiara Cammarota
We analyze the energy barriers that allow escapes from a given local minimum in a mean-field model of glasses. We perform this study by using the Kac-Rice method and computing the…
The jamming transition as a paradigm to understand the loss landscape of deep neural networks
Mario Geiger, Stefano Spigler, Stéphane d'Ascoli +4
Deep learning has been immensely successful at a variety of tasks, ranging from classification to AI. Learning corresponds to fitting training data, which is implemented by descend…