no code implementations • 17 Jun 2020 • Jonas Paccolat, Stefano Spigler, Matthieu Wyart
(ii) Next we consider support-vector binary classification and introduce the stripe model where the data label depends on a single coordinate $y(\underline{x}) = y(x_1)$, corresponding to parallel decision boundaries separating labels of different signs, and consider that there is no margin at these interfaces.
no code implementations • 19 Jun 2019 • Mario Geiger, Stefano Spigler, Arthur Jacot, Matthieu Wyart
Two distinct limits for deep learning have been derived as the network width $h\rightarrow \infty$, depending on how the weights of the last layer scale with $h$.
no code implementations • 26 May 2019 • Stefano Spigler, Mario Geiger, Matthieu Wyart
We extract $a$ from real data by performing kernel PCA, leading to $\beta\approx0. 36$ for MNIST and $\beta\approx0. 07$ for CIFAR10, in good agreement with observations.
1 code implementation • 6 Jan 2019 • Mario Geiger, Arthur Jacot, Stefano Spigler, Franck Gabriel, Levent Sagun, Stéphane d'Ascoli, Giulio Biroli, Clément Hongler, Matthieu Wyart
At this threshold, we argue that $\|f_{N}\|$ diverges.
no code implementations • 22 Oct 2018 • Stefano Spigler, Mario Geiger, Stéphane d'Ascoli, Levent Sagun, Giulio Biroli, Matthieu Wyart
We argue that in fully-connected networks a phase transition delimits the over- and under-parametrized regimes where fitting can or cannot be achieved.
2 code implementations • 25 Sep 2018 • Mario Geiger, Stefano Spigler, Stéphane d'Ascoli, Levent Sagun, Marco Baity-Jesi, Giulio Biroli, Matthieu Wyart
In the vicinity of this transition, properties of the curvature of the minima of the loss are critical.
no code implementations • ICML 2018 • Marco Baity-Jesi, Levent Sagun, Mario Geiger, Stefano Spigler, Gerard Ben Arous, Chiara Cammarota, Yann Lecun, Matthieu Wyart, Giulio Biroli
We analyze numerically the training dynamics of deep neural networks (DNN) by using methods developed in statistical physics of glassy systems.