University of Cambridge > Talks.cam > Applied and Computational Analysis > On the Training of Infinitely Deep and Wide ResNets

On the Training of Infinitely Deep and Wide ResNets

Add to your list(s) Download to your calendar using vCal

If you have a question about this talk, please contact Matthew Colbrook.

Overparametrization is a key factor in the absence of convexity to explain global convergence of gradient descent (GD) for neural networks. Beside the well studied lazy regime, infinite width (mean field) analysis has been developed for shallow networks, using convex optimization technics. To bridge the gap between the lazy and mean field regimes, we study Residual Networks (ResNets) in which the residual block has linear parametrization while still being nonlinear. Such ResNets admit both infinite depth and width limits, encoding residual blocks in a Reproducing Kernel Hilbert Space (RKHS). In this limit, we prove a local Polyak-Lojasiewicz inequality. Thus, every critical point is a global minimizer and a local convergence result of GD holds, retrieving the lazy regime. In contrast with other mean-field studies, it applies to both parametric and non-parametric cases under an expressivity condition on the residuals. Our analysis leads to a practical and quantified recipe: starting from a universal RKHS , Random Fourier Features are applied to obtain a finite dimensional parameterization satisfying with high-probability our expressivity condition. This is a joint work with Raphaël Barboni and François-Xavier Vialard.

This talk is part of the Applied and Computational Analysis series.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.

 

© 2006-2024 Talks.cam, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity