no code implementations • 26 Nov 2023 • Cédric Gerbelot, Avetik Karagulyan, Stefani Karp, Kavya Ravichandran, Menachem Stern, Nathan Srebro
Although statistical learning theory provides a robust framework to understand supervised learning, many theoretical aspects of deep learning remain unclear, in particular how different architectures may lead to inductive bias when trained using gradient based methods.
1 code implementation • 22 Mar 2022 • Elisabetta Cornacchia, Francesca Mignacco, Rodrigo Veiga, Cédric Gerbelot, Bruno Loureiro, Lenka Zdeborová
For Gaussian teacher weights, we investigate the performance of ERM with both cross-entropy and square losses, and explore the role of ridge regularisation in approaching Bayes-optimality.
no code implementations • 31 Jan 2022 • Bruno Loureiro, Cédric Gerbelot, Maria Refinetti, Gabriele Sicuro, Florent Krzakala
From the sampling of data to the initialisation of parameters, randomness is ubiquitous in modern Machine Learning practice.
no code implementations • 24 Sep 2021 • Cédric Gerbelot, Raphaël Berthier
Approximate-message passing (AMP) algorithms have become an important element of high-dimensional statistical inference, mostly due to their adaptability and concentration properties, the state evolution (SE) equations.
2 code implementations • 7 Jun 2021 • Bruno Loureiro, Gabriele Sicuro, Cédric Gerbelot, Alessandro Pacco, Florent Krzakala, Lenka Zdeborová
Generalised linear models for multi-class classification problems are one of the fundamental building blocks of modern machine learning tasks.
1 code implementation • NeurIPS 2021 • Bruno Loureiro, Cédric Gerbelot, Hugo Cui, Sebastian Goldt, Florent Krzakala, Marc Mézard, Lenka Zdeborová
While still solvable in a closed form, this generalization is able to capture the learning curves for a broad range of realistic data sets, thus redeeming the potential of the teacher-student framework.
no code implementations • 11 Feb 2020 • Cédric Gerbelot, Alia Abbara, Florent Krzakala
We consider the problem of learning a coefficient vector $x_{0}$ in $R^{N}$ from noisy linear observations $y=Fx_{0}+w$ in $R^{M}$ in the high dimensional limit $M, N$ to infinity with $\alpha=M/N$ fixed.