1 code implementation • 2 Oct 2023 • Antoine Gonon, Nicolas Brisebarre, Elisa Riccietti, Rémi Gribonval
The versatility of the toolkit and its ease of implementation allow us to challenge the concrete promises of path-norm-based generalization bounds, by numerically evaluating the sharpest known bounds for ResNets on ImageNet.
no code implementations • 5 Jun 2023 • Quoc-Tung Le, Elisa Riccietti, Rémi Gribonval
Then, the existence of a global optimum is proved for every concrete optimization problem involving a shallow sparse ReLU neural network of output dimension one.
no code implementations • 23 May 2023 • Serge Gratton, Valentin Mercier, Elisa Riccietti, Philippe L. Toint
Multi-level methods are widely used for the solution of large-scale problems, because of their computational advantages and exploitation of the complementarity between the involved sub-problems.
1 code implementation • 28 Jul 2022 • Léon Zheng, Gilles Puy, Elisa Riccietti, Patrick Pérez, Rémi Gribonval
We introduce a regularization loss based on kernel mean embeddings with rotation-invariant kernels on the hypersphere (also known as dot-product kernels) for self-supervised learning of image representations.
no code implementations • 24 May 2022 • Antoine Gonon, Nicolas Brisebarre, Rémi Gribonval, Elisa Riccietti
This is achieved using a new lower-bound on the Lipschitz constant of the map that associates the parameters of ReLU networks to their realization, and an upper-bound generalizing classical results.
no code implementations • 4 Oct 2021 • Léon Zheng, Elisa Riccietti, Rémi Gribonval
In particular, in the case of fixed-support sparse matrix factorization, we give a general sufficient condition for identifiability based on rank-one matrix completability, and we derive from it a completion algorithm that can verify if this sufficient condition is satisfied, and recover the entries in the two sparse factors if this is the case.
1 code implementation • 4 Oct 2021 • Léon Zheng, Elisa Riccietti, Rémi Gribonval
Our main contribution is to prove that any $N \times N$ matrix having the so-called butterfly structure admits an essentially unique factorization into $J$ butterfly factors (where $N = 2^{J}$), and that the factors can be recovered by a hierarchical factorization method, which consists in recursively factorizing the considered matrix into two factors.
no code implementations • 29 Sep 2021 • Elisa Riccietti, Valentin Mercier, Serge Gratton, Pierre Boudier
In this paper we introduce multilevel physics informed neural networks (MPINNs).
no code implementations • 9 Apr 2019 • Henri Calandra, Serge Gratton, Elisa Riccietti, Xavier Vasseur
Here a feedforward neural network is used to approximate the solution of the partial differential equation.