35 citations · 81 across the 22 of their papers we have counts for
8 papers · 1 filter
Convergence of Shallow ReLU Networks on Weakly Interacting Data
Léo Dana, Francis Bach, Loucas Pillaud-Vivien
We analyse the convergence of one-hidden-layer ReLU networks trained by gradient flow on data points. Our main contribution leverages the high dimensionality of the ambient spa…
Variational Inference for Uncertainty Quantification: an Analysis of Trade-offs
Charles C. Margossian, Loucas Pillaud-Vivien, Lawrence K. Saul
Given an intractable distribution , the problem of variational inference (VI) is to find the best approximation from some more tractable family . Commonly, one chooses to…
Batch and match: black-box variational inference with a score-based divergence
Diana Cai, Chirag Modi, Loucas Pillaud-Vivien +4
Most leading implementations of black-box variational inference (BBVI) are based on optimizing a stochastic evidence lower bound (ELBO). But such approaches to BBVI often converge…
On Learning Gaussian Multi-index Models with Gradient Flow
Alberto Bietti, Joan Bruna, Loucas Pillaud-Vivien
We study gradient flow on the multi-index regression problem for high-dimensional Gaussian data. Multi-index functions consist of a composition of an unknown low-rank linear projec…
Kernelized Diffusion maps
Loucas Pillaud-Vivien, Francis Bach
Spectral clustering and diffusion maps are celebrated dimensionality reduction algorithms built on eigen-elements related to the diffusive structure of the data. The core of these…
Label noise (stochastic) gradient descent implicitly solves the Lasso for quadratic parametrisation
Loucas Pillaud-Vivien, Julien Reygner, Nicolas Flammarion
Understanding the implicit bias of training algorithms is of crucial importance in order to explain the success of overparametrised neural networks. In this paper, we study the rol…
Gradient flow dynamics of shallow ReLU networks for square loss and orthogonal inputs
Etienne Boursier, Loucas Pillaud-Vivien, Nicolas Flammarion
The training of neural networks by gradient descent methods is a cornerstone of the deep learning revolution. Yet, despite some recent progress, a complete theory explaining its su…
Overcoming the curse of dimensionality with Laplacian regularization in semi-supervised learning
Vivien Cabannes, Loucas Pillaud-Vivien, Francis Bach +1
As annotations of data can be scarce in large-scale practical problems, leveraging unlabelled examples is one of the most important aspects of machine learning. This is the aim of…