Guillaume Lauga

Guillaume Lauga, Cesare Molinari, Samuel Vaiter

Global optimization is a challenging problem, with plenty of algorithms displaying empirical success, but scarce theoretical backing. In this work, we propose a new theoretical framework called Proximal Basin Hopping (PBH), carefully tailored to combine proximal optimization and local minimization. We use it to construct a practical algorithm that converges to the global minimizer with high probability, when using a finite amount of samples. Proximal Basin Hopping outperforms well known algorithms with theoretical backing on standard synthetic hard functions, and real problems such as fitting scaling laws for deep learning. Furthermore, the higher the dimension, the better the performance gap.

Antoine Gonon, Léon Zheng, Clément Lalanne et al.

This article measures how sparsity can make neural networks more robust to membership inference attacks. The obtained empirical results show that sparsity improves the privacy of the network, while preserving comparable performances on the task at hand. This empirical study completes and extends existing literature.

Antoine Gonon, Léon Zheng, Clément Lalanne et al.

Sparse neural networks are mainly motivated by ressource efficiency since they use fewer parameters than their dense counterparts but still reach comparable accuracies. This article empirically investigates whether sparsity could also improve the privacy of the data used to train the networks. The experiments show positive correlations between the sparsity of the model, its privacy, and its classification error. Simply comparing the privacy of two models with different sparsity levels can yield misleading conclusions on the role of sparsity, because of the additional correlation with the classification error. From this perspective, some caveats are raised about previous works that investigate sparsity and privacy.

Guillaume Lauga

Block-coordinate descent (BCD) is the method of choice to solve numerous large scale optimization problems, however their theoretical study for non-convex optimization, has received less attention. In this paper, we present a new block-coordinate descent (BCD) framework to tackle non-convex composite optimization problems, ensuring decrease of the objective function and convergence to a solution. This framework is general enough to include variable metric proximal gradient updates, proximal Newton updates, and alternated minimization updates. This generality allows to encompass three versions of the most used solvers in the sparse precision matrix estimation problem, deemed Graphical Lasso: graphical ISTA, Primal GLasso, and QUIC. We demonstrate the value of this new framework on non-convex sparse precision matrix estimation problems, providing convergence guarantees and up to a $100$-fold reduction in the number of iterations required to reach state-of-the-art estimation quality.

Guillaume Lauga, Maël Chaumette, Edgar Desainte-Maréville et al.

In this article, we investigate the potential of multilevel approaches to accelerate the training of transformer architectures. Using an ordinary differential equation (ODE) interpretation of these architectures, we propose an appropriate way of varying the discretization of these ODE Transformers in order to accelerate the training. We validate our approach experimentally by a comparison with the standard training procedure.