no code implementations • 2 May 2024 • Simon Vary, Pierre Ablin, Bin Gao, P. -A. Absil

Optimization over the set of matrices that satisfy $X^\top B X = I_p$, referred to as the generalized Stiefel manifold, appears in many applications involving sampled covariance matrices such as canonical correlation analysis (CCA), independent component analysis (ICA), and the generalized eigenvalue problem (GEVP).

1 code implementation • 26 Feb 2024 • Zhenzhang Ye, Gabriel Peyré, Daniel Cremers, Pierre Ablin

As a function of the error of the inner problem resolution, we study the error of the IFT method.

no code implementations • 5 Feb 2024 • Yu-Guan Hsieh, James Thornton, Eugene Ndiaye, Michal Klein, Marco Cuturi, Pierre Ablin

Beyond minimizing a single training loss, many deep learning estimation pipelines rely on an auxiliary objective to quantify and encourage desirable properties of the model (e. g. performance on another dataset, robustness, agreement with a prior).

no code implementations • 2 Feb 2024 • David Grangier, Angelos Katharopoulos, Pierre Ablin, Awni Hannun

Large language models have emerged as a versatile tool but are challenging to apply to tasks lacking large inference budgets and large in-domain training sets.

Ranked #1 on Language Modelling on The Pile (Test perplexity metric)

no code implementations • 22 Dec 2023 • Valérie Castin, Pierre Ablin, Gabriel Peyré

This allows us to generalize attention to inputs of infinite length, and to derive an upper bound and a lower bound on the Lipschitz constant of self-attention on compact sets.

no code implementations • 1 Dec 2023 • Ambroise Heurtebise, Pierre Ablin, Alexandre Gramfort

Linear Independent Component Analysis (ICA) is a blind source separation technique that has been used in various domains to identify independent latent sources from observed signals.

no code implementations • 20 Nov 2023 • David Grangier, Pierre Ablin, Awni Hannun

Large neural networks pretrained on web-scale corpora are central to modern machine learning.

no code implementations • 26 Oct 2023 • Anastasia Ivanova, Pierre Ablin

In many scenarios, one uses a large training set to train a model with the goal of performing well on a smaller testing set with a different distribution.

no code implementations • 20 Jun 2023 • Michal Klein, Aram-Alexandre Pooladian, Pierre Ablin, Eugène Ndiaye, Jonathan Niles-Weed, Marco Cuturi

Given a source and a target probability measure supported on $\mathbb{R}^d$, the Monge problem asks to find the most efficient way to map one distribution to the other.

no code implementations • 24 May 2023 • Zaccharie Ramzi, Pierre Ablin, Gabriel Peyré, Thomas Moreau

Implicit deep learning has recently gained popularity with applications ranging from meta-learning to Deep Equilibrium Networks (DEQs).

no code implementations • 29 Mar 2023 • Pierre Ablin, Simon Vary, Bin Gao, P. -A. Absil

Finally, our experiments demonstrate the promise of our approach to an array of machine-learning problems that involve orthogonality constraints.

no code implementations • 17 Feb 2023 • Mathieu Dagréou, Thomas Moreau, Samuel Vaiter, Pierre Ablin

Bilevel optimization problems, which are problems where two optimization problems are nested, have more and more applications in machine learning.

no code implementations • 8 Feb 2023 • Marco Cuturi, Michal Klein, Pierre Ablin

Optimal transport (OT) theory focuses, among all maps $T:\mathbb{R}^d\rightarrow \mathbb{R}^d$ that can morph a probability measure onto another, on those that are the ``thriftiest'', i. e. such that the averaged cost $c(x, T(x))$ between $x$ and its image $T(x)$ be as small as possible.

3 code implementations • 27 Jun 2022 • Thomas Moreau, Mathurin Massias, Alexandre Gramfort, Pierre Ablin, Pierre-Antoine Bannier, Benjamin Charlier, Mathieu Dagréou, Tom Dupré La Tour, Ghislain Durif, Cassio F. Dantas, Quentin Klopfenstein, Johan Larsson, En Lai, Tanguy Lefort, Benoit Malézieux, Badr Moufad, Binh T. Nguyen, Alain Rakotomamonjy, Zaccharie Ramzi, Joseph Salmon, Samuel Vaiter

Numerical validation is at the core of machine learning research as it allows to assess the actual impact of new methods, and to confirm the agreement between theory and practice.

no code implementations • 29 May 2022 • Michael E. Sander, Pierre Ablin, Gabriel Peyré

As a byproduct of our analysis, we consider the use of a memory-free discrete adjoint method to train a ResNet by recovering the activations on the fly through a backward pass of the network, and show that this method theoretically succeeds at large depth if the residual functions are Lipschitz with the input.

1 code implementation • 31 Jan 2022 • Mathieu Dagréou, Pierre Ablin, Samuel Vaiter, Thomas Moreau

However, computing the gradient of the value function involves solving a linear system, which makes it difficult to derive unbiased stochastic estimates.

1 code implementation • NeurIPS 2021 • Hugo Richard, Pierre Ablin, Bertrand Thirion, Alexandre Gramfort, Aapo Hyvärinen

While ShICA-J is based on second-order statistics, we further propose to leverage non-Gaussianity of the components using a maximum-likelihood method, ShICA-ML, that is both more accurate and more costly.

1 code implementation • 22 Oct 2021 • Michael E. Sander, Pierre Ablin, Mathieu Blondel, Gabriel Peyré

We show that the row-wise stochastic attention matrices in classical Transformers get close to doubly stochastic matrices as the number of epochs increases, justifying the use of Sinkhorn normalization as an informative prior.

2 code implementations • 20 May 2021 • Anna Korba, Pierre-Cyril Aubin-Frankowski, Szymon Majewski, Pierre Ablin

We investigate the properties of its Wasserstein gradient flow to approximate a target probability distribution $\pi$ on $\mathbb{R}^d$, known up to a normalization constant.

no code implementations • 22 Feb 2021 • Hugo Richard, Pierre Ablin, Aapo Hyvärinen, Alexandre Gramfort, Bertrand Thirion

By contrast, we propose Adaptive multiView ICA (AVICA), a noisy ICA model where each view is a linear mixture of shared independent sources with additive noise on the sources.

1 code implementation • 15 Feb 2021 • Pierre Ablin, Gabriel Peyré

We consider the problem of minimizing a function over the manifold of orthogonal matrices.

1 code implementation • 15 Feb 2021 • Michael E. Sander, Pierre Ablin, Mathieu Blondel, Gabriel Peyré

We show on CIFAR and ImageNet that Momentum ResNets have the same accuracy as ResNets, while having a much smaller memory footprint, and show that pre-trained Momentum ResNets are promising for fine-tuning models.

Ranked #127 on Image Classification on CIFAR-10

no code implementations • 27 Nov 2020 • Pierre Ablin

We consider the problem of training a deep orthogonal linear network, which consists of a product of orthogonal matrices, with no non-linearity in-between.

no code implementations • 21 Aug 2020 • Pierre Ablin, Jean-François Cardoso, Alexandre Gramfort

Signals are modelled as a linear mixing of independent sources corrupted by additive noise, where sources and the noise are stationary Gaussian time series.

1 code implementation • NeurIPS 2020 • Hugo Richard, Luigi Gresele, Aapo Hyvärinen, Bertrand Thirion, Alexandre Gramfort, Pierre Ablin

Group studies involving large cohorts of subjects are important to draw general conclusions about brain functional organization.

no code implementations • 25 May 2020 • Ronan Perry, Gavin Mischler, Richard Guo, Theodore Lee, Alexander Chang, Arman Koul, Cameron Franz, Hugo Richard, Iain Carmichael, Pierre Ablin, Alexandre Gramfort, Joshua T. Vogelstein

As data are generated more and more from multiple disparate sources, multiview data sets, where each sample has features in distinct views, have ballooned in recent years.

no code implementations • ICML 2020 • Pierre Ablin, Gabriel Peyré, Thomas Moreau

In most cases, the minimum has no closed-form, and an approximation is obtained via an iterative algorithm.

1 code implementation • NeurIPS 2019 • David Sabbagh, Pierre Ablin, Gael Varoquaux, Alexandre Gramfort, Denis A. Engemann

We show that Wasserstein and geometric distances allow perfect out-of-sample prediction on the generative models.

1 code implementation • NeurIPS 2019 • Pierre Ablin, Thomas Moreau, Mathurin Massias, Alexandre Gramfort

We demonstrate that for a large class of unfolded algorithms, if the algorithm converges to the solution of the Lasso, its last layers correspond to ISTA with learned step sizes.

1 code implementation • 28 Nov 2018 • Pierre Ablin, Jean-François Cardoso, Alexandre Gramfort

The approximate joint diagonalization of a set of matrices consists in finding a basis in which these matrices are as diagonal as possible.

1 code implementation • 6 Nov 2018 • Pierre Ablin, Dylan Fagot, Herwig Wendt, Alexandre Gramfort, Cédric Févotte

Nonnegative matrix factorization (NMF) is a popular method for audio spectral unmixing.

no code implementations • 25 Jun 2018 • Pierre Ablin, Jean-François Cardoso, Alexandre Gramfort

We study optimization methods for solving the maximum likelihood formulation of independent component analysis (ICA).

1 code implementation • 25 May 2018 • Pierre Ablin, Alexandre Gramfort, Jean-François Cardoso, Francis Bach

We derive an online algorithm for the streaming setting, and an incremental algorithm for the finite sum setting, with the following benefits.

1 code implementation • 29 Nov 2017 • Pierre Ablin, Jean-François Cardoso, Alexandre Gramfort

Independent Component Analysis (ICA) is a technique for unsupervised exploration of multi-channel data widely used in observational sciences.

2 code implementations • 25 Jun 2017 • Pierre Ablin, Jean-François Cardoso, Alexandre Gramfort

Independent Component Analysis (ICA) is a technique for unsupervised exploration of multi-channel data that is widely used in observational sciences.

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