Rémi Flamary
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Je suis Professeur au sein du département de Mathématiques Appliquées et au Laboratoire CMAP de l'École Polytechnique. J'étais précédemment Maître de Conférence à l'Université Côte d'Azur au sein du département d'Électronique et du Laboratoire Lagrange de l'Observatoire de la Côte d'Azur. J'ai préparé une thèse, sous la direction d'Alain Rakotomamonjy, à l'Université de Rouen et au Laboratoire LITIS.
Sur ce site web, vous trouverez une liste de mes publications, des supports de cours et de présentations, ainsi que divers logiciels et code source.
Intérêts de recherche
- Apprentissage statistique et traitement statistique du signal
- Transport Optimal pour l'apprentissage, TO sur les graphes
- Adaptation de domaine, transfer et multi-tache, décalage de données
- Optimisation avec sélection de variable, normes mixtes, non-convexes
- Apprentissage de représentations, apprentissage profond
- Applications d’apprentissage statistique
- Traitement de signaux biomédicaux, Interfaces Cerveaux-Machine
- Télédétection et imagerie hyperspectrale
- Énergie et climat
- Traitement d'images astrophysiques
Travaux récents
| S. Mazelet, R. Flamary, B. Thirion, Unsupervised Learning for Optimal Transport plan prediction between unbalanced graphs, Neural Information Processing Systems (NeurIPS), 2025. |
| Abstract: Optimal transport between graphs, based on Gromov-Wasserstein and other extensions, is a powerful tool for comparing and aligning graph structures. However, solving the associated non-convex optimization problems is computationally expensive, which limits the scalability of these methods to large graphs. In this work, we present Unbalanced Learning of Optimal Transport (ULOT), a deep learning method that predicts optimal transport plans between two graphs. Our method is trained by minimizing the fused unbalanced Gromov-Wasserstein (FUGW) loss. We propose a novel neural architecture with cross-attention that is conditioned on the FUGW tradeoff hyperparameters. We evaluate ULOT on synthetic stochastic block model (SBM) graphs and on real cortical surface data obtained from fMRI. ULOT predicts transport plans with competitive loss up to two orders of magnitude faster than classical solvers. Furthermore, the predicted plan can be used as a warm start for classical solvers to accelerate their convergence. Finally, the predicted transport plan is fully differentiable with respect to the graph inputs and FUGW hyperparameters, enabling the optimization of functionals of the ULOT plan. |
BibTeX:
@inproceedings{mazelet2025learning,
author = {Sonia Mazelet and Rémi Flamary and Bertrand Thirion},
title = {Unsupervised Learning for Optimal Transport plan prediction between unbalanced graphs},
booktitle = {Neural Information Processing Systems (NeurIPS)},
year = {2025}
} |
| P. Krzakala, G. Melo, C. Laclau, F. d'Alché-Buc, R. Flamary, The quest for the GRAph Level autoEncoder (GRALE), Neural Information Processing Systems (NeurIPS), 2025. |
| Abstract: Although graph-based learning has attracted a lot of attention, graph representation learning is still a challenging task whose resolution may impact key application fields such as chemistry or biology. To this end, we introduce GRALE, a novel graph autoencoder that encodes and decodes graphs of varying sizes into a shared embedding space. GRALE is trained using an Optimal Transport-inspired loss that compares the original and reconstructed graphs and leverages a differentiable node matching module, which is trained jointly with the encoder and decoder. The proposed attention-based architecture relies on Evoformer, the core component of AlphaFold, which we extend to support both graph encoding and decoding. We show, in numerical experiments on simulated and molecular data, that GRALE enables a highly general form of pre-training, applicable to a wide range of downstream tasks, from classification and regression to more complex tasks such as graph interpolation, editing, matching, and prediction. |
BibTeX:
@inproceedings{krzakala2025quest,
author = {Paul Krzakala and Gabriel Melo and Charlotte Laclau and Florence d'Alché-Buc and Rémi Flamary},
title = {The quest for the GRAph Level autoEncoder (GRALE)},
booktitle = {Neural Information Processing Systems (NeurIPS)},
year = {2025}
} |
| Y. Lalou, T. Gnassounou, A. Collas, A. de Mathelin, O. Kachaiev, A. Odonnat, A. Gramfort, T. Moreau, R. Flamary, SKADA-Bench: Benchmarking Unsupervised Domain Adaptation Methods with Realistic Validation, Transactions of Machine Learning Research (TMLR), 2025. |
| Abstract: Unsupervised Domain Adaptation (DA) consists of adapting a model trained on a labeled source domain to perform well on an unlabeled target domain with some data distribution shift. While many methods have been proposed in the literature, fair and realistic evaluation remains an open question, particularly due to methodological difficulties in selecting hyperparameters in the unsupervised setting. With SKADA-Bench, we propose a framework to evaluate DA methods and present a fair evaluation of existing shallow algorithms, including reweighting, mapping, and subspace alignment. Realistic hyperparameter selection is performed with nested cross-validation and various unsupervised model selection scores, on both simulated datasets with controlled shifts and real-world datasets across diverse modalities, such as images, text, biomedical, and tabular data with specific feature extraction. Our benchmark highlights the importance of realistic validation and provides practical guidance for real-life applications, with key insights into the choice and impact of model selection approaches. SKADA-Bench is open-source, reproducible, and can be easily extended with novel DA methods, datasets, and model selection criteria without requiring re-evaluating competitors. SKADA-Bench is available on GitHub at |
BibTeX:
@article{lalou2025skadabench,
author = {Yanis Lalou and Théo Gnassounou and Antoine Collas and de Mathelin, Antoine and Oleksii Kachaiev and Ambroise Odonnat and Alexandre Gramfort and Thomas Moreau and Rémi Flamary},
title = {SKADA-Bench: Benchmarking Unsupervised Domain Adaptation Methods with Realistic Validation},
journal = { Transactions of Machine Learning Research (TMLR)},
year = {2025}
} |
| P. Krzakala, J. Yang, R. Flamary, F. d'Alché-Buc, C. Laclau, M. Labeau, Any2Graph: Deep End-To-End Supervised Graph Prediction With An Optimal Transport Loss, Neural Information Processing Systems (NeurIPS), 2024. |
| Abstract: We propose Any2graph, a generic framework for end-to-end Supervised Graph Prediction (SGP) i.e. a deep learning model that predicts an entire graph for any kind of input. The framework is built on a novel Optimal Transport loss, the Partially-Masked Fused Gromov-Wasserstein, that exhibits all necessary properties (permutation invariance, differentiability and scalability) and is designed to handle any-sized graphs. Numerical experiments showcase the versatility of the approach that outperform existing competitors on a novel challenging synthetic dataset and a variety of real-world tasks such as map construction from satellite image (Sat2Graph) or molecule prediction from fingerprint (Fingerprint2Graph). |
BibTeX:
@inproceedings{krzakala2024endtoend,
author = {Paul Krzakala and Junjie Yang and Rémi Flamary and Florence d'Alché-Buc and Charlotte Laclau and Matthieu Labeau},
title = {Any2Graph: Deep End-To-End Supervised Graph Prediction With An Optimal Transport Loss},
booktitle = {Neural Information Processing Systems (NeurIPS)},
year = {2024}
} |
| T. Gnassounou, R. Flamary, A. Gramfort, Convolutional Monge Mapping Normalization for learning on biosignals, Neural Information Processing Systems (NeurIPS), 2023. |
| Abstract: In many machine learning applications on signals and biomedical data, especially electroencephalogram (EEG), one major challenge is the variability of the data across subjects, sessions, and hardware devices. In this work, we propose a new method called Convolutional Monge Mapping Normalization (CMMN), which consists in filtering the signals in order to adapt their power spectrum density (PSD) to a Wasserstein barycenter estimated on training data. CMMN relies on novel closed-form solutions for optimal transport mappings and barycenters and provides individual test time adaptation to new data without needing to retrain a prediction model. Numerical experiments on sleep EEG data show that CMMN leads to significant and consistent performance gains independent from the neural network architecture when adapting between subjects, sessions, and even datasets collected with different hardware. Notably our performance gain is on par with much more numerically intensive Domain Adaptation (DA) methods and can be used in conjunction with those for even better performances. |
BibTeX:
@inproceedings{gnassounou2023convolutional,
author = {Gnassounou, Théo and Flamary, Rémi and Gramfort, Alexandre},
title = {Convolutional Monge Mapping Normalization for learning on biosignals},
booktitle = {Neural Information Processing Systems (NeurIPS)},
year = {2023}
} |
| H. Van Assel, T. Vayer, R. Flamary, N. Courty, SNEkhorn: Dimension Reduction with Symmetric Entropic Affinities, Neural Information Processing Systems (NeurIPS), 2023. |
| Abstract: Many approaches in machine learning rely on a weighted graph to encode the similarities between samples in a dataset. Entropic affinities (EAs), which are notably used in the popular Dimensionality Reduction (DR) algorithm t-SNE, are particular instances of such graphs. To ensure robustness to heterogeneous sampling densities, EAs assign a kernel bandwidth parameter to every sample in such a way that the entropy of each row in the affinity matrix is kept constant at a specific value, whose exponential is known as perplexity. EAs are inherently asymmetric and row-wise stochastic, but they are used in DR approaches after undergoing heuristic symmetrization methods that violate both the row-wise constant entropy and stochasticity properties. In this work, we uncover a novel characterization of EA as an optimal transport problem, allowing a natural symmetrization that can be computed efficiently using dual ascent. The corresponding novel affinity matrix derives advantages from symmetric doubly stochastic normalization in terms of clustering performance, while also effectively controlling the entropy of each row thus making it particularly robust to varying noise levels. Following, we present a new DR algorithm, SNEkhorn, that leverages this new affinity matrix. We show its clear superiority to state-of-the-art approaches with several indicators on both synthetic and real-world datasets. |
BibTeX:
@inproceedings{van2023snekhorn,
author = {Van Assel, Hugues and Vayer, Titouan and Flamary, Rémi and Courty, Nicolas},
title = {SNEkhorn: Dimension Reduction with Symmetric Entropic Affinities},
booktitle = {Neural Information Processing Systems (NeurIPS)},
year = {2023}
} |
| C. Vincent-Cuaz, R. Flamary, M. Corneli, T. Vayer, N. Courty, Template based Graph Neural Network with Optimal Transport Distances, Neural Information Processing Systems (NeurIPS), 2022. |
| Abstract: Current Graph Neural Networks (GNN) architectures generally rely on two important components: node features embedding through message passing, and aggregation with a specialized form of pooling. The structural (or topological) information is implicitly taken into account in these two steps. We propose in this work a novel point of view, which places distances to some learnable graph templates at the core of the graph representation. This distance embedding is constructed thanks to an optimal transport distance: the Fused Gromov-Wasserstein (FGW) distance, which encodes simultaneously feature and structure dissimilarities by solving a soft graph-matching problem. We postulate that the vector of FGW distances to a set of template graphs has a strong discriminative power, which is then fed to a non-linear classifier for final predictions. Distance embedding can be seen as a new layer, and can leverage on existing message passing techniques to promote sensible feature representations. Interestingly enough, in our work the optimal set of template graphs is also learnt in an end-to-end fashion by differentiating through this layer. After describing the corresponding learning procedure, we empirically validate our claim on several synthetic and real life graph classification datasets, where our method is competitive or surpasses kernel and GNN state-of-the-art approaches. We complete our experiments by an ablation study and a sensitivity analysis to parameters. |
BibTeX:
@inproceedings{vincentcuaz2022template,
author = { Vincent-Cuaz, Cédric and Flamary, Rémi and Corneli, Marco and Vayer, Titouan and Courty, Nicolas},
title = {Template based Graph Neural Network with Optimal Transport Distances},
booktitle = {Neural Information Processing Systems (NeurIPS)},
year = {2022}
} |
| A. Thual, H. Tran, T. Zemskova, N. Courty, R. Flamary, S. Dehaene, B. Thirion, Aligning individual brains with Fused Unbalanced Gromov-Wasserstein, Neural Information Processing Systems (NeurIPS), 2022. |
| Abstract: Individual brains vary in both anatomy and functional organization, even within a given species. Inter-individual variability is a major impediment when trying to draw generalizable conclusions from neuroimaging data collected on groups of subjects. Current co-registration procedures rely on limited data, and thus lead to very coarse inter-subject alignments. In this work, we present a novel method for inter-subject alignment based on Optimal Transport, denoted as Fused Unbalanced Gromov Wasserstein (FUGW). The method aligns cortical surfaces based on the similarity of their functional signatures in response to a variety of stimulation settings, while penalizing large deformations of individual topographic organization. We demonstrate that FUGW is well-suited for whole-brain landmark-free alignment. The unbalanced feature allows to deal with the fact that functional areas vary in size across subjects. Our results show that FUGW alignment significantly increases between-subject correlation of activity for independent functional data, and leads to more precise mapping at the group level. |
BibTeX:
@inproceedings{thual2022aligning,
author = { Thual, Alexis and Tran, Huy and Zemskova, Tatiana and Courty, Nicolas and Flamary, Rémi and Dehaene, Stanislas and Thirion, Bertrand},
title = {Aligning individual brains with Fused Unbalanced Gromov-Wasserstein},
booktitle = {Neural Information Processing Systems (NeurIPS)},
year = {2022}
} |
| C. Vincent-Cuaz, R. Flamary, M. Corneli, T. Vayer, N. Courty, Semi-relaxed Gromov Wasserstein divergence with applications on graphs, International Conference on Learning Representations (ICLR), 2022. |
| Abstract: Comparing structured objects such as graphs is a fundamental operation involved in many learning tasks. To this end, the Gromov-Wasserstein (GW) distance, based on Optimal Transport (OT), has proven to be successful in handling the specific nature of the associated objects. More specifically, through the nodes connectivity relations, GW operates on graphs, seen as probability measures over specific spaces. At the core of OT is the idea of conservation of mass, which imposes a coupling between all the nodes from the two considered graphs. We argue in this paper that this property can be detrimental for tasks such as graph dictionary or partition learning, and we relax it by proposing a new semi-relaxed Gromov-Wasserstein divergence. Aside from immediate computational benefits, we discuss its properties, and show that it can lead to an efficient graph dictionary learning algorithm. We empirically demonstrate its relevance for complex tasks on graphs such as partitioning, clustering and completion. |
BibTeX:
@inproceedings{vincent2022semi,
author = {Vincent-Cuaz, Cédric and Flamary, Rémi and Corneli, Marco and Vayer, Titouan and Courty, Nicolas},
title = {Semi-relaxed Gromov Wasserstein divergence with applications on graphs},
booktitle = {International Conference on Learning Representations (ICLR)},
year = {2022}
} |
News
NeurIPS 2023
2023-12-01
Je serai présent à NeurIPS 2023 à la Nouvelle Orléans. J'y présenterai avec mes formidables co-auteurs deux posters et je suis un orateur invité au workshop Optimal Transport for Machine Learning (OTML).
N'hésitez pas à venir me voir et voir mes collaborateurs à nos posters ou lors du workshop OTML (nous avons aussi des posters là-bas).
T. Gnassounou, R. Flamary, A. Gramfort, Convolutional Monge Mapping Normalization for learning on biosignals, Neural Information Processing Systems (NeurIPS), 2023.
[Abstract] [BibTeX] [PDF] [Code]
Abstract: In many machine learning applications on signals and biomedical data, especially electroencephalogram (EEG), one major challenge is the variability of the data across subjects, sessions, and hardware devices. In this work, we propose a new method called Convolutional Monge Mapping Normalization (CMMN), which consists in filtering the signals in order to adapt their power spectrum density (PSD) to a Wasserstein barycenter estimated on training data. CMMN relies on novel closed-form solutions for optimal transport mappings and barycenters and provides individual test time adaptation to new data without needing to retrain a prediction model. Numerical experiments on sleep EEG data show that CMMN leads to significant and consistent performance gains independent from the neural network architecture when adapting between subjects, sessions, and even datasets collected with different hardware. Notably our performance gain is on par with much more numerically intensive Domain Adaptation (DA) methods and can be used in conjunction with those for even better performances.
BibTeX:
@inproceedings{gnassounou2023convolutional,
author = {Gnassounou, Théo and Flamary, Rémi and Gramfort, Alexandre},
title = {Convolutional Monge Mapping Normalization for learning on biosignals},
booktitle = {Neural Information Processing Systems (NeurIPS)},
editor = {},
year = {2023}
} H. Van Assel, T. Vayer, R. Flamary, N. Courty, SNEkhorn: Dimension Reduction with Symmetric Entropic Affinities, Neural Information Processing Systems (NeurIPS), 2023.
[Abstract] [BibTeX] [PDF] [Code]
Abstract: Many approaches in machine learning rely on a weighted graph to encode the similarities between samples in a dataset. Entropic affinities (EAs), which are notably used in the popular Dimensionality Reduction (DR) algorithm t-SNE, are particular instances of such graphs. To ensure robustness to heterogeneous sampling densities, EAs assign a kernel bandwidth parameter to every sample in such a way that the entropy of each row in the affinity matrix is kept constant at a specific value, whose exponential is known as perplexity. EAs are inherently asymmetric and row-wise stochastic, but they are used in DR approaches after undergoing heuristic symmetrization methods that violate both the row-wise constant entropy and stochasticity properties. In this work, we uncover a novel characterization of EA as an optimal transport problem, allowing a natural symmetrization that can be computed efficiently using dual ascent. The corresponding novel affinity matrix derives advantages from symmetric doubly stochastic normalization in terms of clustering performance, while also effectively controlling the entropy of each row thus making it particularly robust to varying noise levels. Following, we present a new DR algorithm, SNEkhorn, that leverages this new affinity matrix. We show its clear superiority to state-of-the-art approaches with several indicators on both synthetic and real-world datasets.
BibTeX:
@inproceedings{van2023snekhorn,
author = {Van Assel, Hugues and Vayer, Titouan and Flamary, Rémi and Courty, Nicolas},
title = {SNEkhorn: Dimension Reduction with Symmetric Entropic Affinities},
booktitle = {Neural Information Processing Systems (NeurIPS)},
editor = {},
year = {2023}
} La stratégie du moindre effort pour apprendre aux machines
2023-04-12
Gabriel Peyré et moi avons présenté le 13 mars 2023 à Sorbonne Université à Jussieu, une conférence pour un large public où nous avons discuté de l'utilisation du transport optimal et de la théorie du moindre effort dans les applications d'intelligence artificielle.
Je met à disposition les supports de présentation et le lien vers la vidéo sur le site de la Société Mathématique de France.
Présentation orale à NeurIPS 2022
2022-11-20
Les travaux de thèse de Cédric Vincent-Cuaz sur le Transport Optimal pour les réseau de neurones sur graph ont été acceptés pour une présentation orale très selective à NeurIPS 2022.
Cédric et moi serons présents à la Nouvelle Orleans pour NeurIPS. N'hésitez pas à venir nous voir à notre poster.
C. Vincent-Cuaz, R. Flamary, M. Corneli, T. Vayer, N. Courty, Template based Graph Neural Network with Optimal Transport Distances, Neural Information Processing Systems (NeurIPS), 2022.
[Abstract] [BibTeX] [PDF] [Code]
Abstract: Current Graph Neural Networks (GNN) architectures generally rely on two important components: node features embedding through message passing,
and aggregation with a specialized form of pooling. The structural (or
topological) information is implicitly taken into account in these two steps.
We propose in this work a novel point of view, which places distances to some
learnable graph templates at the core of the graph representation. This
distance embedding is constructed thanks to an optimal transport distance: the
Fused Gromov-Wasserstein (FGW) distance, which encodes simultaneously feature
and structure dissimilarities by solving a soft graph-matching problem. We
postulate that the vector of FGW distances to a set of template graphs has a
strong discriminative power, which is then fed to a non-linear classifier for
final predictions. Distance embedding can be seen as a new layer, and can
leverage on existing message passing techniques to promote sensible feature
representations. Interestingly enough, in our work the optimal set of template
graphs is also learnt in an end-to-end fashion by differentiating through this
layer. After describing the corresponding learning procedure, we empirically
validate our claim on several synthetic and real life graph classification
datasets, where our method is competitive or surpasses kernel and GNN
state-of-the-art approaches. We complete our experiments by an ablation study
and a sensitivity analysis to parameters.
BibTeX:
@inproceedings{vincentcuaz2022template,
author = { Vincent-Cuaz, Cédric and Flamary, Rémi and Corneli, Marco and Vayer, Titouan and Courty, Nicolas},
title = {Template based Graph Neural Network with Optimal Transport Distances},
booktitle = {Neural Information Processing Systems (NeurIPS)},
editor = {},
year = {2022}
} Optimal Transport for Machine Learning tutorial at Hi! Paris Summer School 2022
2022-06-15
Je donnerai un tutoriel sur le Transport optimal pour l'apprentissage automatique pour l'Hi! Paris Summer School 2022 le 4 juillet 2022 à l'Ecole Polytechnique à Paris/Saclay, France.
Les supports de présentation sont disponibles ci-dessous (en anglais):