Eduardo Fernandes Montesuma

Paris, France

I am an AI researcher specializing in optimal transport, domain adaptation, transfer learning, and foundation models. I completed my PhD in Mathematical Computer Science at Université Paris-Saclay in 2024, where I focused on multi-source domain adaptation through Wasserstein barycenters. Prior to that, I earned a Master’s degree in Electronic Engineering and Industrial Informatics from INSA de Rennes and a Bachelor’s in Computer Engineering from Universidade Federal do Ceará in Brazil. You can take a look on my recent publications at Google Scholar.

Since August 2025 I work as an AI researcher at Sigma Nova, where I work on pre-training, fine-tuning, and transfer learning of large-scale foundation models for neuroscience and time series forecasting. My research bridges theoretical advances in optimal transport with practical machine learning applications, particularly in scenarios where models need to adapt across different domains or data distributions.

news

Oct 01, 2026	📄 Gromov-Wasserstein Distillation for Inductive Multi-View Embedding, with Rafael Pereira Eufrazio and Charles Casimiro Cavalcante, accepted at the GDDL workshop at NeurIPS 2026.
Aug 01, 2026	📄 Nonlinear Dimensionality Reduction through Optimal Transport between Incomparable Spaces, with Rafael Pereira Eufrazio and Charles Casimiro Cavalcante, is published in Information Geometry.
Jun 01, 2026	📄 Wasserstein Gradient Flows for Scalable and Regularized Barycenter Computation accepted at UAI 2026.
Mar 27, 2026	📄 Our paper ReBaPL: Repulsive Bayesian Prompt Learning was accepted at CVPR 2026.
Aug 01, 2025	🚀 Started a new role as AI Researcher at Sigma Nova, working on pre-training, fine-tuning, and transfer learning of large-scale foundation models for neuroscience and time series forecasting.

latest posts

Sep 16, 2026	The Sliced Wasserstein Distance
May 04, 2022	Optimal Transport for Domain Adaptation

selected publications

arXiv
Towards Universal Wasserstein Barycenters through Flow Matching

Eduardo Fernandes Montesuma

2026

Under review

Abs arXiv Bib PDF

Defining a weighted mean over probability measures under probability metrics is a central tool in probabilistic machine learning. Under the Wasserstein metric, these are called Wasserstein barycenters. While most approaches compute barycenters for a fixed weight vector, approximating the whole family of barycenters over the simplex, which we call the Wasserstein simplex, remains underexplored. We refer to this problem as Universal Barycenter Approximation, and propose BaryFM, a flow matching model transporting the marginal measures into any barycenter in the Wasserstein simplex. Once trained, the network can draw samples from measures in the Wasserstein simplex through an ordinary differential equation. We validate our method on 4 downstream tasks: domain adaptation, generalization, Bayesian posterior aggregation and algorithmic fairness. BaryFM achieves the best average rank among 15 competing methods across 10 domain adaptation benchmarks, matching or surpassing non-universal solvers.
@misc{montesuma2026universal, title = {Towards Universal Wasserstein Barycenters through Flow Matching}, author = {Fernandes Montesuma, Eduardo}, year = {2026}, note = {Under review}, }
CVPR
ReBaPL: Repulsive Bayesian Prompt Learning

Yassir Bendou, Omar Ezzahir, Eduardo Fernandes Montesuma, and 3 more authors

In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2026

Abs arXiv Bib PDF Code

Conventional prompt learning methods are prone to overfitting and can struggle with out-of-distribution generalization. We frame prompt optimization as a Bayesian inference problem and propose ReBaPL, which integrates a cyclical step-size schedule with a stochastic gradient Hamiltonian Monte Carlo (SGHMC) algorithm and a repulsive force derived from probability metrics (Maximum Mean Discrepancy, Wasserstein) to diversify exploration of the prompt posterior and prevent premature collapse to a single mode.
@inproceedings{bendou2026rebapl, title = {ReBaPL: Repulsive Bayesian Prompt Learning}, author = {Bendou, Yassir and Ezzahir, Omar and Fernandes Montesuma, Eduardo and Mahuas, Gabriel and Shevchenko, Victoria and Gartrell, Mike}, booktitle = {Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)}, year = {2026}, }
UAI
Wasserstein Gradient Flows for Scalable and Regularized Barycenter Computation

Eduardo Fernandes Montesuma, Yassir Bendou, and Mike Gartrell

In Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence (UAI), 2026

Abs arXiv Bib PDF Code

We present a method for computing Wasserstein barycenters via gradient flows in probability measure space. The approach yields a scalable algorithm that (i) relies on mini-batch optimal transport, (ii) accepts modular regularization through task-aware functions, and (iii) admits supervised information in the cost function. Experiments on domain adaptation tasks across computer vision, neuroscience, and chemical engineering show that incorporating label information improves over existing barycenter approaches.
@inproceedings{montesuma2026wgf, title = {Wasserstein Gradient Flows for Scalable and Regularized Barycenter Computation}, author = {Fernandes Montesuma, Eduardo and Bendou, Yassir and Gartrell, Mike}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence (UAI)}, series = {Proceedings of Machine Learning Research}, volume = {337}, pages = {4595--4606}, year = {2026}, publisher = {PMLR}, }

TMLR

Optimal Transport for Domain Adaptation through Gaussian Mixture Models

Eduardo Fernandes Montesuma, Fred Maurice Ngolè Mboula, and Antoine Souloumiac

Transactions on Machine Learning Research, 2025

arXiv Bib PDF Code

@article{montesuma2025optimal,
  title = {Optimal Transport for Domain Adaptation through Gaussian Mixture Models},
  author = {Fernandes Montesuma, Eduardo and Mboula, Fred Maurice Ngol{\`e} and Souloumiac, Antoine},
  journal = {Transactions on Machine Learning Research},
  issn = {2835-8856},
  year = {2025},
  url = {https://openreview.net/forum?id=DCAeXwLenB},
}

TPAMI
Recent Advances in Optimal Transport for Machine Learning

Eduardo Fernandes Montesuma, Fred Maurice Ngolè Mboula, and Antoine Souloumiac

IEEE Transactions on Pattern Analysis and Machine Intelligence, 2024

Abs arXiv Bib PDF Code

Optimal Transport (OT) is a probabilistic framework for comparing and manipulating probability distributions. We survey the contributions of OT to machine learning over 2012-2023 across supervised, unsupervised, transfer, and reinforcement learning, including computational OT, partial, unbalanced, Gromov, and Neural OT and their interplay with ML practice.
@article{montesuma2024recent, title = {Recent Advances in Optimal Transport for Machine Learning}, author = {Fernandes Montesuma, Eduardo and Mboula, Fred Maurice Ngol{\`e} and Souloumiac, Antoine}, journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence}, volume = {47}, number = {2}, pages = {1161--1180}, year = {2024}, publisher = {IEEE}, }

ECML-PKDD

Lighter, Better, Faster Multi-Source Domain Adaptation with Gaussian Mixture Models and Optimal Transport

Eduardo Fernandes Montesuma, Fred Maurice Ngolè Mboula, and Antoine Souloumiac

In Joint European Conference on Machine Learning and Knowledge Discovery in Databases (ECML-PKDD), 2024

arXiv Bib PDF Code

@inproceedings{montesuma2024lighter,
  title = {Lighter, Better, Faster Multi-Source Domain Adaptation with Gaussian Mixture Models and Optimal Transport},
  author = {Fernandes Montesuma, Eduardo and Mboula, Fred Maurice Ngol{\`e} and Souloumiac, Antoine},
  booktitle = {Joint European Conference on Machine Learning and Knowledge Discovery in Databases (ECML-PKDD)},
  pages = {21--38},
  year = {2024},
  organization = {Springer},
}

ECAI

Multi-Source Domain Adaptation through Dataset Dictionary Learning in Wasserstein Space

Eduardo Fernandes Montesuma, Fred Maurice Ngolè Mboula, and Antoine Souloumiac

In 26th European Conference on Artificial Intelligence (ECAI), 2023

arXiv Bib PDF Code

@inproceedings{montesuma2023multi,
  title = {Multi-Source Domain Adaptation through Dataset Dictionary Learning in Wasserstein Space},
  author = {Fernandes Montesuma, Eduardo and Mboula, Fred Maurice Ngol{\`e} and Souloumiac, Antoine},
  booktitle = {26th European Conference on Artificial Intelligence (ECAI)},
  pages = {1739--1746},
  year = {2023},
  publisher = {IOS Press},
}

CVPR
Wasserstein Barycenter for Multi-Source Domain Adaptation

Eduardo Fernandes Montesuma and Fred Maurice Ngolè Mboula

In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2021

Abs Bib PDF Code

Multi-source domain adaptation is a key technique that allows a model to be trained on data coming from various probability distributions. We propose a method for constructing an intermediate domain between sources and target domain via the barycenter on Wasserstein spaces (WBT). After aggregating sources, they are transported to the target domain using standard OT for Domain Adaptation. We evaluate on object recognition, face recognition, music genre recognition, and music-speech discrimination.
@inproceedings{montesuma2021wasserstein, title = {Wasserstein Barycenter for Multi-Source Domain Adaptation}, author = {Fernandes Montesuma, Eduardo and Mboula, Fred Maurice Ngol{\`e}}, booktitle = {Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)}, pages = {16785--16793}, year = {2021}, }