Manuel Lecha

I am a PhD student in the ELLIS program, jointly affiliated with the Italian Institute of Technology and the University of Oxford, supervised by Alessio Del Bue and Michael Bronstein.

My research investigates how topological and geometric methods can enhance deep learning models, enabling them to more faithfully capture and exploit the intrinsic structure of data. I work on geometric deep learning, equivariant architectures and foundation models.

Before joining ELLIS, I completed an MSc in Advanced Mathematics at the Universitat Politècnica de Catalunya, and two BScs — in Mathematics and in Computer Science — at the Universitat de Barcelona, including an exchange year at the University of Warwick.

news

Apr 27, 2026	Directed Semi-Simplicial Learning with Applications to Brain Activity Decoding accepted at ICLR 2026.
Apr 24, 2026	Co-organizing the GRaM Workshop (Geometry-grounded Representation Learning and Generative Modeling) at ICLR 2026.
Feb 15, 2026	Invited talk at the Applied Algebraic Topology Research Network (AATRN) on Directed Topological Deep Learning and Brain Networks.

selected publications

ICLR
Directed Semi-Simplicial Learning with Applications to Brain Activity Decoding

Manuel Lecha, Andrea Cavallo, Francesca Dominici, and 5 more authors

In International Conference on Learning Representations (ICLR), 2026

Abs arXiv Bib Code

Graph Neural Networks excel at learning from pairwise interactions but often overlook multi-way and hierarchical relationships. Topological Deep Learning addresses this limitation by leveraging combinatorial topological spaces. However, existing TDL models are restricted to undirected settings and fail to capture the higher-order directed patterns prevalent in many complex systems, e.g., brain networks, where such interactions are both abundant and functionally significant. To fill this gap, we introduce Semi-Simplicial Neural Networks (SSNs), a principled class of TDL models that operate on semi-simplicial sets — combinatorial structures that encode directed higher-order motifs and their directional relationships. To enhance scalability, we propose Routing-SSNs, which dynamically select the most informative relations in a learnable manner. SSNs achieve state-of-the-art performance on brain dynamics classification tasks, outperforming the second-best model by up to 27%, and message-passing GNNs by up to 50% in accuracy.
@inproceedings{lecha2026directed, title = {Directed Semi-Simplicial Learning with Applications to Brain Activity Decoding}, author = {Lecha, Manuel and Cavallo, Andrea and Dominici, Francesca and Levi, Ran and Del Bue, Alessio and Isufi, Elvin and Morerio, Pietro and Battiloro, Claudio}, booktitle = {International Conference on Learning Representations (ICLR)}, year = {2026}, url = {https://openreview.net/forum?id=YR3CNvFfCr} }
ICASSP
Higher-Order Topological Directionality and Directed Simplicial Neural Networks

Manuel Lecha, Andrea Cavallo, Francesca Dominici, and 2 more authors

In IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2025

Abs arXiv Bib Code

We introduce a notion of higher-order directionality and design Directed Simplicial Neural Networks (Dir-SNNs), message-passing networks operating on directed simplicial complexes that leverage directed interactions among simplices. To our knowledge, this is the first TDL model using a notion of higher-order directionality. We prove that Dir-SNNs are strictly more expressive than their directed graph counterparts in distinguishing isomorphic directed graphs, and show empirically that they outperform undirected SNNs when the underlying complex is directed.
@inproceedings{lecha2025higherorder, title = {Higher-Order Topological Directionality and Directed Simplicial Neural Networks}, author = {Lecha, Manuel and Cavallo, Andrea and Dominici, Francesca and Isufi, Elvin and Battiloro, Claudio}, booktitle = {IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)}, year = {2025}, }