Manuel Lecha

I’m a predoctoral fellow at AITHYRA in Michael Bronstein’s group and an ELLIS PhD student working on representation learning. My recent paper, Intrinsic Geometry Matching, learns the intrinsic geometry of a process independently of how it is observed. Previously, I worked on graph and higher-order neural networks.

I hold bachelor’s degrees in Mathematics and in Computer Science from the Universitat de Barcelona, and a master’s in Advanced Mathematics from the Universitat Politècnica de Catalunya.

Manuel Lecha

Selected work

All publications
Preprint 2026

Intrinsic Geometry Matching: Learning Observation-Equivariant Process Geometry

M. Lecha, M. Bronstein, I. Jones

Learn the geometry of the process behind the data, not of how it was observed.

ICLR 2026

Directed Semi-Simplicial Learning with Applications to Brain Activity Decoding

M. Lecha, A. Cavallo, F. Dominici, R. Levi, A. Del Bue, E. Isufi, P. Morerio, C. Battiloro

Neural networks on semi-simplicial sets capture directed higher-order motifs in brain networks.

ICASSP 2025

Higher-Order Topological Directionality and Directed Simplicial Neural Networks

M. Lecha, A. Cavallo, F. Dominici, E. Isufi, C. Battiloro

A notion of higher-order directionality, and message passing that provably exploits it.

  1. New preprint: Intrinsic Geometry Matching: Learning Observation-Equivariant Process Geometry, with Michael Bronstein and Iolo Jones.

  2. Joined AITHYRA in Vienna as a predoctoral fellow in Michael Bronstein’s group.

  3. Co-organized the GRaM workshop on Geometry-grounded Representation Learning and Generative Modeling at ICLR 2026.

  4. Invited talk at the Applied Algebraic Topology Research Network: Learning with Directed Higher-Order Structure (recording).