jeudi 19 mars 2026

par BUTEL Nathalie

Salvish Goomanee, enseignant-chercheur, dans le pôle SIS, équipe MORPHEME, donnera un séminaire en visioconférence, le jeudi 19 mars 2026 à 14h00, au Centre Inria d'Université Côte d'Azur dans la salle Euler Violet.

 

TITLE : 

Geometric diffusion and stability in graph neural networks on evolving structures

ABSTRACT : 

Graph neural networks (GNNs) have emerged as a powerful framework for learning on structured data, yet their theoretical properties and long-term stability under iterative graph evolution remain incompletely understood. In this work, we introduce a geometric, equivariant graph learning framework designed to emulate complex dynamical processes on evolving 3D geometric graphs. Our representation encodes interacting entities as nodes and their pairwise interactions as weighted edges, allowing continuous geometric information to be coupled with discrete topology. The model integrates geometric message passing with diffusion-based updates, enabling stable propagation of information while respecting symmetry constraints. This construction is motivated by recent theoretical results on information loss in GNNs, including analyses based on functional inequalities (Cheeger, Log-Sobolev & Poincaré) that quantify mixing, contraction, and oversmoothing phenomena in deep message passing networks. By incorporating geometric diffusion mechanisms and topology-aware attention, in the spirit of topology-constrained graph transformers, our framework mitigates representation collapse and maintains discriminative features across successive topological updates. More broadly, this work contributes to the mathematical understanding of information propagation, symmetry preservation, and stability in geometric graph learning, with potential implications for a wide range of applications involving dynamical systems on evolving networks.