Papers

Publications within the TopoBench Ecosystem for Topological Deep Learning

TopoBench: A Framework for Benchmarking Topological Deep Learning

Lev Telyatnikov, Guillermo Bernardez, Marco Montagna, et al., Nina Miolane, Simone Scardapane, Theodore Papamarkou

This work introduces TopoBench, an open-source library designed to standardize benchmarking and accelerate research in topological deep learning (TDL). TopoBench decomposes TDL into a sequence of independent modules for data generation, loading, transforming and processing, as well as model training, optimization and evaluation...

TopoTune: A Framework for Generalized Combinatorial Complex Neural Networks

Mathilde Papillon, Guillermo Bernárdez, Claudio Battiloro, Nina Miolane

Graph Neural Networks (GNNs) excel in learning from relational datasets, processing node and edge features in a way that preserves the symmetries of the graph domain. However, many complex systems -- such as biological or social networks--involve multiway complex interactions that are more naturally represented by higher-order topological domains. The emerging field of Topological Deep Learning (TDL) aims to accommodate and leverage these higher-order structures...

HOPSE: Scalable Higher-Order Positional and Structural Encoder for Combinatorial Representations

Martin Carrasco, Guillermo Bernardez, Marco Montagna, Nina Miolane, Lev Telyatnikov

Existing TDL methods often extend GNNs through Higher-Order Message Passing (HOMP), but face critical scalability challenges due to a combinatorial explosion of message-passing routes and significant complexity overhead from the propagation mechanism. To overcome these limitations, we propose HOPSE (Higher-Order Positional and Structural Encoder) -- a message passing-free framework that uses Hasse graph decompositions to derive efficient and expressive encodings over arbitrary higher-order domains. Notably, HOPSE scales linearly with dataset size while preserving expressive power and permutation equivariance.