6 papers
Expressivity Saturation: Reduced Affine Region Usage Under Increasing Task Complexity
Xuan Qi, Yi Wei, Fanqi Yu +1
Piecewise-affine neural networks (e.g., with ReLU or LeakyReLU activations) implement continuous piecewise-affine maps, and the number of affine regions provides a natural proxy fo…
Directed Semi-Simplicial Learning with Applications to Brain Activity Decoding
Manuel Lecha, Andrea Cavallo, Francesca Dominici +5
Graph Neural Networks (GNNs) excel at learning from pairwise interactions but often overlook multi-way and hierarchical relationships. Topological Deep Learning (TDL) addresses thi…
E-M3RF: An Equivariant Multimodal 3D Re-assembly Framework
Adeela Islam, Stefano Fiorini, Manuel Lecha +4
3D reassembly is a fundamental geometric problem, and in recent years it has increasingly been challenged by deep learning methods rather than classical optimization. While learnin…
TopoBench: A Framework for Benchmarking Topological Deep Learning
Lev Telyatnikov, Guillermo Bernardez, Marco Montagna +34
This work introduces TopoBench, an open-source library designed to standardize benchmarking and accelerate research in topological deep learning (TDL). TopoBench decomposes TDL int…
Higher-Order Topological Directionality and Directed Simplicial Neural Networks
Manuel Lecha, Andrea Cavallo, Francesca Dominici +2
Topological Deep Learning (TDL) has emerged as a paradigm to process and learn from signals defined on higher-order combinatorial topological spaces, such as simplicial or cell com…
TopoX: A Suite of Python Packages for Machine Learning on Topological Domains
Mustafa Hajij, Mathilde Papillon, Florian Frantzen +40
We introduce TopoX, a Python software suite that provides reliable and user-friendly building blocks for computing and machine learning on topological domains that extend graphs: h…