Carrasco, M., Bernardez, G., Montagna, M., Miolane, N., Telyatnikov, L.
Graph Neural Networks (GNNs) model pairwise relations well but struggle with the higher-order interactions present in many real-world systems. Topological Deep Learning (TDL) extends GNNs using higher-order message passing (HOMP) on simplicial or cellular complexes, but suffers from combinatorial blowup and high complexity. To address this, HOPSE (Higher-Order Positional and Structural Encoder) avoids message passing entirely, instead using Hasse graph decompositions for efficient, expressive encodings. HOPSE scales linearly with data size, maintains expressive power and permutation equivariance, and achieves state-of-the-art accuracy with up to 7× speedups over HOMP-based models across molecular, expressivity, and topological benchmarks—opening a scalable path for TDL.
