Researchers propose HOPSE (Higher-Order Positional and Structural Encoder), a novel framework that achieves linear scalability for Topological Deep Learning (TDL) models by using Hasse graph decompositions instead of computationally expensive message passing layers.
While Graph Neural Networks (GNNs) are effective for pairwise relationships, modeling complex multi-way interactions requires incorporating higher-order combinatorial representations (like simplicial or cellular complexes). Existing Topological Deep Learning (TDL) methods often extend GNNs via Higher-Order Message Passing (HOMP), but suffer from significant scalability challenges due to the overhead of message propagation through combinatorial structures. HOPSE addresses this limitation by introducing a framework free of message passing layers, leveraging Hasse graph decompositions to derive efficient and expressive encodings over arbitrary higher-order domains. Crucially, HOPSE scales linearly with the size of the combinatorial representations while maintaining the expressive power and permutation equivariance of HOMP methods. Experiments on molecular and topological benchmarks demonstrate that HOPSE matches or surpasses state-of-the-art performance and offers speedups over HOMP-based models, opening a new scalable path for TDL.