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

• URL: http://arxiv.org/abs/2505.15405v1
• Date: Wed, 21 May 2025 11:47:40 GMT
• Title: HOPSE: Scalable Higher-Order Positional and Structural Encoder for Combinatorial Representations
• Authors: Martin Carrasco, Guillermo Bernardez, Marco Montagna, Nina Miolane, Lev Telyatnikov,
• Abstract summary: HOPSE is an expressive emphmessage passing-free framework that uses Hasse graph decompositions to derive efficient encodings.<n>Experiments show that HOPSE matches or surpasses state-of-the-art performance while achieving up to 7 $times scalable speedups.
• Score: 3.0097956531484233
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: While Graph Neural Networks (GNNs) have proven highly effective at modeling relational data, pairwise connections cannot fully capture multi-way relationships naturally present in complex real-world systems. In response to this, Topological Deep Learning (TDL) leverages more general combinatorial representations -- such as simplicial or cellular complexes -- to accommodate higher-order interactions. Existing TDL methods often extend GNNs through Higher-Order Message Passing (HOMP), but face critical \emph{scalability challenges} due to \textit{(i)} a combinatorial explosion of message-passing routes, and \textit{(ii)} significant complexity overhead from the propagation mechanism. To overcome these limitations, we propose HOPSE (Higher-Order Positional and Structural Encoder) -- a \emph{message passing-free} framework that uses Hasse graph decompositions to derive efficient and expressive encodings over \emph{arbitrary higher-order domains}. Notably, HOPSE scales linearly with dataset size while preserving expressive power and permutation equivariance. Experiments on molecular, expressivity and topological benchmarks show that HOPSE matches or surpasses state-of-the-art performance while achieving up to 7 $times$ speedups over HOMP-based models, opening a new path for scalable TDL.

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