Research map / Graph learning / GNN architectures

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

NeurIPS 2026 · Graph learning › GNN architectures · approach: Expressive equivariant message passing · 0 citations (OpenAlex)

Read the paperCheck your idea against 108,967 papers

AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.

Proposes HOPSE, a message-passing-free encoder for combinatorial complexes that precomputes graph PSEs on Hasse graph decompositions, achieving linear scaling and competitive accuracy with faster training than HOMP models.

Problem

Higher-order message passing (HOMP) in topological neural networks is computationally expensive and scales poorly, with a combinatorial explosion of message passing routes over combinatorial complexes.

Approach

Decompose a combinatorial complex into strictly augmented Hasse graphs per neighborhood function, compute standard graph positional/structural encodings on each as a one-time preprocessing step, concatenate them per cell, and process with MLPs instead of message passing.

Key results

• HOPSE-M-C reaches state-of-the-art on MANTRA beta_1 (90.33) and beta_2 (83.70) in the simplicial setting.
• HOPSE-GPSE (cell) achieves the best results on Cl.Hep., BBB, NCI1, and NCI109 among compared models.
• HOPSE models show lower per-epoch and total training time than HOMP baselines such as SCCNN, CWN, and CCCN.

Surprising findings

• Simpler neighborhood configurations (Adj-1, Adj-2) often perform competitively on molecular regression tasks, acting as a regularizer.

Limitations

• Parameter count larger than GNN baselines and some HOMP baselines in the simplicial domain.
• Expressivity guarantees assume injectivity, which practical instantiations only approximate.
• HOPSE-GPSE uses a frozen pretrained encoder; end-to-end training not explored.

Experimental setup

Datasets: MUTAG PROTEINS NCI1 NCI109 BBB CYP3A4 Cl.Hep. Caco2 MANTRA

Benchmarks: MUTAG PROTEINS NCI1 NCI109 BBB CYP3A4 Cl.Hep. Caco2 MANTRA NAME MANTRA ORIENT MANTRA beta_1 MANTRA beta_2

Metrics: accuracy F1 MAE runtime per epoch

Baselines: GCN GAT GIN SCCNN SANN CWN CCCN TopoTune

Builds on: TopoBench TopoTune GPSE CCWL test Hasse graphs

Closest papers by meaning

• Topological Blindspots: Understanding and Extending Topological Deep Learning Through the Lens of Expressivity (ICLR 2025 · similarity 0.90)
• TopoTune: A Framework for Generalized Combinatorial Complex Neural Networks (ICML 2025 · similarity 0.88)
• Topological Neural Networks go Persistent, Equivariant, and Continuous (ICML 2024 · similarity 0.86)
• Homomorphism Counts as Structural Encodings for Graph Learning (ICLR 2025 · similarity 0.86)
• E(n) Equivariant Topological Neural Networks (ICLR 2025 · similarity 0.85)
• Demystifying Topological Message-Passing with Relational Structures: A Case Study on Oversquashing in Simplicial Message-Passing (ICLR 2025 · similarity 0.85)