arXiv Machine Learning June 17, 2026 By Jiawen Chen, Qi Shao, Zhiqiang Ge, Duxin Chen, Wenwu Yu

Weisfeiler Lehman Test on Combinatorial Complexes: Generalized Expressive Power of Topological Neural Networks

Read the original on arXiv Machine Learning →

arXiv:2605. 00725v2 Announce Type: replace Abstract: Topological neural networks have emerged as effective tools for modeling higher-order relational structures beyond pairwise graphs, including hypergraphs, simplicial complexes, and cell complexes.

Summary generated by The Flow from the publisher's feed. The full article lives at arXiv Machine Learning.

benchmarks

arXiv Machine Learning

Jun 5

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

arXiv:2505. 15405v3 Announce Type: replace 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.

By Guillermo Bern\'ardez, Marco Montagna, Louis Van Langendonck, Martin Carrasco, Amirreza Akbari, Louisa Cornelis, Mathilde Papillon, Pere Barlet-Ros, Nina Miolane, Lev Telyatnikov

benchmarks

arXiv Machine Learning

Aug 4

Differentiable Lifting for Topological Neural Networks

arXiv:2608. 01160v1 Announce Type: new Abstract: Topological neural networks (TNNs) enable leveraging high-order structures on graphs (e.

By Jorge Luiz Franco, Gabriel Duarte, Alexander Nikitin, Moacir Ponti, Diego Mesquita, Amauri H. Souza

benchmarks

arXiv Machine Learning

Jun 30

Lost in Aggregation: On a Fundamental Expressivity Limit of Message-Passing Graph Neural Networks

arXiv:2603. 14846v3 Announce Type: replace Abstract: We define an information-complexity property for aggregation functions, capturing a vast range of practical aggregations, and prove that any Message-Passing Graph Neural Network (MP-GNN) model with such aggregations induces only a polynomial number of equivalence classes on all graphs - while the number of non-isomorphic graphs is super-exponential (in number of vertices).

By Eran Rosenbluth

arXiv Machine Learning

Jul 31

TopoFormer: Topology Meets Attention for Graph Learning

arXiv:2607. 28259v1 Announce Type: new Abstract: We introduce Topoformer, a lightweight and scalable framework for graph representation learning that encodes topological structure into attention-friendly sequences.

By Md Joshem Uddin, Astrit Tola, Cuneyt Gurcan Akcora, Baris Coskunuzer

llms rag benchmarks

arXiv Machine Learning

1d ago

Look Before You Lift: Visual and Quantitative Diagnostics for Topological Deep Learning

arXiv:2608. 15388v1 Announce Type: new Abstract: Topological deep learning (TDL) methods rely on lifting raw data into higher-order discrete domains such as simplicial complexes, cell complexes, and hypergraphs.

By Mathilde Papillon, Guillermo Bern\'ardez, \'Alvaro Ball\'on Barreiro, Marco Montagna, R\'emi Devaux, Antoine Jardin, Nina Miolane

arXiv AI

Jul 23

A Sheaf-Theoretic and Topological Perspective on Complex Network Modeling and Attention Mechanisms in Graph Neural Models

arXiv:2601. 21207v4 Announce Type: replace-cross Abstract: Combinatorial and topological structures, such as graphs, simplicial complexes, and cell complexes, form the foundation of geometric and topological deep learning (GDL and TDL) architectures.

By Chuan-Shen Hu

diffusion

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

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