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
arXiv:2609.17061v1 Announce Type: cross
Abstract: Message-passing Graph Neural Networks (GNNs) iteratively propagate and aggregate local neighborhood information followed by global readout to learn g...
By Sanyam Sanjay Jain, Anshika Krishnatray, Aditya Sharma, Vinti Agarwal
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
Message-passing Graph Neural Networks (GNNs) iteratively propagate and aggregate local neighborhood information followed by global readout to learn graph representations. However, their discriminative...
arXiv:2609.37884v1 Announce Type: new
Abstract: Topological structures such as simplicial complexes, hypergraphs, and cell complexes extend standard graph models by modeling higher-order relationship...
By Florian Frantzen, Ibrahem AlJabea, Ines Henriques-Cadby, Theodore Papamarkou, Mustafa Hajij, Michael T. Schaub
The paper introduces higher-order positional encodings that enrich graph representations by incorporating topological information from lifted incidence structures, without altering existing graph learning backbones. It theoretically shows that these encodings can mix graph Laplacian frequencies beyond what scalar spectral filters achieve, and demonstrates their effectiveness on Graph Transformers for datasets like ZINC and synthetic benchmarks. The approach bridges graph positional encodings and topological deep learning, enabling standard models to exploit higher-order interactions.
By Caleb Stam, Aagrim Hoysal, Sanjukta Krishnagopal