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
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
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
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
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: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.
By Jiawen Chen, Qi Shao, Zhiqiang Ge, Duxin Chen, Wenwu Yu
Message-passing Graph Neural Networks (GNNs) iteratively propagate and aggregate local neighborhood information followed by global readout to learn graph representations. However, their discriminative...
DeltaGNN introduces an information flow control mechanism that uses a new connectivity measure, the information flow score, to mitigate over‑smoothing and over‑squashing in Graph Neural Networks. This approach enables linear computational and memory overhead while effectively capturing both short‑range and long‑range node interactions. Experiments on ten diverse real‑world datasets demonstrate superior performance with limited computational complexity.
By Kevin Mancini, Islem Rekik
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:2608. 09031v1 Announce Type: new Abstract: Graph neural networks typically propagate information through repeated message-passing layers, coupling the distance over which information travels with the number of nonlinear transformations applied.
By Isuru Herath, Arin Gopakumar, Sharan Sahu
arXiv:2602. 01553v3 Announce Type: replace-cross Abstract: Link prediction is a core challenge in graph machine learning, demanding models that capture rich and complex topological dependencies.
By Quang Truong, Yu Song, Donald Loveland, Mingxuan Ju, Tong Zhao, Neil Shah, Jiliang Tang
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