The paper introduces Message‑Passing Graph Persistence (MGP), a new family of topological descriptors that integrates message‑passing into graph filtrations. By updating node embeddings at each filtration step and using them to determine persistence events and component representatives, MGP remains invariant under graph isomorphism and is proven to be strictly more expressive than existing PH‑based descriptors. Experiments on expressivity benchmarks and various graph classification and regression datasets demonstrate that MGP outperforms other PH‑based methods on most tasks.
By Jorge Luiz Franco, Arthur Queiroz Moura, Moacir Ponti, Amauri Souza
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
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:2507. 07156v2 Announce Type: replace-cross Abstract: Supervised machine learning pipelines trained on features derived from persistent homology have been experimentally observed to ignore much of the information contained in a persistence diagram.
By Nicole Abreu, Parker B. Edwards, Francis Motta
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
arXiv:2609.08152v1 Announce Type: new
Abstract: Graph representation learning has largely focused on designing increasingly sophisticated models to transform graph topology into vector representation...
By Meng Qin, Jinqiang Cui, Hongwei Zheng, Weihua Li, Sen Pei
The paper introduces a unified pipeline that classifies univariate time series by first converting them into graphs using one of five constructions from three families (visibility, transition, proximity). The resulting graph is turned into a dissimilarity matrix, from which a Vietoris–Rips filtration produces persistence diagrams that are vectorized via persistence landscapes and topological summary statistics. Experiments on twelve UCR benchmarks reveal that no single graph construction dominates, diffusion distance consistently outperforms shortest-path metrics, and persistence-based features remain robust to noise.
By \.Ismail G\"uzel
The paper demonstrates that high‑quality graph embeddings can be produced without complex models or training by propagating random features through topological structures derived from random walks and anonymous walks. These training‑free embeddings capture node proximity and structural roles, respectively, and perform competitively on node, edge, and graph tasks while often requiring less computation. Combining the two embedding types further improves inference quality for some tasks.
arXiv:2606. 11911v1 Announce Type: cross Abstract: Persistence diagrams are common representations in topological data analysis, but they do not naturally live in a vector space, and the statistical tools developed for comparing them have largely evolved separately from those used for downstream prediction.
By Juliette Murris, Bernadette Stolz, Karsten Borgwardt
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:2606. 21333v2 Announce Type: replace Abstract: Graph Neural Networks (GNNs) have emerged as a powerful paradigm for learning on graph-structured data by iteratively propagating and aggregating information across edges.
By Hugo Attali, Rachid El Jouhri