arXiv:2305. 06315v3 Announce Type: replace-cross Abstract: For deep learning problems on graph-structured data, pooling layers are important for down sampling, reducing computational cost, and to minimize overfitting.
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...
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.
arXiv:2608. 01160v1 Announce Type: new Abstract: Topological neural networks (TNNs) enable leveraging high-order structures on graphs (e.
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.
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.
The paper introduces Topology-Preserving Adaptive Graph Pooling (TPAGP), a method that partitions graphs into granular balls by combining node features and topology to create multi-granularity representations. TPAGP captures both global and local structural patterns, unlike prior pooling methods that coarsen graphs by removing or clustering nodes. Experiments show TPAGP outperforms existing pooling techniques on benchmark datasets, reducing information loss from fixed-granularity strategies.
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.
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.
arXiv:2606. 09051v1 Announce Type: new Abstract: Convolutions have successfully transitioned from image processing to the complex realm of non-Euclidean higher-order domains, particularly in hypergraphs.
The paper introduces MGHRL, a framework for hypergraph representation learning that adapts hyperedge granularity through a granular-ball splitting strategy. It constructs hyperedges at multiple levels of detail, capturing high-order relationships tailored to the graph’s topology. A multi-granularity hypergraph network then processes these hyperedges with sub-networks and hierarchical reversible connections, achieving superior performance on benchmark datasets.
Combinatorial Network-Based Manifold Topological Deep Learning (CNMTDL) is a new framework that represents medical images as discrete manifolds and decomposes them into three Hodge components. Features from these components are concatenated and fed into a combinatorial complex architecture, enabling higher‑order message passing between 0‑cells and 2‑cells via attention‑based blocks. CNMTDL was evaluated on six 2D and 3D datasets from the MedMNIST v2 benchmark, showing improved performance for medical image analysis.
arXiv:2511. 04539v2 Announce Type: replace-cross Abstract: In network neuroscience, functional brain systems are often characterized using separate yet related graph-theoretic or spectral descriptors, overlooking how these properties covary and partially overlap across individuals and conditions.