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:2606. 29763v1 Announce Type: cross Abstract: Topological data analysis (TDA), particularly persistent homology (PH), captures geometric structural properties in medical images (e.
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:2606. 09806v1 Announce Type: cross Abstract: We introduce Topological Neural Operators (TNOs), a principled framework for operator learning on cell complexes that lifts neural operators (NOs) from functions on points and/or edges to topological domains.
arXiv:2401. 14381v3 Announce Type: replace Abstract: We propose two graph neural network layers for graphs with features in a Riemannian manifold.
arXiv:2609.35436v2 Announce Type: replace Abstract: Recently, deep neural networks on manifold-valued representations have garnered significant attention across various machine learning applications....
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.
The paper introduces GDMRG, a Graph-Augmented Dual-Stream Medical Report Generation framework that incorporates a Topological Knowledge Internalization module using a Graph Convolutional Network to encode disease co-occurrence priors. It employs a dual-stream classifier—one branch generating diagnostic prompts under topological constraints and an auxiliary branch dynamically calibrating decision boundaries for imbalanced samples—alongside a Diagnosis-Guided Spatial Attention mechanism to align visual features with clinical semantics. Experiments on MIMIC-CXR show competitive clinical efficacy and natural language fluency, with strong zero-shot performance on IU X-Ray.
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:2609.36172v1 Announce Type: cross Abstract: Figuring out how objects relate to each other, like whether they touch, overlap, stay completely separate or one sits inside another, matters a lot i...
arXiv:2606. 06342v1 Announce Type: cross Abstract: Topological Data Analysis (TDA) offers a principled, intrinsic lens for comparing neural 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.
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.