arXiv:2606. 29763v1 Announce Type: cross Abstract: Topological data analysis (TDA), particularly persistent homology (PH), captures geometric structural properties in medical images (e.
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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.
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: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: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.
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. 02841v1 Announce Type: new Abstract: Deep neural networks learn representations where individual features often lack interpretable meaning; a single neuron may activate for scattered, unrelated inputs.