Combinatorial Network-Based Manifold Topological Deep Learning for Image Analysis

Researchers introduced CNMTDL, a manifold topological deep learning framework that combines Hodge decomposition with a combinatorial attention mechanism for medical image analysis, according to a new arXiv paper (arXiv:2609.25453v1). The framework represents medical images as discrete manifolds, decomposes them into three Hodge components, and embeds the concatenated features into a combinatorial complex architecture to enable higher-order message passing between 0-cells and 2-cells via attention-based blocks. CNMTDL was evaluated on six two-dimensional and three-dimensional datasets from the MedMNIST v2 benchmark, demonstrating its effectiveness for medical image analysis.

arXiv:2609.25453v1 Announce Type: new Abstract: Medical image analysis remains fundamentally challenging because of the intricate geometric and topological structures present in medical data. Conventional convolutional neural networks model images as regular Euclidean grids, limiting their ability to preserve geometric relationships and higher-order structural information. Recently, manifold topological deep learning MTDL has emerged as a promising paradigm that integrates deep learning with geometric and topological representations. Nevertheless, existing methods have not yet fully exploited discrete manifold structures within combinatorial complex neural networks. To bridge this gap, we introduce CNMTDL, a MTDL framework that integrates Hodge decomposition with a combinatorial attention mechanism. In our approach, medical images are represented as discrete manifolds and decomposed into three Hodge components. Features extracted from these components are concatenated and embedded into a combinatorial complex architecture, enabling enhanced higher-order message passing between $0$-cells and $2$-cells through attention-based blocks. We evaluate CNMTDL on six two-dimensional and three-dimensional datasets from the MedMNIST v2 benchmark, demonstrating its effectiveness for medical image analysis.