# Combinatorial Network-Based Manifold Topological Deep Learning for Image Analysis

arXiv: https://arxiv.org/abs/2609.25453 · HTML: https://mlsanity.com/paper/2609.25453/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 45 references that are in the map.
- First posted on arXiv 21 Sep 2026.

## Builds on (most cited first, 19 of 19)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [MedMNIST v2 -- A large-scale lightweight benchmark for 2D and 3D biomedical image classification](https://mlsanity.com/paper/2110.14795/) (2021)
- [A review of deep learning in medical imaging: Imaging traits, technology trends, case studies with progress highlights, and future promises](https://mlsanity.com/paper/2008.09104/) (2020)
- [Auto-Keras: An Efficient Neural Architecture Search System](https://mlsanity.com/paper/1806.10282/) (2018)
- [Topological Deep Learning: Going Beyond Graph Data](https://mlsanity.com/paper/2206.00606/) (2022)
- [MedViT: A Robust Vision Transformer for Generalized Medical Image Classification](https://mlsanity.com/paper/2302.09462/) (2023)
- [Cell Complex Neural Networks](https://mlsanity.com/paper/2010.00743/) (2020)
- [Position: Topological Deep Learning is the New Frontier for Relational Learning](https://mlsanity.com/paper/2402.08871/) (2024)
- [Deep Learning Approaches for Data Augmentation in Medical Imaging: A Review](https://mlsanity.com/paper/2307.13125/) (2023)
- [Topological Deep Learning: A Review of an Emerging Paradigm](https://mlsanity.com/paper/2302.03836/) (2023)
- [TopoTune : A Framework for Generalized Combinatorial Complex Neural Networks](https://mlsanity.com/paper/2410.06530/) (2024)
- [Complex Mixer for MedMNIST Classification Decathlon](https://mlsanity.com/paper/2304.10054/) (2023)
- [BSDA: Bayesian Random Semantic Data Augmentation for Medical Image Classification](https://mlsanity.com/paper/2403.06138/) (2024)
- [Manifold Topological Deep Learning for Biomedical Data](https://mlsanity.com/paper/2503.00175/) (2025)
- [unORANIC: Unsupervised Orthogonalization of Anatomy and Image-Characteristic Features](https://mlsanity.com/paper/2308.15507/) (2023)
- [ILPO-NET: Network for the invariant recognition of arbitrary volumetric patterns in 3D](https://mlsanity.com/paper/2403.19612/) (2024)
- [Persistent de Rham-Hodge Laplacians in Eulerian representation for manifold topological learning](https://mlsanity.com/paper/2408.00220/) (2024)

## Abstract (arXiv)

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.