# Manifold Topological Deep Learning for Biomedical Data

arXiv: https://arxiv.org/abs/2503.00175 · HTML: https://mlsanity.com/paper/2503.00175/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 50 references that are in the map.
- First posted on arXiv 28 Feb 2025.

## Builds on (most cited first, 17 of 17)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Decoupled Weight Decay Regularization](https://mlsanity.com/paper/1711.05101/) (2017)
- [ChestX-ray8: Hospital-scale Chest X-ray Database and Benchmarks on Weakly-Supervised Classification and Localization of Common Thorax Diseases](https://mlsanity.com/paper/1705.02315/) (2017)
- [MedMNIST v2 -- A large-scale lightweight benchmark for 2D and 3D biomedical image classification](https://mlsanity.com/paper/2110.14795/) (2021)
- [Skin Lesion Analysis Toward Melanoma Detection 2018: A Challenge Hosted by the International Skin Imaging Collaboration (ISIC)](https://mlsanity.com/paper/1902.03368/) (2019)
- [The Liver Tumor Segmentation Benchmark (LiTS)](https://mlsanity.com/paper/1901.04056/) (2019)
- [MedMNIST Classification Decathlon: A Lightweight AutoML Benchmark for Medical Image Analysis](https://mlsanity.com/paper/2010.14925/) (2020)
- [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)
- [Position: Topological Deep Learning is the New Frontier for Relational Learning](https://mlsanity.com/paper/2402.08871/) (2024)
- [IntrA: 3D Intracranial Aneurysm Dataset for Deep Learning](https://mlsanity.com/paper/2003.02920/) (2020)
- [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)
- [Specialty-Oriented Generalist Medical AI for Chest CT Screening](https://mlsanity.com/paper/2304.02649/) (2023)
- [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)

## Built on by (most cited first, 4 of 4)

- [COLORA: Efficient Fine-Tuning for Convolutional Models with a Study Case on Optical Coherence Tomography Image Classification](https://mlsanity.com/paper/2505.18315/) (2025)
- [Multi-dimensional Persistent Sheaf Laplacians for Image Analysis](https://mlsanity.com/paper/2602.14846/) (2026)
- [Combinatorial Network-Based Manifold Topological Deep Learning for Image Analysis](https://mlsanity.com/paper/2609.25453/) (2026)
- [LabFactory: Building and Evaluating Executable AI Labs](https://mlsanity.com/paper/2609.28697/) (2026)

## Abstract (arXiv)

Recently, topological deep learning (TDL), which integrates algebraic topology with deep neural networks, has achieved tremendous success in processing point-cloud data, emerging as a promising paradigm in data science. However, TDL has not been developed for data on differentiable manifolds, including images, due to the challenges posed by differential topology. We address this challenge by introducing manifold topological deep learning (MTDL) for the first time. To highlight the power of Hodge theory rooted in differential topology, we consider a simple convolutional neural network (CNN) in MTDL. In this novel framework, original images are represented as smooth manifolds with vector fields that are decomposed into three orthogonal components based on Hodge theory. These components are then concatenated to form an input image for the CNN architecture. The performance of MTDL is evaluated using the MedMNIST v2 benchmark database, which comprises 717,287 biomedical images from eleven 2D and six 3D datasets. MTDL significantly outperforms other competing methods, extending TDL to a wide range of data on smooth manifolds.