# Topological Learning for Brain Networks

arXiv: https://arxiv.org/abs/2012.00675 · HTML: https://mlsanity.com/paper/2012.00675/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Nov 2020.

## Built on by (most cited first, 6 of 6)

- [Fast Topological Clustering with Wasserstein Distance](https://mlsanity.com/paper/2112.00101/) (2021)
- [Persistent Homological State-Space Estimation of Functional Human Brain Networks at Rest](https://mlsanity.com/paper/2201.00087/) (2022)
- [Augmenting Bias Detection in LLMs Using Topological Data Analysis](https://mlsanity.com/paper/2508.07516/) (2025)
- [Topological Invariant-Based Iris Identification via Digital Homology and Machine Learning](https://mlsanity.com/paper/2508.09555/) (2025)
- [Leveraging LLMs for Early Alzheimer's Prediction](https://mlsanity.com/paper/2510.23946/) (2025)
- [Data-driven techniques for translational neuroscience and personalized neuro-health](https://mlsanity.com/paper/2608.13749/) (2026)

## Abstract (arXiv)

This paper proposes a novel topological learning framework that integrates networks of different sizes and topology through persistent homology. Such challenging task is made possible through the introduction of a computationally efficient topological loss. The use of the proposed loss bypasses the intrinsic computational bottleneck associated with matching networks. We validate the method in extensive statistical simulations to assess its effectiveness when discriminating networks with different topology. The method is further demonstrated in a twin brain imaging study where we determine if brain networks are genetically heritable. The challenge here is due to the difficulty of overlaying the topologically different functional brain networks obtained from resting-state functional MRI onto the template structural brain network obtained through diffusion MRI.