# Probability-Invariant Random Walk Learning on Gyral Folding-Based Cortical Similarity Networks for Alzheimer's and Lewy Body Dementia Diagnosis

arXiv: https://arxiv.org/abs/2602.17557 · HTML: https://mlsanity.com/paper/2602.17557/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 32 references that are in the map.
- First posted on arXiv 19 Feb 2026.

## Builds on (most cited first, 11 of 11)

- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Revisiting Random Walks for Learning on Graphs](https://mlsanity.com/paper/2407.01214/) (2024)
- [Core-Periphery Principle Guided State Space Model for Functional Connectome Classification](https://mlsanity.com/paper/2503.14655/) (2025)
- [Using Structural Similarity and Kolmogorov-Arnold Networks for Anatomical Embedding of Cortical Folding Patterns](https://mlsanity.com/paper/2410.23598/) (2024)
- [GyralNet Subnetwork Partitioning via Differentiable Spectral Modularity Optimization](https://mlsanity.com/paper/2503.19823/) (2025)
- [Gyral-Sulcal-Net: An Integrated Network Representation of Brain Folding Patterns](https://mlsanity.com/paper/2601.08818/) (2026)
- [Community-Level Modeling of Gyral Folding Patterns for Robust and Anatomically Informed Individualized Brain Mapping](https://mlsanity.com/paper/2602.01482/) (2026)

## Abstract (arXiv)

Alzheimer's disease (AD) and Lewy body dementia (LBD) present overlapping clinical features yet require distinct diagnostic strategies. While neuroimaging-based brain network analysis is promising, atlas-based representations may obscure individualized anatomy. Gyral folding-based networks using three-hinge gyri provide a biologically grounded alternative, but inter-individual variability in cortical folding results in inconsistent landmark correspondence and highly irregular network sizes, violating the fixed-topology and node-alignment assumptions of most existing graph learning methods, particularly in clinical datasets where pathological changes further amplify anatomical heterogeneity. We therefore propose a probability-invariant random-walk-based framework that classifies individualized gyral folding networks without explicit node alignment. Cortical similarity networks are built from local morphometric features and represented by distributions of anonymized random walks, with an anatomy-aware encoding that preserves permutation invariance. Experiments on a large clinical cohort of AD and LBD subjects show consistent improvements over existing gyral folding and atlas-based models, demonstrating robustness and potential for dementia diagnosis.