# It's the Geometry, Not the Model: Effective Rank and Subspace Alignment in Functional Connectivity Classification

arXiv: https://arxiv.org/abs/2609.29932 · HTML: https://mlsanity.com/paper/2609.29932/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 14 references that are in the map.
- First posted on arXiv 24 Sep 2026.

## Builds on (most cited first, 4 of 4)

- [Benign Overfitting in Linear Regression](https://mlsanity.com/paper/1906.11300/) (2019)
- [Benign overfitting in ridge regression](https://mlsanity.com/paper/2009.14286/) (2020)
- [Brain Network Transformer](https://mlsanity.com/paper/2210.06681/) (2022)
- [Rethinking Functional Brain Connectome Analysis: Do Graph Deep Learning Models Help](https://mlsanity.com/paper/2501.17207/) (2025)

## Abstract (arXiv)

Resting-state functional connectivity (FC) is widely used to classify brain phenotypes and disorders. Most pipelines use the full connectome and seek gains through model design. We instead examine how FC geometry constrains classification and cross-site transfer. Across-subject FC variation concentrates in a small effective subspace, suggesting substantial redundancy in nominal dimensions. Across cohorts, these subspaces may differ in orientation even when their effective ranks are comparable, potentially limiting transfer. Across 2,330 subjects from HCP, ABIDE, and ADHD-200, effective-rank analysis reveals strong spectral concentration. Projection onto leading components at the effective-rank scale recovers most of the full-FC classification performance. In ABIDE, site-specific effective subspaces are weakly aligned, and their principal-angle overlap predicts pairwise transfer after covariate adjustment despite comparable per-site effective ranks. Controlled rotations that alter subspace orientation while preserving the mean and covariance spectrum drive transfer toward chance, whereas displacement-matched label-orthogonal rotations do not. These results identify subspace orientation as a key factor in transfer degradation under controlled perturbations. This study offers a geometric diagnostic of FC generalization and suggests evaluating cross-site harmonization by its ability to align effective subspaces alongside classification accuracy.