Metric Similarity Analysis (MSA) uses Riemannian geometry to compare the intrinsic geometry of neural representations.
March 31, 2026
Original Paper
Geometry-aware similarity metrics for neural representations on Riemannian and statistical manifolds
arXiv · 2603.28764
The Takeaway
Unlike standard similarity metrics (CKA/RSA) that look at extrinsic state space, MSA captures the underlying geometric structure of neural manifolds. This allows researchers to disentangle different computational strategies in networks that appear similar under traditional metrics.
From the abstract
Similarity measures are widely used to interpret the representational geometries used by neural networks to solve tasks. Yet, because existing methods compare the extrinsic geometry of representations in state space, rather than their intrinsic geometry, they may fail to capture subtle yet crucial distinctions between fundamentally different neural network solutions. Here, we introduce metric similarity analysis (MSA), a novel method which leverages tools from Riemannian geometry to compare the