Geometry-aware similarity metrics for neural representations on Riemannian and statistical manifolds

N Alex Cayco Gajic, Arthur Pellegrino|March 30, 2026arXiv

Key Takeaway

Comparing neural representations by their intrinsic geometric structure—not just their raw values—reveals deeper insights into how different networks solve the same problem, enabling better interpretation of neural computations.

Summary

This paper introduces metric similarity analysis (MSA), a new method for comparing how neural networks represent information by analyzing the intrinsic geometry of their learned representations rather than just their surface-level structure.

evaluation

Key Terms

riemannian-geometry intrinsic-geometry manifold-hypothesis representational-geometry