# Representation Geometry as a Diagnostic for Out-of-Distribution Robustness

arXiv: https://arxiv.org/abs/2602.03951 · HTML: https://mlsanity.com/paper/2602.03951/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 22 references that are in the map.
- First posted on arXiv 3 Feb 2026.

## Builds on (most cited first, 14 of 14)

- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)
- [Fantastic Generalization Measures and Where to Find Them](https://mlsanity.com/paper/1912.02178/) (2019)
- [Understanding over-squashing and bottlenecks on graphs via curvature](https://mlsanity.com/paper/2111.14522/) (2021)
- [SWAD: Domain Generalization by Seeking Flat Minima](https://mlsanity.com/paper/2102.08604/) (2021)
- [Do Wide and Deep Networks Learn the Same Things? Uncovering How Neural Network Representations Vary with Width and Depth](https://mlsanity.com/paper/2010.15327/) (2020)
- [Invariant Risk Minimization Games](https://mlsanity.com/paper/2002.04692/) (2020)
- [Neural Persistence: A Complexity Measure for Deep Neural Networks Using Algebraic Topology](https://mlsanity.com/paper/1812.09764/) (2018)
- [Representation Topology Divergence: A Method for Comparing Neural Network Representations](https://mlsanity.com/paper/2201.00058/) (2021)
- [On Characterizing the Capacity of Neural Networks using Algebraic Topology](https://mlsanity.com/paper/1802.04443/) (2018)

## Built on by (most cited first, 4 of 4)

- [Analytic Torsion and Spectral Gap Capture Persistent-Laplacian Performance](https://mlsanity.com/paper/2606.16990/) (2026)
- [STAMP: Predicting Out-of-Distribution Generalization without Target Data](https://mlsanity.com/paper/2609.32672/) (2026)
- [Pretraining Shapes Spectral Structure: Architecture- and Strategy-Conditional Prediction of OOD Robustness in Foundation Models](https://mlsanity.com/paper/2610.09709/) (2026)
- [Dataset-Specific Encoding of Image Content Underlies Cross-Dataset Failure in Brain MRI Foundation Models](https://mlsanity.com/paper/2610.13027/) (2026)

## Abstract (arXiv)

Robust generalization under distribution shift remains difficult to monitor and optimize in the absence of target-domain labels, as models with similar in-distribution accuracy can exhibit markedly different out-of-distribution (OOD) performance. While prior work has focused on training-time regularization and low-order representation statistics, little is known about whether the geometric structure of learned embeddings provides reliable post-hoc signals of robustness. We propose a geometry-based diagnostic framework that constructs class-conditional mutual k-nearest-neighbor graphs from in-distribution embeddings and extracts two complementary invariants: a global spectral complexity proxy based on the reduced log-determinant of the normalized Laplacian, and a local smoothness measure based on Ollivier--Ricci curvature. Across multiple architectures, training regimes, and corruption benchmarks, we find that lower spectral complexity and higher mean curvature consistently predict stronger OOD accuracy across checkpoints. Controlled perturbations and topological analyses further show that these signals reflect meaningful representation structure rather than superficial embedding statistics. Our results demonstrate that representation geometry enables interpretable, label-free robustness diagnosis and supports reliable unsupervised checkpoint selection under distribution shift.