Farid Hazratian

Farid Hazratian, Ali Zia, Hien Duy Nguyen

Out-of-distribution (OOD) robustness is difficult to diagnose when target-domain labels are unavailable. We consider a more restrictive source-only variant of unsupervised accuracy estimation: selecting robust checkpoints using only source-domain representations, with no target samples or target labels. We propose \textbf{TopoGeoScore}, a source-only geometric scorer for label-free OOD checkpoint selection. Given a trained checkpoint, we construct class-conditional mutual $k$-nearest-neighbour graphs from source embeddings and extract three interpretable signals: a torsion-inspired reduced Laplacian log-determinant for global class-manifold complexity, Ollivier--Ricci curvature for local neighbourhood regularity, and higher-order topological summaries for fragmented connectivity, loops, and global--local inconsistency. Instead of fixing their weights by hand, TopoGeoScore learns a non-negative linear score through a self-supervised objective that enforces invariance under approximately geometry-preserving embedding views and separation from structure-breaking views. The score remains interpretable and uses no target-domain samples or labels. Results across CIFAR-based corruption and distribution-shift benchmarks, ImageNet-C, MNLI$\to$HANS transfer, and OGBN-Arxiv suggest that source representations contain measurable global--local--topological evidence of robustness, supporting practical checkpoint selection before deployment under distribution shift.

Ali Zia, Farid Hazratian

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.