TopoGeoScore: A Self-Supervised Source-Only Geometric Framework for OOD Checkpoint Selection
This work addresses the practical problem of selecting robust models before deployment under distribution shift, when target data is unavailable.
TopoGeoScore selects robust OOD checkpoints using only source-domain representations, without target samples or labels. It achieves strong performance across CIFAR-based corruptions, ImageNet-C, MNLI→HANS, and OGBN-Arxiv benchmarks.
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.