TopoGeoScore: A Self-Supervised Source-Only Geometric Framework for OOD Checkpoint Selection

TL;DR

TopoGeoScore introduces a self-supervised, source-only geometric scoring method for selecting robust checkpoints in out-of-distribution scenarios without target labels.

Contribution

It proposes a novel geometric scorer that leverages class-conditional graphs and learns a score without target data, enhancing OOD robustness assessment.

Findings

Effective across CIFAR, ImageNet-C, MNLI-HANS, and OGBN-Arxiv benchmarks.

Utilizes interpretable signals like Laplacian log-determinant, Ricci curvature, and topological summaries.

Score correlates with robustness, enabling checkpoint selection before deployment.

Abstract

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.