Locally Robust Alignment Between Distinct Spaces

ABSTRACT The Gromov‐Wasserstein (GW) distance serves as a measure of discrepancy between two distributions that are supported on distinct ambient spaces. Emerging as the optimal expected departure from isometry, it keeps finding continual usage in tasks such as object matching and network analysis. However, its merit is often undermined by its susceptibility to outliers present in data. Thus, in this work, we focus on studying the statistical properties of Locally Robust GW , a newly introduced robust formulation that preserves topological properties from the original distance. We show that it recovers unperturbed GW values under contamination, making it a suitable proxy loss for several machine learning tasks. Based on the same, we also develop a robust transform sampling framework with supporting concentration bounds.