Constant-Curvature Sliced Gromov-Wasserstein for Heterogeneous Cross-Curvature Alignment

תקציר מקורי באנגליתarXiv:2610.07218v1 Announce Type: new Abstract: Recent advances in representation learning have highlighted the utility of constant-curvature models, such as hyperbolic and spherical spaces, for modeling complex data. Mixed-curvature models further enhance this by integrating multiple constant-curvature components. However, these models typically learn each component space independently because spaces with different curvatures are inherently heterogeneous and lack a unified metric. Consequently, they lack explicit mechanisms to enforce geometric consistency across various spaces. Moreover, the problem of comparing probability distributions across mixed-curvature spaces remains unexplored. To compare distributions on heterogeneous spaces, Gromov-Wasserstein (GW) distances provide a principl