# Shape Correspondence

Dense shape correspondence on high-resolution 3D meshes has been held back by the quadratic cost of spatial-spectral coupling: for two shapes with k vertices each, a single coupling occupies roughly GB in single precision, so existing methods downsample heavily and transfer predictions back. Geo-FlashAttention rewrites that coupling as scaled dot-product attention and evaluates the exact softmax only over surface patches selected by geodesic distance, giving near-linear empirical scaling while preserving the correspondence accuracy of exact implementations. At vertices, peak training memory falls from 106.08 to 5.67 GiB, and each training step is faster than FlashAttention, making end-to-end correspondence learning feasible on meshes such as cortical surfaces.

Dense shape correspondence on high-resolution 3D meshes has been held back by the quadratic cost of spatial-spectral coupling: for two shapes with k vertices each, a single coupling occupies roughly GB in single precision, so existing methods downsample heavily and transfer predictions back. Geo-FlashAttention rewrites that coupling as scaled dot-product attention and evaluates the exact softmax only over surface patches selected by geodesic distance, giving near-linear empirical scaling while preserving the correspondence accuracy of exact implementations. At vertices, peak training memory falls from 106.08 to 5.67 GiB, and each training step is faster than FlashAttention, making end-to-end correspondence learning feasible on meshes such as cortical surfaces.