Intrinsic Riemannian cross-covariance defines manifold-valued covariance via parallel transport to a common tangent space, yielding coordinate-independent second-order descriptors with Euclidean-like properties and verified asymptotic behavior.
3DSPMR leverages 3D spatial memory with field-of-view geometric priors to reuse exploration knowledge across sequential embodied tasks, significantly improving reasoning and navigation performance on the SEER-Bench benchmark.