ROSETTA: Rotation Subspace Estimation for Training-free Transmodal Alignment

When a query must be matched against a database built with a different sensor or processed by a different encoder, the independently trained encoders impose distinct coordinate systems on the feature space. No canonical reference frame exists to which all encoders can be aligned, and no single training procedure has fully closed this gap. We show that the relative transformation between any two such systems is a spatially preserving rotation in whitened feature space, whose angular velocity exhibits white-noise characteristics: large in norm, temporally uncorrelated, and unpredictable from the features themselves. However, the cross-covariance between encoder outputs has low effective rank, constraining only a small fraction of the rotation parameters, therefore local alignment is tractable. ROSETTA is a training-free calibration layer that estimates the local rotation via an expectation-maximization procedure, requiring no coobservation at query time. We validate ROSETTA on three public driving datasets spanning LiDAR, camera, thermal, and event modalities in cross-modal, cross-device, cross-representation, and cross-backbone settings, with milliseconds overhead per query.