Geometry-Conditioned Fixed-Scaffold Encoders for Time-Warp Robust Sequence Retrieval

Cassandra Yang, Yufan Tang

Embedding-based retrieval is attractive for long sequence collections because each item can be encoded once and searched by nearest-neighbor ranking. The difficulty is that the objects being indexed are often observed under a noncanonical clock: cardiac cycles stretch with rate, speech changes with tempo, and sensor traces reach comparable states at different speeds. This paper studies a specific source of instability in patch-based encoders for this regime. If patch boundaries are chosen from signal geometry, then the tokenization can change under the same temporal deformation that the representation is expected to tolerate. We propose GeoPatch, a fixed-scaffold patch encoder that keeps token support independent of geometry and uses slope, curvature, acceleration, affine-residual, and confidence descriptors only as continuous conditioning variables. The design turns boundary variation into feature modulation: geometry can change the embedding through a controlled pathway, but it cannot change the number, order, or support of local tokens. We formalize this distinction through a mechanism-level stability analysis that separates boundary drift, affine timing variation,…