Extending SSMs with the Exponentially Weighted Signature

Excerpt

arXiv:2603.19198v3 Announce Type: replace-cross Abstract: We introduce the exponentially weighted signature (EWS), a continuous-time model that computes iterated integrals of a path, where each increment is weighted by the matrix exponential of a learnable generator over elapsed clock time. We prove that it solves a linear controlled differential equation, keeps the group-like structure and the universality of the signature, and satisfies a modified Chen identity, enabling a parallel scan. At de