Extending SSMs with the Exponentially Weighted Signature
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 depth one the EWS is a state-space model (SSM), and we map linear time-invariant SSMs, Mamba channels and Mamba-$2$ heads to it in closed form. The EWS extends SSMs through an arbitrary matrix generator, a clock that generalises the step size to causal func...
| Authors | Alexandre Bloch, Benjamin Walker, Joël Mouterde et al. |
|---|---|
| Primary category | stat.ML |
| Published | 19 March 2026 |
| Last updated at source | 30 September 2026 |
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