The Volterra signature
Modern approaches for learning from non-Markovian time series, such as recurrent neural networks, neural controlled differential equations or transformers, typically rely on implicit memory mechanisms that can be difficult to interpret or to train over long horizons. We propose the \emph{Volterra signature} $\mathrm{VSig}(x;K)$ as a principled, explicit feature representation for history-dependent systems. By developing the input path $x$ weighted by a temporal kernel $K$ into the tensor algebra, we leverage the associated Volterra--Chen identity to derive rigorous learning-theoretic guarantees. Specifically, we prove an \emph{injectivity} statement (identifiability under augmentation) th...
| Authors | Paul P. Hager, Fabian N. Harang, Luca Pelizzari et al. |
|---|---|
| Primary category | stat.ML |
| Published | 4 March 2026 |
| Last updated at source | 21 May 2026 |
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