The Volterra signature is a kernel-weighted tensor feature map for paths that is injective, universally approximating, and computable via linear ODEs or a two-parameter integral equation.
JMLR, 20, (31), pp 1–45
3 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We present a novel framework for kernel learning with sequential data of any kind, such as time series, sequences of graphs, or strings. Our approach is based on signature features which can be seen as an ordered variant of sample (cross-)moments; it allows to obtain a "sequentialized" version of any static kernel. The sequential kernels are efficiently computable for discrete sequences and are shown to approximate a continuous moment form in a sampling sense. A number of known kernels for sequences arise as "sequentializations" of suitable static kernels: string kernels may be obtained as a special case, and alignment kernels are closely related up to a modification that resolves their open non-definiteness issue. Our experiments indicate that our signature-based sequential kernel framework may be a promising approach to learning with sequential data, such as time series, that allows to avoid extensive manual pre-processing.
years
2026 3verdicts
UNVERDICTED 3representative citing papers
Algorithms for Volterra signature computation achieve O(J^2), O(J log J) via FFT, and O(J R^2) via recursion, plus a predictor-corrector scheme, all implemented in a public JAX package.
ARL lifts states into signature-augmented manifolds and employs self-consistent proxies of future path-laws to enable deterministic expected-return evaluation while preserving contraction mappings in jump-diffusion environments.
citing papers explorer
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The Volterra signature
The Volterra signature is a kernel-weighted tensor feature map for paths that is injective, universally approximating, and computable via linear ODEs or a two-parameter integral equation.
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Computational aspects of the Volterra Signature
Algorithms for Volterra signature computation achieve O(J^2), O(J log J) via FFT, and O(J R^2) via recursion, plus a predictor-corrector scheme, all implemented in a public JAX package.
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Anticipatory Reinforcement Learning: From Generative Path-Laws to Distributional Value Functions
ARL lifts states into signature-augmented manifolds and employs self-consistent proxies of future path-laws to enable deterministic expected-return evaluation while preserving contraction mappings in jump-diffusion environments.