arXiv:2603.04525v2 Announce Type: replace-cross Abstract: 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--Che
This research emerges as the limitations of existing recurrent and transformer models for long-horizon, non-Markovian time series become more apparent and are actively being addressed by the research community.
Improved explicit feature representations for history-dependent systems could dramatically enhance the interpretability, training stability, and performance of AI models dealing with complex sequential data.
The development of a principled, explicit feature representation like the Volterra signature offers a potential alternative to implicit memory mechanisms, making AI models more robust and easier to understand.
- · AI researchers and data scientists
- · Sectors with complex time series data (e.g., finance, climate, robotics)
- · Developers of interpretable AI systems
- · Traditional black-box recurrent networks
- · Systems heavily reliant on implicit memory mechanisms
More accurate and stable AI models for long-term prediction and analysis within specific domains.
Accelerated development of AI agents capable of handling extended, complex historical contexts and planning.
Enhanced trust and adoption of AI in critical applications due to increased interpretability and reliability in handling time-dependent systems.
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