Random Controlled Differential Equations for Time-Series Learning

This paper introduces a novel framework for time-series learning that combines the efficiency of random features with the expressiveness of controlled differential equations (CDEs). The use of random features allows for training-efficient models, while the CDEs provide a continuous-time reservoir for capturing complex temporal dependencies. The paper's contribution lies in proposing two variants (RF-CDEs and R-RDEs) and demonstrating their theoretical connections to kernel methods and path-signature theory. The empirical evaluation on various time-series benchmarks further validates the practical utility of the proposed approach.

• •Introduces a training-efficient framework for time-series learning using random features and CDEs.
• •Proposes two variants: RF-CDEs (Random Fourier CDEs) and R-RDEs (Random Rough DEs).
• •Establishes theoretical connections to kernel methods and path-signature theory.
• •Demonstrates competitive or state-of-the-art performance on time-series benchmarks.