Learnable Path in Neural Controlled Differential Equations

TL;DR

This paper introduces a learnable path mechanism in neural controlled differential equations (NCDEs), enabling the model to optimize the interpolation path for better time-series classification and forecasting performance.

Contribution

It proposes a novel method to learn an optimal interpolation path within NCDEs, replacing traditional fixed interpolation algorithms, and demonstrates improved results.

Findings

Achieved state-of-the-art performance in time-series classification.

Enhanced forecasting accuracy over existing NCDE methods.

Validated the effectiveness of learnable paths through extensive experiments.

Abstract

Neural controlled differential equations (NCDEs), which are continuous analogues to recurrent neural networks (RNNs), are a specialized model in (irregular) time-series processing. In comparison with similar models, e.g., neural ordinary differential equations (NODEs), the key distinctive characteristics of NCDEs are i) the adoption of the continuous path created by an interpolation algorithm from each raw discrete time-series sample and ii) the adoption of the Riemann--Stieltjes integral. It is the continuous path which makes NCDEs be analogues to continuous RNNs. However, NCDEs use existing interpolation algorithms to create the path, which is unclear whether they can create an optimal path. To this end, we present a method to generate another latent path (rather than relying on existing interpolation algorithms), which is identical to learning an appropriate interpolation method. We design an encoder-decoder module based on NCDEs and NODEs, and a special training method for it. Our method shows the best performance in both time-series classification and forecasting.