  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.
