  The problem of processing very long time-series data (e.g., a length of more
than 10,000) is a long-standing research problem in machine learning. Recently,
one breakthrough, called neural rough differential equations (NRDEs), has been
proposed and has shown that it is able to process such data. Their main concept
is to use the log-signature transform, which is known to be more efficient than
the Fourier transform for irregular long time-series, to convert a very long
time-series sample into a relatively shorter series of feature vectors.
However, the log-signature transform causes non-trivial spatial overheads. To
this end, we present the method of LOweR-Dimensional embedding of log-signature
(LORD), where we define an NRDE-based autoencoder to implant the higher-depth
log-signature knowledge into the lower-depth log-signature. We show that the
encoder successfully combines the higher-depth and the lower-depth
log-signature knowledge, which greatly stabilizes the training process and
increases the model accuracy. In our experiments with benchmark datasets, the
improvement ratio by our method is up to 75\% in terms of various
classification and forecasting evaluation metrics.
