  Forming accurate memory of sequential stimuli is a fundamental function of
biological agents. However, the computational mechanism underlying sequential
memory in the brain remains unclear. Inspired by neuroscience theories and
recent successes in applying predictive coding (PC) to \emph{static} memory
tasks, in this work we propose a novel PC-based model for \emph{sequential}
memory, called \emph{temporal predictive coding} (tPC). We show that our tPC
models can memorize and retrieve sequential inputs accurately with a
biologically plausible neural implementation. Importantly, our analytical study
reveals that tPC can be viewed as a classical Asymmetric Hopfield Network (AHN)
with an implicit statistical whitening process, which leads to more stable
performance in sequential memory tasks of structured inputs. Moreover, we find
that tPC exhibits properties consistent with behavioral observations and
theories in neuroscience, thereby strengthening its biological relevance. Our
work establishes a possible computational mechanism underlying sequential
memory in the brain that can also be theoretically interpreted using existing
memory model frameworks.
