A general theory of Hebbian sequence learning

Understanding how neural circuits generate sequential activity is a longstanding challenge. While theoretical models have previously demonstrated how sequences can be stored as memories with Hebbian plasticity rules, these models considered only a particular Hebbian rule that is not observed in experiments. Here we consider a recently introduced model for arbitrary Hebbian plasticity rules and show how the choice of these rules and of the neural activity patterns influences memorized sequence retrieval. In particular, we derive a general theory that predicts the speed of sequence traversal. This theory also explains how temporally heterogeneous sequences -- that is, sequences with fast and slow parts -- arise and behave. This theory lays a foundation for explaining how cortical tutor signals might give rise to motor actions that eventually become “second nature”. Our theory captures the impact of changing the speed of the tutor signal, both in the case when Hebbian learning is much slower as well as on the same order as the speed of the tutor signal. This model also has relevance in artificial intelligence by laying the foundation for a framework whereby slow and computationally expensive deliberatation can be stored as memories and eventually replaced by inexpensive recall.