Learning sequences with fast and slow parts

Sequential neural activity is hypothesized to underlie driven motor actions, memories of linked sequences of causal relationships, planning and reflection on navigation through environments, and the tracking of the passage of time, among other brain functions. Sequences arise in recurrent networks with asymmetric connectivity structures [1]. These models are of particular interest because they can be learned with biologically plausible temporal asymmetric Hebbian learning (TAH) rules, providing a foundation for modeling of sequential activity in neural circuits. In existing models, the time interval between each part of the sequence is constant, which does not reflect the reality of behaviorially relevant sequences which may have fast and slow parts. Starting from a mathematical framework derived in [2], we show that the addition of a temporal symmetric Hebbian associative memory term allows for the modulation of the propagation speed of the sequences. By selectively strengthening and weakening the symmetric term corresponding to particular elements of the sequence, we show that the propagation speed can be modulated to be faster and slower at different parts of the sequence. This provides an answer to a key mystery: how can the brain learn sequences with fast and slow parts? [1] H. Sompolinsky and I. Kanter. "Temporal Association in Asymmetric Neural Networks". Phys. Rev. Lett. 57.22 (1986). [2] M. Gillett, U. Pereira, and N. Brunel. "Characteristics of sequential activity in networks with temporally asymmetric Hebbian learning". Proc. Natl. Acad. Sci. 117.47 (2020).