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Sequential transitions between metastable states are ubiquitously observed inthe neural system and underlie various cognitive functions. Although a numberof studies with asymmetric Hebbian connectivity have investigated how suchsequences are generated, the focused sequences are simple Markov ones. On theother hand, supervised machine learning methods can generate complex non-Markovsequences, but these sequences are vulnerable against perturbations. Further,concatenation of newly learned sequence to the already learned one is difficultdue to catastrophe forgetting, although concatenation is essential forcognitive functions such as inference. How stable complex sequences aregenerated still remains unclear. We have developed a neural network with fastand slow dynamics, which are inspired by the experiments. The slow dynamicsstore history of inputs and outputs and affect the fast dynamics depending onthe stored history. We show the learning rule that requires only localinformation can form the network generating the complex and robust sequences inthe fast dynamics. The slow dynamics work as bifurcation parameters for thefast one, wherein they stabilize the next pattern of the sequence before thecurrent pattern is destabilized. This co-existence period leads to the stabletransition between the current and the next pattern in the sequence. We furtherfind that timescale balance is critical to this period. Our study provides anovel mechanism generating the robust complex sequences with multipletimescales in neural dynamics. Considering the multiple timescales are widelyobserved, the mechanism advances our understanding of temporal processing inthe neural system.

Multiple-timescale Neural Networks: Generation of Context-dependent Sequences and Inference through Autonomous Bifurcations