Understanding how the structural organization of neural networks influences their computational capabilities is of great interest to both machine learning and neuroscience communities. In our previous work, we introduced a novel learning system, called the reservoir of basal dynamics (reBASICS), which features a modular neural architecture (small-sized random neural networks) capable of reducing chaoticity of neural activity and of producing stable self-sustained limit cycle activities. The integration of these limit cycles is achieved by linear summation of their weights, and arbitrary time series are learned by modulating these weights. Despite its excellent learning performance, interpreting a modular structure of isolated small networks as a brain network has posed a significant challenge. Here, we investigate how local connectivity, a well-known characteristic of brain networks, contributes to reducing neural system chaoticity and generates self-sustained limit cycles based on empirical experiments. Moreover, we present the learning performance of the locally connected reBASICS in two tasks: a motor timing task and a learning task of the Lorenz time series. Although its performance was inferior to that of modular reBASICS, locally connected reBASICS could learn a time series of tens of seconds while the time constant of neural units was ten milliseconds. This work indicates that the locality of connectivity in neural networks may contribute to generation of stable self-sustained oscillations to learn arbitrary long-term time series, as well as the economy of wiring cost.
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