We argue that reservoir computing is a pertinent framework to model local cortical dynamics and their contribution to higher cognitive function.
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We compared reservoir activity to neural activity of dorsal anterior cingulate cortex of monkeys which revealed similar network dynamics. This second version of the model demonstrates how a hybrid dynamical regime combining spatio-temporal processing of reservoirs, and input driven attracting dynamics generated by the feedback neuron, can be used to solve a complex cognitive task. The pre-coded representation of context was amplified by training a feedback neuron to explicitly represent this context, thereby reproducing the effect of learning and allowing the model to perform more robustly. The reservoir model inherently displayed a dynamic form of mixed selectivity, key to the representation of the behavioral context over time. We thus explored their representational power and dynamical properties after training a reservoir to perform a complex cognitive task initially developed for monkeys. These representations can then be selectively amplified through learning to solve the task at hand. Recombining present and past inputs, random recurrent networks from the reservoir computing framework generate mixed selectivity which provides pre-coded representations of an essentially universal set of contexts. In this context, these reservoir networks reproduce the highly recurrent nature of local cortical connectivity. It has been observed that mixed selectivity in cortical neurons contributes to represent diverse situations defined by a combination of the current stimuli, and that mixed selectivity is readily obtained in randomly connected recurrent networks. Thus, one can ask how cortical dynamics generate representations of these complex situations. Determining what is most pertinent in these situations is not always possible based only on the current sensory inputs, and often also depends on recent inputs and behavioral outputs that contribute to internal states. Primates display a remarkable ability to adapt to novel situations. Surprisingly, the ESN was unable to fully learn the dependency problem, suggesting the major shift towards this class of models may be premature. Analysis of the internal representations of the networks, reveals that sluggish state-based representations of the MRN are best able to latch on to critical temporal dependencies spanning variable time delays, to maintain distinct and stable representations of all underlying grammar states.
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We demonstrate that an MRN, optimised with noise injection, is able to learn the long term dependency within a complex grammar induction task, significantly outperforming the SRN, NARX and ESN. We show that memory units embedded within its architecture can ameliorate against the vanishing gradient problem, by providing variable sensitivity to recent and more historic information through layer- and self-recurrent links with varied weights, to form a so-called sluggish state-based memory. This paper re-opens the case for SRN-based approaches, by considering a variant, the Multi-recurrent Network (MRN). The vanishing gradients problem inherent in Simple Recurrent Networks (SRN) trained with back-propagation, has led to a significant shift towards the use of Long Short-term Memory (LSTM) and Echo State Networks (ESN), which overcome this problem through either second order error-carousel schemes or different learning algorithms respectively.