One of the most important subjects in neural science is to unveil underlying neural mechanism in cognitive function. As neural activity of a large number of neurons can be observed simultaneously during cognitive tasks, these observations reveal that dynamic neural activity pattern, which is represented as a trajectory in neural state space, underlies the decision-making process, motor control and other cognitive processes. It is believed that such neural trajectory is shaped through the learning process during task training, however, how the trajectory is formed is not uncovered well.
In this study, we model and analyze the formation of neural trajectory during training in a decision-making task, motivated by a experiment in our laboratory on an auditory-motor decision making task, in which a rat has to push a different lever according to different frequency tone after some delay time. Here, we adopt reservoir network, which corresponds to neural circuit in the cortex. In order to implement the learning process with delay time, we also adopt eligibility trace and reward-modulated Hebbian rule for biological plausibility, while ordinary reservoir computing modifies the synaptic efficacy in on-line way. Under this setting, we demonstrate that the log-normal distribution of synaptic efficacy and multiple time-scale of synaptic change play an important role in stable learning. Further, distinct sequential neural activity patterns depending on the external inputs emerge during the learning process, which are similar to the neural behavior observed in the experimental study.