Neural network regulation driven by autonomous neural firings

Biological neurons naturally fire spontaneously due to the existence of a noisy current. Such autonomous firings may provide a driving force for network formation because synaptic connections can be modified due to neural firings. Here, we study the effect of autonomous firings on network formation. For the temporally asymmetric Hebbian learning, bidirectional connections lose their balance easily and become unidirectional ones. Defining the difference between reciprocal connections as new variables, we could express the learning dynamics as if Ising model spins interact with each other in magnetism. We present a theoretical method to estimate the interaction between the new variables in a neural system. We apply the method to some network systems and find some tendencies of autonomous neural network regulation.