Learning Shapes Bifurcations of Neural Dynamics upon External Stimuli

Abstract

Memory is often considered to be embedded into one of the attractors in neural dynamical systems, which provides an appropriate output depending on the initial state specified by an input. However, memory is recalled only under the presence of external inputs. Without such inputs, neural states do not provide such memorized outputs. Hence, each of memories do not necessarily correspond to an attractor of the dynamical system without input and do correspond to an attractor of the dynamics system with input. With this background, we propose that memory recall occurs when the neural activity changes to an appropriate output activity upon the application of an input. We introduce a neural network model that enables learning of such memories. After the learning process is complete, the neural dynamics is shaped so that it changes to the desired target with each input. This change is analyzed as bifurcation in a dynamical system. Conditions on timescales for synaptic plasticity are obtained to achieve the maximal memory capacity.