Student author: Ritwik K. Niyogi
Physical Review E
We investigate the role of the learning rate in a Kuramoto Model of coupled phase oscillators in which the coupling coefficients dynamically vary according to a Hebbian learning rule. According to the Hebbian theory, a synapse between two neurons is strengthened if they are simultaneously coactive. Two stable synchronized clusters in antiphase emerge when the learning rate is larger than a critical value. In such a fast learning scenario, the network eventually constructs itself into an all-to-all coupled structure, regardless of initial conditions in connectivity. In contrast, when learning is slower than this critical value, only a single synchronized cluster can develop. Extending our analysis, we explore whether self-development of neuronal networks can be achieved through an interaction between spontaneous neural synchronization and Hebbian learning. We find that self-development of such neural systems is impossible if learning is too slow. Finally, we demonstrate that similar to the acquisition and consolidation of long-term memory, this network is capable of generating and remembering stable patterns.
Niyogi, Ritwik K., and Lars Q. English. "Learning-Rate-Dependent Clustering and Self-development in a Network of Coupled Phase Oscillators." Physical Review E 80, no. 6 (2009): e066213. https://journals.aps.org/pre/abstract/10.1103/PhysRevE.80.066213