On Learning, Uncertainty and Synchronization in Stochastic Neural Ensembles

We consider learning in coupled stochastic neural ensembles obeying a nonlinear gradient dynamics, where the task for the neural population is to learn a decision function in the presence of noise. Given that there is noise corrupting the learning process, how can one assign a confidence to the predictions of such a function and how can the organism reduce uncertainty in its decisions? In this paper we explore quantitatively the role of synchronization in determining uncertainty in neural learning. We show that uncertainty can be controlled in large part by trading off coupling strength among multiple neural populations against the noise amplitude. The impact of the coupling strength is quantified by the spectrum of the network Laplacian, and we discuss the role of network topology in synchronization and in reducing the effect of noise. Simulations comparing theoretical bounds to the relevant empirical quantities show that the estimates can be tight.