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Learning and decision making in the brain are key processes critical tosurvival, and yet are processes implemented by non-ideal biological buildingblocks which can impose significant error. We explore quantitatively how thebrain might cope with this inherent source of error by taking advantage of twoubiquitous mechanisms, redundancy and synchronization. In particular weconsider a neural process whose goal is to learn a decision function byimplementing a nonlinear gradient dynamics. The dynamics, however, are assumedto be corrupted by perturbations modeling the error which might be incurred dueto limitations of the biology, intrinsic neuronal noise, and imperfectmeasurements. We show that error, and the associated uncertainty surrounding alearned solution, can be controlled in large part by trading offsynchronization strength among multiple redundant neural systems against thenoise amplitude. The impact of the coupling between such redundant systems isquantified by the spectrum of the network Laplacian, and we discuss the role ofnetwork topology in synchronization and in reducing the effect of noise. Arange of situations in which the mechanisms we model arise in brain science arediscussed, and we draw attention to experimental evidence suggesting thatcortical circuits capable of implementing the computations of interest here canbe found on several scales. Finally, simulations comparing theoretical boundsto the relevant empirical quantities show that the theoretical estimates wederive can be tight.

Synchronization and Redundancy: Implications for Robustness of Neural Learning and Decision Making