Abstract

It is widely believed that learning is due, at least in part, to long-lasting modifications of the strengths of synapses in the brain. Theoretical studies have shown that a family of synaptic plasticity rules, in which synaptic changes are driven by covariance, is particularly useful for many forms of learning, including associative memory, gradient estimation, and operant conditioning. Covariance-based plasticity is inherently sensitive. Even a slight mistuning of the parameters of a covariance-based plasticity rule is likely to result in substantial changes in synaptic efficacies. Therefore, the biological relevance of covariance-based plasticity models is questionable. Here, we study the effects of mistuning parameters of the plasticity rule in a decision making model in which synaptic plasticity is driven by the covariance of reward and neural activity. An exact covariance plasticity rule yields Herrnstein's matching law. We show that although the effect of slight mistuning of the plasticity rule on the synaptic efficacies is large, the behavioral effect is small. Thus, matching behavior is robust to mistuning of the parameters of the covariance-based plasticity rule. Furthermore, the mistuned covariance rule results in undermatching, which is consistent with experimentally observed behavior. These results substantiate the hypothesis that approximate covariance-based synaptic plasticity underlies operant conditioning. However, we show that the mistuning of the mean subtraction makes behavior sensitive to the mistuning of the properties of the decision making network. Thus, there is a tradeoff between the robustness of matching behavior to changes in the plasticity rule and its robustness to changes in the properties of the decision making network.

Highlights

  • Synaptic plasticity that is driven by covariance is the basis of numerous models in computational neuroscience

  • We study the effect of incomplete mean subtraction in a model of operant conditioning, which is based on synaptic plasticity that is driven by the covariance of reward and neural activity

  • We showed that an approximate phenomenological law of behavior called ‘‘the matching law’’ naturally emerges if synapses change according to the covariance rule

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Summary

Introduction

Synaptic plasticity that is driven by covariance is the basis of numerous models in computational neuroscience. Covariance-based plasticity arises when synaptic changes are driven by the product of two stochastic variables, provided that the mean of one or both of these variables is subtracted such that they are measured relative to their mean value. In order for a synapse to implement covariance-based plasticity, it must estimate and subtract the mean of a stochastic variable. If mean subtraction is incomplete, the synapse is expected to potentiate constantly Over time, this potentiation could accumulate and drive the synapse to saturation values that differ considerably from those predicted by the ideal covariance rule (see below). Even if neurobiological systems implement approximate covariance-based plasticity, the relevance of the idealized covariance models to the actual behavior is not clear

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