Robustness of Learning That Is Based on Covariance-Driven Synaptic Plasticity

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.Author Summary: It is widely believed that learning is due, at least in part, to modifications of synapses in the brain. The ability of a synapse to change its strength is called “synaptic plasticity,” and the rules governing these changes are a subject of intense research. Theoretical studies have shown that a particular family of synaptic plasticity rules, known as covariance rules, could underlie many forms of learning. While it is possible that a biological synapse would be able to approximately implement such abstract rules, it seems unlikely that this implementation would be exact. Covariance rules are inherently sensitive, and even a slight inaccuracy in their implementation is likely to result in substantial changes in synaptic strengths. Thus, the biological relevance of these rules remains questionable. Here we study the consequences of the mistuning of a covariance plasticity rule in the context of operant conditioning. In a previous study, we showed that an approximate phenomenological law of behavior called “the matching law” naturally emerges if synapses change according to the covariance rule. Here we show that although the effect of slight mistuning of the covariance rule on synaptic strengths is substantial, it leads to only small deviations from the matching law. Furthermore, these deviations are observed experimentally. Thus, our results support the hypothesis that covariance synaptic plasticity underlies operant conditioning.