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How a biological decision network can implement a statistically optimal test

Neurophysiological evidence due to Schall, Newsome and others indicates that decision processes in certain cortical areas (e.g. FEF and LIP) involve the integration of noisy evidence. Within this paradigm, we ask which neuronal architectures and parameter values would allow an animal to make the fastest and most accurate decisions. Since evolutionary pressure promotes such optimality (e.g. in prey capture and predator avoidance), it is plausible that biological decision networks realise or approximate optimal performance. We consider a simple decision model proposed by Usher & McClelland consisting of two populations of neurons integrating evidence in support of two alternatives, and we analyze the dynamics of this model. We show that in order to implement the optimal decision algorithm (sequential probability ratio test) the linearised network must satisfy the following two constraints: (i) it must accumulate the difference between evidence in support of each alternative, as would be implemented by mutual inhibition between the populations; and (ii) the strength of mutual inhibition must be equal to the leak of activity from each population.