Network structure and input integration in competing firing rate models for decision-making

Making a decision among numerous alternatives is a pervasive and central undertaking encountered by mammals in natural settings. While decision making for two-option tasks has been studied extensively both experimentally and theoretically, characterizing decision making in the face of a large set of alternatives remains challenging. We explore this issue by formulating a scalable mechanistic network model for decision making and analyzing the dynamics evoked given various potential network structures. In the case of a fully-connected network, we provide an analytical characterization of the model fixed points and their stability with respect to winner-take-all behavior for fair tasks. We compare several means of input integration, demonstrating a more gradual sigmoidal transfer function is likely evolutionarily advantageous relative to binary gain commonly utilized in engineered systems. We show via asymptotic analysis and numerical simulation that sigmoidal transfer functions with smaller steepness yield faster response times but depreciation in accuracy. However, in the presence of noise or degradation of connections, a sigmoidal transfer function garners significantly more robust and accurate decision-making dynamics. For fair tasks and sigmoidal gain, our model network also exhibits a stable parameter regime that produces high accuracy and persists across tasks with diverse numbers of alternatives and difficulties, satisfying physiological energetic constraints. In the case of more sparse and structured network topologies, including random, regular, and small-world connectivity, we show the high-accuracy parameter regime persists for biologically realistic connection densities. Our work shows how neural system architecture is potentially optimal in making economic, reliable, and advantageous decisions across tasks.