Neurobiological Models of Two-Choice Decision Making Can Be Reduced to a One-Dimensional Nonlinear Diffusion Equation

The response behaviors in many two-alternative choice tasks are well described by so-called sequential sampling models. In these models, the evidence for each one of the two alternatives accumulates over time until it reaches a threshold, at which point a response is made. At the neurophysiological level, single neuron data recorded while monkeys are engaged in two-alternative choice tasks are well described by winner-take-all network models in which the two choices are represented in the firing rates of separate populations of neurons. Here, we show that such nonlinear network models can generally be reduced to a one-dimensional nonlinear diffusion equation, which bears functional resemblance to standard sequential sampling models of behavior. This reduction gives the functional dependence of performance and reaction-times on external inputs in the original system, irrespective of the system details. What is more, the nonlinear diffusion equation can provide excellent fits to behavioral data from two-choice decision making tasks by varying these external inputs. This suggests that changes in behavior under various experimental conditions, e.g. changes in stimulus coherence or response deadline, are driven by internal modulation of afferent inputs to putative decision making circuits in the brain. For certain model systems one can analytically derive the nonlinear diffusion equation, thereby mapping the original system parameters onto the diffusion equation coefficients. Here, we illustrate this with three model systems including coupled rate equations and a network of spiking neurons.Author Summary: The brain holds a central position in scientific theories of rational behavior. For example, brain activity is thought to stand in a causal relation to the decision making behavior observed in two-choice perceptual discrimination tasks. Although a lot is known about both the brain activity and the response behavior during these tasks, the relationships between the two are not fully understood. In particular, how can one relate the high-dimensional dynamic activity of the brain to the low-dimensional descriptions of response behavior such as performance and reaction-times? Our approach to this question is to relate existing neurobiological models of brain activity to existing models of response behavior. In this paper we establish a formal link between standard, winner-take-all models of brain activity during two-choice tasks and a family of one-dimensional behavioral models known as diffusion models. Our analysis demonstrates a universal functional dependence between the external inputs to the neural populations in the neurobiological model on the one hand, and reaction times and performance in the one-dimensional model on the other. Importantly, we show that experimentally measured performance and reaction-times can be predicted through changes in these external inputs alone.