Drift\u2013diffusion models for multiple-alternative forced-choice decision making

Alex Roxin

doi:10.1186/s13408-019-0073-4

Abstract

The canonical computational model for the cognitive process underlying two-alternative forced-choice decision making is the so-called drift–diffusion model (DDM). In this model, a decision variable keeps track of the integrated difference in sensory evidence for two competing alternatives. Here I extend the notion of a drift–diffusion process to multiple alternatives. The competition between n alternatives takes place in a linear subspace of n-1 dimensions; that is, there are n-1 decision variables, which are coupled through correlated noise sources. I derive the multiple-alternative DDM starting from a system of coupled, linear firing rate equations. I also show that a Bayesian sequential probability ratio test for multiple alternatives is, in fact, equivalent to these same linear DDMs, but with time-varying thresholds. If the original neuronal system is nonlinear, one can once again derive a model describing a lower-dimensional diffusion process. The dynamics of the nonlinear DDM can be recast as the motion of a particle on a potential, the general form of which is given analytically for an arbitrary number of alternatives.

Highlights

Perceptual decision-making tasks require a subject to make a categorical decision based on noisy or ambiguous sensory evidence
To leading order there is no dependence on the mean input, indicating that the dynamics is dominated by the behavior right at the bifurcation.a The upshot is that Eq (40) is as similar to the corresponding linear drift–diffusion model (DDM) with absorbing boundaries as possible for a nonlinear system without fine tuning
6 Discussion In this paper I have illustrated how to derive drift–diffusion models starting from models of neuronal competition for n-alternative decision-making tasks

Summary

Introduction

Perceptual decision-making tasks require a subject to make a categorical decision based on noisy or ambiguous sensory evidence. When faced with two possible alternatives, accumulating the difference in evidence for the two alternatives until a fixed threshold is reached is an optimal strategy, in that it minimizes the mean reaction time for a desired level of performance This is the computation carried out by the sequential probability ratio test devised by Wald [1], and its continuous-time variant, the drift–diffusion model (DDM) [2]. Previous work has shown that attractor network models for twoalternative DM operate in the vicinity of pitchfork bifurcation, which is what underlies the winner-take-all competition leading to the decision dynamics [17] In this regime the neuronal dynamics is well described by a stochastic normal-form equation which right at the bifurcation is precisely equivalent to the DDM with an additional cubic nonlinearity. The dynamics of such a nonlinear DDM can be recast as the diffusion of particle on a potential, which is obtained analytically, for arbitrary n

Results

Derivation of DDMs for n-alternative DM

Discussion