Modeling a Simple Choice Task: Stochastic Dynamics of Mutually Inhibitory Neural Groups

Abstract

We describe the dynamical and bifurcational behavior of two mutually inhibitory, leaky, neural units subject to external stimulus, random noise, and "priming biases". The model describes a simple forced choice experiment and accounts for varying levels of expectation and control. By projecting the model's dynamics onto slow manifolds, using judicious linear approximations, and solving for one-dimensional (reduced) probability densities, analytical estimates are developed for reaction time distributions and shown to compare satisfactorily with "full" numerical data. A sensitivity analysis is performed and the effects of parameters assessed. The predictions are also compared with behavioral data. These results may help correlate low-dimensional models of stochastic neural networks with cognitive test data, and hence assist in parameter choices and model building.

A Recurrent Network Mechanism of Time Integration in Perceptual Decisions

“…Thus, our model in regime II can perform decision computation ( Fig. 13 A, C) without working memory function, similar to previously studied connectionists models (Brown and Holmes, 2001;Usher and McClelland, 2001). Furthermore, we found that, for the whole range of 0 , the unstable time constant of the saddle point is of a few seconds, an order of magnitude greater than the stable time constant (Fig.…”

“…Such a reduction represents a significant step in bridging the gap between the biologically based model of Wang (2002) and abstract mathematical models, and allow for a comparison between our model and previously proposed models of decision making. Like other models (Usher and Cohen, 1999;Brown and Holmes, 2001;Usher and McClelland, 2001;Machens et al, 2005), our model is a nonlinear dynamical system that can be conceptualized as a circuit of neural populations coupled effectively by mutual inhibition. However, it is important to emphasize that recurrent excitation plays an indispensible role in producing reverberatory dynamics underlying winner-take-all competition in our model.…”

“…13B). Thus, qualitatively, the network dynamics may be approximated by a picture in which the system initially collapses onto the unstable manifold, followed by a one-dimensional diffusion-like dynamics for the difference S 1 Ϫ S 2 (Brown and Holmes, 2001). However, quantitatively, the dynamics along the stable manifold is still slow (a few hundreds of milliseconds) (Fig.…”

“…First, the system can be approximately described by a single dynamical variable, the firing rate difference between the two neural populations. Second, the time constant for this dynamical variable is arbitrarily long, which typically requires fine-tuning of parameters (Brown and Holmes, 2001;Usher and McClelland, 2001). Our biophysically based spiking neuron network model provides an opportunity to assess whether, or how, these conditions can be satisfied in a realistic cortical circuit.…”

“…The diffusion model fits well to many psychophysical data, is mathematically tractable for analysis, and thus has been a benchmark for other models. Furthermore, it has been shown that the diffusion model can be approximately realized by "connectionist models," which may include a leak term; time integration becomes nearly perfect when fine-tuning of parameters cancels out the leakage by network recurrent dynamics (Brown and Holmes, 2001;Usher and McClelland, 2001;Bogacz et al, 2003).…”