Neural drift-diffusion models bridge the gap between abstract mathematical models of decision making and the biophysics of neural circuits. Neurophysiological recordings in monkeys performing perceptual discrimination tasks — particularly the random-dot motion task — revealed that neurons in the lateral intraparietal area (LIP) and frontal eye fields (FEF) exhibit ramping activity that resembles evidence accumulation (Shadlen & Newsome, 2001; Gold & Shadlen, 2007). This discovery motivated the development of neural circuit models that implement drift-diffusion at the level of spiking neurons and synaptic dynamics.
The Wang (2002) Model
τ · drᵦ/dt = −rᵦ + f(w₊ · rᵦ − w₋ · rₐ + Iᵦ + ξᵦ)
w₊ = recurrent self-excitation (NMDA-mediated)
w₋ = mutual inhibition (GABA-mediated)
Iₐ, Iᵦ = sensory inputs (favoring option A or B)
ξ = neural noise
Wang (2002) developed a biophysically detailed spiking neural network model of two-choice decision making. The model consists of two populations of excitatory neurons, each representing one choice alternative, coupled through inhibitory interneurons. Each excitatory population has strong recurrent self-excitation (mediated by slow NMDA receptors) and receives competitive inhibition from the other population (mediated by fast GABA receptors). Sensory input biased toward one alternative drives the corresponding population, and the decision is made when one population reaches a high firing-rate state while suppressing the other — a winner-take-all competition.
Reduction to Drift-Diffusion
A remarkable theoretical result, demonstrated by Bogacz, Brown, Moehlis, Holmes, and Cohen (2006), is that under certain parameter regimes, the two-population neural model can be mathematically reduced to the drift-diffusion model. The difference in firing rates between the two populations follows an approximate diffusion process, with the drift rate determined by the difference in sensory inputs and the noise determined by the stochastic spiking of neurons. This reduction establishes a formal link between the abstract diffusion model used in mathematical psychology and the biophysical mechanisms of neural decision circuits.
The neural implementation provides a biological interpretation of each diffusion model parameter. Drift rate corresponds to the difference in sensory input to the two neural populations, which depends on stimulus strength and the quality of sensory processing. Boundary separation corresponds to the firing-rate threshold that triggers a response, which can be modulated by baseline inhibition from structures like the subthalamic nucleus. Starting point corresponds to asymmetric pre-stimulus activity, which can be driven by prior expectations. The basal ganglia, particularly the striatum and subthalamic nucleus, have been implicated in setting and adjusting the decision threshold.
Neural drift-diffusion models have been extended to account for multi-alternative decisions, urgency signals that lower the threshold over time, confidence judgments (post-decision evidence accumulation), and changes of mind. They provide a bridge between cognitive modeling and neuroscience, allowing predictions from mathematical models to be tested at the level of single-neuron recordings, fMRI, and pharmacological manipulations. The convergence between abstract mathematical models and biophysical neural models is one of the most successful examples of cross-level explanation in cognitive science.