Response times from ensembles of accumulators

Abstract

Decision-making is explained by psychologists through stochastic accumulator models and by neurophysiologists through the activity of neurons believed to instantiate these models. We investigated an overlooked scaling problem: How does a response time (RT) that can be explained by a single model accumulator arise from numerous, redundant accumulator neurons, each of which individually appears to explain the variability of RT? We explored this scaling problem by developing a unique ensemble model of RT, called e pluribus unum, which embodies the wellknown dictum "out of many, one." We used the e pluribus unum model to analyze the RTs produced by ensembles of redundant, idiosyncratic stochastic accumulators under various termination mechanisms and accumulation rate correlations in computer simulations of ensembles of varying size. We found that predicted RT distributions are largely invariant to ensemble size if the accumulators share at least modestly correlated accumulation rates and RT is not governed by the most extreme accumulators. Under these regimes the termination times of individual accumulators was predictive of ensemble RT. We also found that the threshold measured on individual accumulators, corresponding to the firing rate of neurons measured at RT, can be invariant with RT but is equivalent to the specified model threshold only when the rate correlation is very high.is a core measure of human decisionmaking in experimental psychology (1). The random variation of RT across otherwise identical trials has been a puzzle since the mid-19th century. Since the 1960s, this variation of RT-measured in a wide range of perceptual, cognitive, and economic tasks (1-5)-has been explained through stochastic accumulator models. These models assume that a response is generated when evidence accumulates at a certain rate (v) over time to a threshold (θ) and that the stochastic variation of RTs arises primarily from random fluctuations in accumulation rates (Fig. 1A). Historically, these models were formulated and tested before data on the underlying neural processes were available.Subsequently, neurons exhibiting accumulating discharge rates in various RT tasks have been found in sensory, sensorimotor, and motor brain structures; in premotor circuits for limb and eye movements it is known that the neurons with accumulating activity are necessary and sufficient for initiating movements (6, 7). Movements are initiated when the trial-averaged accumulating spike rate of these neurons reaches a fixed activation level (6) (A RT ) like a threshold, and the distribution of RTs is accounted for by the stochastic variability in the rate of growth of neural activity toward A RT (Fig. 1B). This discovery inspired the conjecture that individual neurons instantiate the evidence accumulation process described by stochastic accumulator models (6). This conjecture has stimulated extensive research replicating the original observation and equating accumulator model parameters with measures of neural dynamics assessed by spike rates (8...

Using Covert Response Activation to Test Latent Assumptions of Formal Decision-Making Models in Humans

“…However, it is unclear how EMG bounds incorporated into a single-model accumulator map onto activities of numerous accumulator neurons that encode confidence signals in the parietal cortex . The e pluribus unum model developed by Zandbelt et al (2014) sheds light on this issue. The model demonstrates that ensembles of numerous and redundant accumulator neurons can generate a RT distribution similar to that predicted by a single accumulator, provided that accumulation rates are moderately correlated and RT is not determined by the lowest and highest accumulation rates.…”

Interference effects of choice on confidence: Quantum characteristics of evidence accumulation

“…This result, along with quantitatively superior model fits, lends strong support to the modeling of choice and confidence as a quantum random walk process, a model which describes decisionmaking as a constructive process wherein a definite state is created from an indefinite superposition. In addition to the cognitive implications, a QRW model of evidence accumulation potentially sidesteps the problem of how a group of neurons can produce observed behavior that is consistent with a single evidence accumulation trajectory (26). The QRW suggests that the mismatch might lie in the cognitive representation of evidence accumulation: instead of treating evidence accumulation as a single trajectory, it may be more accurate to conceptualize it as a wavelike superposition state.…”

Diffusion Decision Model: Current Issues and History

“…Recent studies have examined models for multi-alternative decision making that use diffusion processes [24,41,72,79-80,182-190] and a number of algorithms have been used: Independent racing accumulators with termination when one reaches its decision criterion.Independent racing accumulators with a relative stopping rule (termination occurs when one accumulator beats the maximum of the others by some amount).Accumulators with dependence between accumulators: inhibition between accumulators that depends on the amount of accumulated evidence.Accumulators with dependence: evidence for one alternative is evidence against the others so that the total evidence is constant. When one accumulator is incremented, the others are decremented (termed constant summed evidence or feedforward inhibition).…”