The Leaky Integrating Threshold and its impact on evidence accumulation models of choice response time (RT).

Abstract

A common assumption in choice response time modelling is that after evidence accumulation reaches a certain decision threshold, the choice is categorically communicated to the motor system that then executes the response. However, neurophysiological findings suggest that motor preparation partly overlaps with evidence accumulation, and is not independent from stimulus difficulty level. We propose to model this entanglement by changing the nature of the decision criterion from a simple threshold to an actual process. More specifically, we propose a secondary, motor preparation related, leaky accumulation process that takes the accumulated evidence of the original decision process as a continuous input, and triggers the actual response when it reaches its own threshold. We analytically develop this Leaky Integrating Threshold (LIT), applying it to a simple constant drift diffusion model, and show how its parameters can be estimated with the D*M method. Reanalyzing three different datasets, the LIT extension is shown to outperform a standard drift diffusion model using multiple statistical approaches. Further, the LIT leak parameter is shown to be better at explaining the speed/accuracy trade-off manipulation than the commonly used boundary separation parameter. These improvements can also be verified using traditional diffusion model analyses, for which the LIT predicts the violation of several common selective parameter influence assumptions. These predictions are consistent with what is found in the data and with what is reported experimentally in the literature. Crucially, this work offers a new benchmark against which to compare neural data to offer neurobiological validation for the proposed processes.

Sensorimotor decisions rely on the entanglement of evidence and motor accumulation processes

“…For this analysis, Speed and Accuracy data are fitted completely independently, resulting in different parameters for each instruction. In line with Verdonck et al 27 , we found that both leak ( p < 10 −17 ) and boundary separation ( p < 10 −8 ) were significantly different between Speed and Accuracy conditions, while relative starting position zr ( p = 0.32) and drift speeds v i =1…4 ( p = 0.55, p = 0.08, p = 0.29, p = 0.20) were indistinguishable.…”

“…For this analysis, Speed and Accuracy data are fitted completely independently, resulting in different parameter values for each instruction. In line with Verdonck et al (2021), we found that inverse leak λ −1 and boundary separation a were significantly smaller in the Speed than in the Accuracy condition looking at their intra-individual differences (∆λ −1 = −0.19 [−0.22, −0.15], ∆a = −0.089 [−0.12, −0.061]). In addition, the relative starting position zr and drift speeds v i=1..…”

“…Next, we define motor-lag as the time between the zero-crossing of the evidence accumulation-RT correlation curve and the actual response, since we expect the motor accumulation signal to reach zero correlation with RT very close to the response itself (this is implied by a fixed threshold, where the signal values of all trials are equal). If we assume the inverse leak parameter λ −1 in the LIT is largely responsible for SAT control (as shown in Verdonck et al (2021) and replicated here -the inverse leak is larger for accuracy than speed in 42 out of 43 participants), then the LIT makes a very specific prediction: the motor-lag for Speed should be markedly smaller than the one for Accuracy (Figure 3c). We indeed see this pattern emerge in our population EEG data (Fig.…”

“…In Verdonck et al (2021), we break with this tradition and propose to broadcast the accumulated evidence into a secondary, leaky motor accumulator and assume that the stopping criterion applies only for this secondary stage of the decision making process. In other words, there is no longer a binary choice stemming from the initial evidence accumulation which then triggers a motor response but rather from a secondary motor accumulation process that simultaneously accumulates to its own threshold by taking the evidence emerging from the first process as input.…”

An integrated theory of deciding and acting.

“…It simply assumes a gate (EMG threshold) at the M1 level above which accumulated evidence is transmitted to the muscle. Verdonck et al (2020) recently proposed a leaky integrated threshold architecture (LIT) that models the flow of information from perceptual evidence accumulation to the motor structures that prepare the response, such as M1. Specifically, LIT models perceptual evidence accumulation with a standard DDM, and assumes that motor preparation builds upon a leaky accumulation process that takes the accumulated evidence of the perceptual process as a continuous input.…”