Does memory noise follow Weber’s Law? An investigation in one temporal binding dataset

Temporal Binding (TB) is standardly regarded as an implicit measure of the sense of agency (Haggard, 2017) though an underlying mechanism has not been agreed upon (Hoerl et al., 2020). Here we propose a memory process as an explanation for the observed effect in two publicly available datasets (Weller et al., 2020). The dataset consisted of two experiments that manipulated ‘action type’ and length of timing intervals. Replotting the data, we found a classic memory pattern (regression to the mean) in both experiments. We simulated the behavioral patterns using a simple Bayesian model of memory (Hemmer & Steyvers, 2009), which assumes memory to be a combination of episodic and semantic memory. The model provided a good qualitative fit in all but one experimental condition. Adjusting the prior mean for the ‘action’ condition resulted in an improved fit. Next, we evaluated whether systematic variation in memory noise values follow Weber’s law. We hypothesized that increased perceptual noise at longer time intervals also influences memory noise and would be observed as a non-linear regression pattern (Huttenlocher et al., 2000), as observed in this dataset. We calculated an overall Weber fraction constant (K) and scaled memory noise by K. The simulation remained ‘too linear’ compared to participant responses. We tested various values a memory noise – scaled by K. Finally, we calculate a K per timing interval and use these values to scale the memory noise at each interval. While the memory model provided a good fit to the empirical data, the qualitative fits varied across simulations, indicating that the underlying mechanism might be more complex. We discuss the results in the context of Weber’s law and TB. Our findings suggest the TB effect may arise, at least in part, from cognitive processes other than experienced agency.