What does scalar timing tell us about neural dynamics

The "Scalar Timing Law", which is a temporal domain generalization of the well known Weber Law, states that the errors in estimating temporal intervals scale linearly with the durations of the intervals. Linear scaling has been studied extensively in human and animal models and holds over several orders of magnitude, though to date there is no agreed upon explanation for its physiological basis. Starting from the assumption that behavioral variability stems from neural variability, this work shows how to derive firing rate functions that are consistent with scalar timing. We show that firing rate functions with a log-power form, and a set of parameters that depend on spike count statistics, can account for scalar timing. Our derivation depends on a linear approximation, but we use simulations to validate the theory and show that log-power firing rate functions result in scalar timing over a large range of times and parameters.Simulation results also show that our theory as first posed exhibits a slight bias towards overestimation.We show that this bias can be corrected using a simple iterative approach to learn a decision threshold.