title: What does scalar timing tell us about neural dynamics?
abstract: The "Scalar Timing Law," which is a temporal domain generalization of the well known Weber Law, states that the errors 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 match the predictions of our model, though our initial formulation results in a slight bias toward overestimation that can be corrected using a simple iterative approach to learn a decision threshold.
authors.affiliation: Deptartment of Neurobiology and Anatomy, University of Texas Medical School at Houston Houston, TX, USA.
authors.forename: Harel Z
authors.initials: HZ
authors.lastname: Shouval
authors.affiliation: Department of Neuroscience, Johns Hopkins University Baltimore, MD, USA.
authors.forename: Marshall G
authors.initials: MG
authors.lastname: Hussain Shuler
authors.affiliation: Deptartment of Neurobiology and Anatomy, University of Texas Medical School at Houston Houston, TX, USA ; Department of Biomedical Engineering, The University of Texas at Austin Austin, TX, USA.
authors.forename: Animesh
authors.initials: A
authors.lastname: Agarwal
authors.affiliation: Department of Brain and Cognitive Sciences, The Picower Institute of Learning and Memory, Massachusetts Institute of Technology Cambridge, MA, USA.
authors.forename: Jeffrey P
authors.initials: JP
authors.lastname: Gavornik
keywords: Weber's law; neural dynamics; scalar timing; temporal coding; temporal intervals