Timescale invariance in the pacemaker-accumulator family of timing models

Abstract

Pacemaker-accumulator (PA) systems have been the most popular kind of timing model in the half-century since their introduction by Treisman (1963). Many alternative timing models have been designed predicated on different abumptions, though the dominant PA model during this period-Gibbon and Church's Scalar Expectancy Theory (SET)-invokes most of them. As in Treisman, SET's implementation abumes a fixed-rate clock-pulse generator and encodes durations by storing average pulse counts; unlike Treisman's model, SET's decision proceb invokes Weber's law of magnitude-comparison to account for timescale-invariant temporal precision in animal behavior. This is one way to deal with the 'Poibon timing' ibue, in which relative temporal precision increases for longer durations, contrafactually, in a simplified version of Treisman's model. First, we review the fact that this problem does not afflict Treisman's model itself due to a key abumption not shared by SET. Second, we develop a contrasting PA model, an extension of Killeen and Fetterman's Behavioral Theory of Timing that accumulates Poibon pulses up to a fixed criterion level, with pulse rates adapting to time different intervals. Like Treisman's model, this time-adaptive, opponent Poibon, drift-diffusion model accounts for timescale invariance without first abuming Weber's law. It also makes new predictions about response times and learning speed and connects interval timing to the popular drift-diffusion model of perceptual decision making. With at least three different routes to timescale invariance, the PA model family can provide a more compelling account of timed behavior than may be generally appreciated.