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 assumptions, 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 assumes a fixed-rate clock-pulse generator and encodes durations by storing average pulse counts; unlike Treisman’s model, SET’s decision process 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 ‘Poisson timing’ issue, 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 assumption not shared by SET. Second, we develop a contrasting PA model, an extension of Killeen and Fetterman’s Behavioral Theory of Timing that accumulates Poisson pulses up to a fixed criterion level, with pulse rates adapting to time different intervals. Like Treisman’s model, this time-adaptive, opponent Poisson, drift–diffusion model accounts for timescale invariance without first assuming 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.

Single trial beta oscillations index time estimation

“…Alternatively, instead of describing time production as a release from a state of inhibition over time, one might also consider that the beta power indexes parameters of an evidence accumulation process that is underlying interval timing (e.g., Balci and Simen, 2014;Luzardo et al, 2011;Simen et al, 2013;Van Rijn et al, 2011). According to accumulation-to-bound models, a decision is reached by accrual of sensory evidence over time.…”

Optimal response rates in humans and rats.

“…This is in line with the recent push to bring the drift-diffusion model of perceptual decision making into the timing domain (Patrick Simen, Balci, de Souza, Cohen, & Holmes, 2011; see also Brunton, Botvinick, & Brody, 2013 for a different model in a related context). Here, the decision to respond is based on accumulating evidence toward a single response threshold (similar to the way SET is conceptualized; Gibbon, Church, & Meck, 1984) where the accumulation rate is related to the target interval (similar to the way BET is conceptualized; Killeen & Fetterman, 1988; P Simen et al, 2013). The drift-diffusion model predicts inverse Gaussian response times (Luce, 1986).…”

Interval timing under a behavioral microscope: Dissociating motivational and timing processes in fixed-interval performance

“…For instance, the behavioral theory of timing suggests that transitions between behavioral states constitute pulses (Killeen & Fetterman, 1988;Machado 1997), whereas the multiple timescales theory of timing suggests that the clock is a form of memory decay (Staddon, 2005;Staddon, Chelaru, & Higa, 2002;Staddon & Higa, 1999). More recently, theorists have attempted to ground this basic mechanism into biologically plausible neural networks (Karmarkar & Buonomano, 2007;Oprisan & Buhusi, 2011) and in drift diffusion models that appear to approximate neuronal dynamics (Simen, Balci, Desouza, Cohen, & Holmes, 2011;Simen, Rivest, Ludvig, Balcı, & Killeen, 2013). The challenge for these theories is to account for a variety of classic properties of interval timing.…”