We show that simple assumptions about neural processing lead to a model of interval timing as a temporal integration process, in which a noisy firing-rate representation of time rises linearly on average toward a response threshold over the course of an interval. Our assumptions include: that neural spike trains are approximately independent Poisson processes; that correlations among them can be largely cancelled by balancing excitation and inhibition; that neural populations can act as integrators; and that the objective of timed behavior is maximal accuracy and minimal variance. The model accounts for a variety of physiological and behavioral findings in rodents, monkeys and humans, including ramping firing rates between the onset of reward-predicting cues and the receipt of delayed rewards, and universally scale-invariant response time distributions in interval timing tasks. It furthermore makes specific, well-supported predictions about the skewness of these distributions, a feature of timing data that is usually ignored. The model also incorporates a rapid (potentially one-shot) duration-learning procedure. Human behavioral data support the learning rule’s predictions regarding learning speed in sequences of timed responses. These results suggest that simple, integration-based models should play as prominent a role in interval timing theory as they do in theories of perceptual decision making, and that a common neural mechanism may underlie both types of behavior.

The drift-diffusion model (DDM) describes decision making in simple, two-alternative forced choice (2AFC) tasks. It accurately fits response-time distributions and implements an optimal decision procedure for stationary 2AFC tasks: for a given accuracy, no other model achieves faster average response times. The value of a decision threshold applied to accumulated information also determines a speed-accuracy tradeoff (SAT) for the DDM, thereby accounting for a ubiquitous feature of human performance in speeded response tasks. However, little is known about how participants settle on particular tradeoffs. One possibility is that they select SATs that maximize the rate of earned rewards. For the DDM, there exist unique, reward-rate-maximizing values for its threshold and starting point parameters in free response tasks that reward correct responses (Bogacz et al, 2006). These optimal values vary as a function of response-stimulus interval, prior stimulus probability and relative reward magnitude for correct responses. We tested the resulting quantitative predictions regarding response time, accuracy and response bias under these task manipulations and found that grouped data conformed well to the predictions of an optimally parameterized DDM.When an organism extracts signals out of noisy inputs from the environment, it faces a fundamental tradeoff: should it spend more time observing a stimulus to increase certainty about its identity and the appropriate response to it, or should it act more quickly at the cost of greater inaccuracy? Such a tradeoff between speed and accuracy has long been recognized as a ubiquitous feature of human behavior in speeded response tasks (Fitts, 1966;Garrett, 1922;Pachella & Pew, 1968;Schouten & Bekker, 1967;Wickelgren, 1977). Yet the factors that lead to a particular tradeoff are still not well understood.Clues about the nature of speed-accuracy tradeoff (SAT) selection have emerged from theoretical and behavioral research on decision making in simple, two-alternative forced choice (2AFC) tasks, which require participants to choose one or the other alternative on every trial (e.g., Audley & Pike, 1965;Busemeyer & Townsend, 1993;LaBerge, 1962;Laming, 1968;Link, 1975;Link & Heath, 1975;Ratcliff, 1978;Smith & Vickers, 1989;Stone, 1960;Usher & McClelland, 2001;Vickers, 1970). Other clues come from physiological research on the neural mechanisms that may underlie this type of decision making (e.g., Carpenter & Williams, 1995;Gold & Shadlen, 2002;Hanes & Schall, 1996;Ratcliff, Cherian, & Segraves, 2003;Roitman & Shadlen, 2002;Schall, 2001;Shadlen & Newsome, 2001;. In particular, a large body of evidence (e.g., Palmer, Huk, & Shadlen, 2005;Ratcliff & Rouder, 2000;Ratcliff, Thapar, Gomez, & McKoon, 2004;Voss, Rothermund, & Voss, 2004) now strongly suggests that decision making in 2AFC tasks can be accurately described by the drift-diffusion model (DDM) (Ratcliff, 1978), for which the SAT can be controlled by adjusting a single parameter (the decision threshold parameter, described bel...

Speed-accuracy tradeoffs strongly influence the rate of reward that can be earned in many decision-making tasks. Previous reports suggest that human participants often adopt suboptimal speed-accuracy tradeoffs in single session, two-alternative forced-choice tasks. We investigated whether humans acquired optimal speed-accuracy tradeoffs when extensively trained with multiple signal qualities. When performance was characterized in terms of decision time and accuracy, our participants eventually performed nearly optimally in the case of higher signal qualities. Rather than adopting decision criteria that were individually optimal for each signal quality, participants adopted a single threshold that was nearly optimal for most signal qualities. However, setting a single threshold for different coherence conditions resulted in only negligible decrements in the maximum possible reward rate. Finally, we tested two hypotheses regarding the possible sources of suboptimal performance: a) favoring accuracy over reward rate and b) misestimating the reward rate due to timing uncertainty. Our findings provide support for both hypotheses, but also for the hypothesis that participants can learn to approach optimality. We find specifically that an accuracy bias dominates early performance, but diminishes greatly with practice. The residual discrepancy between optimal and observed performance can be explained by an adaptive response to uncertainty in time estimation.

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Optimal performance in two-alternative, free response decision-making tasks can be achieved by the drift-diffusion model of decision making--which can be implemented in a neural network--as long as the threshold parameter of that model can be adapted to different task conditions. Evidence exists that people seek to maximize reward in such tasks by modulating response thresholds. However, few models have been proposed for threshold adaptation, and none have been implemented using neurally plausible mechanisms. Here we propose a neural network that adapts thresholds in order to maximize reward rate. The model makes predictions regarding optimal performance and provides a benchmark against which actual performance can be compared, as well as testable predictions about the way in which reward rate may be encoded by neural mechanisms.