Patrick Simen

Extracting temporal regularities and relations from experience/observation is critical for organisms’ adaptiveness (communication, foraging, predation, prediction) in their ecological niches. Therefore, it is not surprising that the internal clock that enables the perception of seconds-to-minutes-long intervals (interval timing) is evolutionarily well-preserved across many species of animals. This comparative claim is primarily supported by the fact that the timing behavior of many vertebrates exhibits common statistical signatures (e.g., on-average accuracy, scalar variability, positive skew). These ubiquitous statistical features of timing behaviors serve as empirical benchmarks for modelers in their efforts to unravel the processing dynamics of the internal clock (namely answering how internal clock “ticks”). In this chapter, we introduce prominent (neuro)computational approaches to modeling interval timing at a level that can be understood by general audience. These models include Treisman’s pacemaker accumulator model, the information processing variant of scalar expectancy theory, the striatal beat frequency model, behavioral expectancy theory, the learning to time model, the time-adaptive opponent Poisson drift-diffusion model, time cell models, and neural trajectory models. Crucially, we discuss these models within an overarching conceptual framework that categorizes different models as threshold vs. clock-adaptive models and as dedicated clock/ramping vs. emergent time/population code models.

Increased dopamine may cause our internal clock to slow down, creating a sense of speeding time

Most psychological models of perceptual decision making are of the accumulation-to-threshold variety. The neural basis of accumulation in parietal and prefrontal cortex is therefore a topic of great interest in neuroscience. In contrast, threshold mechanisms have received less attention, and their neural basis has usually been sought in subcortical structures. Here I analyze a model of a decision threshold that can be implemented in the same cortical areas as evidence accumulators, and whose behavior bears on two open questions in decision neuroscience: (1) When ramping activity is observed in a brain region during decision making, does it reflect evidence accumulation? (2) Are changes in speed-accuracy tradeoffs and response biases more likely to be achieved by changes in thresholds, or in accumulation rates and starting points? The analysis suggests that task-modulated ramping activity, by itself, is weak evidence that a brain area mediates evidence accumulation as opposed to threshold readout; and that signs of modulated accumulation are as likely to indicate threshold adaptation as adaptation of starting points and accumulation rates. These conclusions imply that how thresholds are modeled can dramatically impact accumulator-based interpretations of this data.

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 rule9s 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.

Time is an essential feature of most decisions, because the reward earned from decisions frequently depends on the temporal statistics of the environment (e.g., on whether decisions must be made under deadlines). Accordingly, evolution appears to have favored a mechanism that predicts intervals in the seconds to minutes range with high accuracy on average, but significant variability from trial to trial. Importantly, the subjective sense of time that results is sufficiently imprecise that maximizing rewards in decision-making can require substantial behavioral adjustments (e.g., accumulating less evidence for a decision in order to beat a deadline). Reward maximization in many daily decisions therefore requires optimal temporal risk assessment. Here, we review the temporal decision-making literature, conduct secondary analyses of relevant published datasets, and analyze the results of a new experiment. The paper is organized in three parts. In the first part, we review literature and analyze existing data suggesting that animals take account of their inherent behavioral variability (their “endogenous timing uncertainty”) in temporal decision-making. In the second part, we review literature that quantitatively demonstrates nearly optimal temporal risk assessment with sub-second and supra-second intervals using perceptual tasks (with humans and mice) and motor timing tasks (with humans). We supplement this section with original research that tested human and rat performance on a task that requires finding the optimal balance between two time-dependent quantities for reward maximization. This optimal balance in turn depends on the level of timing uncertainty. Corroborating the reviewed literature, humans and rats exhibited nearly optimal temporal risk assessment in this task. In the third section, we discuss the role of timing uncertainty in reward maximization in two-choice perceptual decision-making tasks and review literature that implicates timing uncertainty as an important factor in performance quality. Together, these studies strongly support the hypothesis that animals take normative account of their endogenous timing uncertainty. By incorporating the psychophysics of interval timing into the study of reward maximization, our approach bridges empirical and theoretical gaps between the interval timing and decision-making literatures.