The Anticipation of Events in Time

Abstract

Humans use sensory input to anticipate events. The brain's capacity to predict cues in time is commonly assumed to be modulated by two uncertainty parameters, the hazard rate (HR) of event probability and the uncertainty in time estimation, which increases with elapsed time.We investigate both assumptions by manipulating event probability density functions (PDF) in three sensory modalities. First we show, contrary to expectation, that perceptual systems use the reciprocal PDF -and not the HR -to model event probability density. Next we demonstrate that temporal uncertainty does not necessarily grow with elapsed time but also diminishes, depending on the event PDF. Finally we show that reaction time (RT) distributions comprise modality-specific and modality-independent components, the latter likely reflecting similarity in processing of probability density across sensory modalities. The results are consistent across vision, audition, and somatosensation, indicating that probability density is more fundamental than hazard rate in terms of the neural operations determining event anticipation and temporal uncertainty. Previous research identified neuronal activitity related to event probability in multiple levels of the cortical hierarchy such as early and higher sensory (V1, V4), association (LIP), motor and other areas. This work proposed that the elementary neuronal computation in estimation of probability across time is the HR. In contrast, our results suggest that the neurobiological implementation of probability estimation is based on a different, much simpler and more stable computation than HR: the reciprocal PDF of events in time.

Two sources of uncertainty independently modulate temporal expectancy

“…S8). This confirms the recent finding that the reciprocal PDF is superior to the HR as a model of RT in anticipation (27) and extends this result to different levels of P O and the uniform distribution of events in time.…”

“…Regarding the effect of γ E , the recently proposed PDF-based model (27) hypothesizes that RT is reciprocally related to the PDF of events, γ E , and that the uncertainty in elapsed time estimation is largely modulated by event probability (probabilistic blurring, SI Appendix, Supplemental Methods). This probabilistic blurring uses a Gaussian kernel whose σ scales inversely with γ E but not with elapsed time itself as suggested by the scalar variability of time estimation (33), which we here refer to as temporal blurring.…”

“…A sharp increase in the HR h(t) at time t suggests the event is imminent. The widely adopted hypothesis that HR drives anticipation was recently challenged, and it was demonstrated that RTs are better captured by the reciprocal of event probability density in the context of a single, fixed P O (27). Here, both hypotheses (Fig.…”

Sequential Temporal Anticipation Characterized by Neural Power Modulation and in Recurrent Neural Networks

“…An alternative interpretation, probably a more intriguing one, for Corrected cluster 234 marking the temporal locations of the target tone (Fig. 2&3) is that this neural signature may represent the probability distribution of event occurrence in time (Grabenhorst et al 2019(Grabenhorst et al , 2021Janssen and Shadlen 2005) (Fig. 1B).…”

“…The white noise piece serves as a global temporal context that constrains the temporal locations of the target tone; the tone locations must be determined by referencing to the noise onset or the passage of the noise period. Previous studies have indirectly studied the temporal anticipation by measuring its effects on behavioral and neural responses to sensory events (Grabenhorst et al 2019;Tavano, Schröger, and Kotz 2019) and by using an encoding framework (Herbst, Fiedler, and Obleser 2018), but we, here, examine directly how the brain carries out the sequential temporal anticipation internally in flat white noise.…”