Continuous carryover of temporal context dissociates response bias from perceptual influence for duration

Abstract

Recent experimental evidence suggests that the perception of temporal intervals is influenced by the temporal context in which they are presented. A longstanding example is the time-order-error, wherein the perception of two intervals relative to one another is influenced by the order in which they are presented. Here, we test whether the perception of temporal intervals in an absolute judgment task is influenced by the preceding temporal context. Human subjects participated in a temporal bisection task with no anchor durations (partition method). Intervals were demarcated by a Gaussian blob (visual condition) or burst of white noise (auditory condition) that persisted for one of seven logarithmically spaced sub-second intervals. Crucially, the order in which stimuli were presented was first-order counterbalanced, allowing us to measure the carryover effect of every successive combination of intervals. The results demonstrated a number of distinct findings. First, the perception of each interval was biased by the prior response, such that each interval was judged similarly to the preceding trial. Second, the perception of each interval was also influenced by the prior interval, such that perceived duration shifted away from the preceding interval. Additionally, the effect of decision bias was larger for visual intervals, whereas auditory intervals engendered greater perceptual carryover. We quantified these effects by designing a biologically-inspired computational model that measures noisy representations of time against an adaptive memory prior while simultaneously accounting for uncertainty, consistent with a Bayesian heuristic. We found that our model could account for all of the effects observed in human data. Additionally, our model could only accommodate both carryover effects when uncertainty and memory were calculated separately, suggesting separate neural representations for each. These findings demonstrate that time is susceptible to similar carryover effects as other basic stimulus attributes, and that the brain rapidly adapts to temporal context.

Figure 1. Task Design (a) Participants performed a 2AFC temporal bisection task, in which they were required to categorize whether an interval belonged to “short” or “long” categories.

On a given trial, participants viewed a fixation point, followed by either a burst of white noise or a Gaussian blur, which persisted for one of seven durations. Participants were then required to respond as quickly but as accurately as possible which category the stimulus belonged to, which initiated the following trial. Separate groups participated in the auditory and visual versions of the task. (b) Temporal distance matrix for de Bruijn sequence. The stimulus set included seven logarithmically-spaced intervals between 300 and 900 ms. The presented matrix displays the distance, in ms, between every possible successive trial combination between current and prior durations. Direct effects are the influence of the present stimulus (t_i) on a response whereas carryover effects are the influence of the preceding trial stimulus (t_{i -1}). (c) Trial order determined by the path guided de Bruijn sequence was modulated by a random pairing of sinusoids, providing a perceptually stochastic sequence with relatively equal spacing of stimulus pairs throughout the entire session; red circles indicate a particular pair of trials (520–433 ms).

Figure 2. Direct effects of duration.

(a) Temporal bisection performance for two representative subjects on different modality versions of the task. The probability of categorizing each duration as Long as well as the best fitting logistic function are displayed. (b) Average chronometric functions for auditory and visual participants. Reaction time decreased as a function of duration, but dropped off faster after the BP was passed and was faster for auditory stimuli at the longest duration tested. Error bars indicate s.e. of the mean. (c) Individual participant performance for the bisection point (x-axis) and coefficient of variation (y-axis) values derived from psychometric data, as well as marginal histograms for each; there were no differences between BP values for auditory or visual participants, but significantly lower CV values for the auditory task.

Figure 3. Carryover effects of duration.

(a) Grand average psychometric curves for auditory and visual participants displaying the response for each duration on trials preceded by a response choice Long or Short. Insets display the average BP across participants for each prior choice condition; participants were more likely to classify an interval as long (or short) if the prior decision, independent of the prior interval, was classified as long (or short). Error bars indicate s.e. of the mean. Asterisks indicate significance at p<0.05. (b) Perceptual influence of the prior interval for visual and auditory participants. The far left point on each graph indicates the BP for the prior null condition; notably, the BP for the null prior condition was in the middle of the range of BPs observed for all prior duration conditions for both auditory and visual stimuli. Auditory participants exhibited a linear effect of prior interval, such that shorter prior intervals were associated with more leftward psychometric curves and smaller BPs, indicating a greater probability of categorizing stimuli as longer. No effect of prior interval was found for visual participants. (c) Response matrices displaying reaction time (RT) for every condition pairing. Slower RTs (hotter pixel colors) were found for shorter durations that were preceded by trials with longer durations. (d) RT data for each prior duration, averaged across current duration; both auditory and visual participants exhibited a strong linear effect of the prior duration.

Figure 4. Relationship between decision bias and perceptual influence in individual participants.

(a) Correlation between decision bias, defined as the signed difference between prior(long) and prior(short) bisection points, and perceptual asymmetry, defined as the slope of the best fitting regression line through bisection points for each prior interval condition; negative slopes indicate assimilative effects whereas positive slopes indicate contrastive effects. Smaller decision bias (closer to zero) was associated with greater contrastive perceptual effects, whereas greater decision bias (more negative) was associated with assimilative effects. Auditory and visual participants occupied separate quadrants, with greater decision bias for visual stimuli and greater perceptual contrast for auditory stimuli. (b) Correlation between decision bias and mean session coefficient of variation (CV); greater decision bias was associated with a larger CV. (c, d) Auditory and visual participant data with model performance from 500 permutations overlaid for both correlations from above. The model was able to account for a wide variety of performances that encompassed the majority of participants.

Figure 5. Implicit memory model schematic.

(a) On a given trial, a temporal interval t (here, auditory) is perceived as a draw from a Gaussian noise distribution f(t) that varies between trials and scales with longer durations (normalized here for presentation). (b) Once the length of the interval is perceived, the estimate is compared to the present criterion, (black dashed line), which changes from trial to trial depending on the prior distribution of trials. An uncertainty threshold, θ (gray dashed lines) indicates the distance surrounding the criterion beyond which an interval can be accurately discriminated, and is also drawn from a Gaussian distribution. (c) The memory criterion was formed by adaptively weighting a limited number of intervals in the immediate stimulus history, limited by a given memory window size (M). The weighting function of preceding intervals (ω) exponentially decayed in time and was proportional to M, such that larger window sizes led to a longer decay function and a greater influence of intervals further back in the stimulus history; curves represent the decay function for different values of M. (d) The decision stage on each trial ideally categorized perceived stimuli as longer or shorter than the criterion if they exceeded uncertainty. The model reproduced patterns of decision bias (top graph: gray line  =  prior resp(shorter); black line  =  prior resp(longer)) by selecting the prior response when uncertainty could not be overcome, and exhibited perceptual carryover (middle graph: gray line  =  prior dur(900 ms); black line  =  prior dur(300 ms)) by judging each stimulus relative to the adaptive prior. Bottom graph displays model data bisection points displaying a linear (contrastive) effect of prior interval.

Figure 6. Model fits of experimental data.

Individual fits indicated that the window size of the memory prior did not differ between participants performing on the auditory or visual versions of the task. However, uncertainty threshold values did significantly differ, with higher thresholds for visual participants (p<0.05). Error bars represent s.e. of the mean.

Figure 7. Alternative model comparisons.

Each graph displays the results of 200 permutations of an alternative model (green points) compared with the original model (faded points). Four models were tested: an unlimited-prior model, which assumed a perfect memory prior that continuously integrated all perceived intervals across the entire session; a zero-uncertainty model, where uncertainty in the comparison of the present duration with the mean of the prior did not impact decisions and θ was set to zero; a zero-weighting model, in which the prior was still limited and varied between permutations, but no adaptation weighting was applied (all remembered intervals contributed equally to the prior); a memory-based uncertainty model, where θ was set to match the variability of the intervals stored in the limited memory prior. None of the alternative models reproduced the full pattern of data observed in participants or in the full model.