Differentiating between Models of Perceptual Decision Making Using Pupil Size Inferred Confidence

Abstract

During perceptual decisions, subjects often rely more strongly on early, rather than late, sensory evidence, even in tasks when both are equally informative about the correct decision. This early psychophysical weighting has been explained by an integration-to-bound decision process, in which the stimulus is ignored after the accumulated evidence reaches a certain bound, or confidence level. Here, we derive predictions about how the average temporal weighting of the evidence depends on a subject's decision confidence in this model. To test these predictions empirically, we devised a method to infer decision confidence from pupil size in 2 male monkeys performing a disparity discrimination task. Our animals' data confirmed the integration-to-bound predictions, with different internal decision bounds and different levels of correlation between pupil size and decision confidence accounting for differences between animals. However, the data were less compatible with two alternative accounts for early psychophysical weighting: attractor dynamics either within the decision area or due to feedback to sensory areas, or a feedforward account due to neuronal response adaptation. This approach also opens the door to using confidence more broadly when studying the neural basis of decision making.SIGNIFICANCE STATEMENT An animal's ability to adjust decisions based on its level of confidence, sometimes referred to as "metacognition," has generated substantial interest in neuroscience. Here, we show how measurements of pupil diameter in macaques can be used to infer their confidence. This technique opens the door to more neurophysiological studies of confidence because it eliminates the need for training on behavioral paradigms to evaluate confidence. We then use this technique to test predictions from competing explanations of why subjects in perceptual decision making often rely more strongly on early evidence: the way in which the strength of this effect should depend on a subject's decision confidence. We find that a bounded decision formation process best explains our empirical data.

Keywords: confidence; integration-to-bound; macaque; perceptual decision making; psychophysical reverse correlation; pupillometry.

Figure 1.

Integration-to-bound models predict characteristic differences in temporal sensory weighting for high- and low-confidence trials. a–e, The PKA is plotted over time for integration-to-bound models with different decision bounds. PKAs for low confidence, high confidence, and averaged across all trials are shown in green, yellow, and black, respectively, and normalized by the peak of the average psychophysical kernel. For intermediate levels of the decision bound, the PKAs cross such that the PKA for low-confidence trials exceeds that for high-confidence trials at the end of the stimulus presentation. The value of the decision bound is marked in each panel. f, PKA_{t_last} is plotted for high (yellow) and low (green) confidence trials. The difference, ΔPKA_{t_last}, depends characteristically on the level of the decision bound in the model and the stimulus strength. The decision bound is normalized by the SD of the sensory variability. The relationship between ΔPKA_{t_last} and the value of the decision bound therefore holds generally across tasks with different stimulus variability. g–l, Same as a–f, but for an integration-to-bound model in which decision confidence is based on both decision time and evidence. Because our analysis only relied on the rank order of the decision confidence, the results are independent of the relative weight of these influences on decision confidence.

Figure 2.

Task and early psychophysical weighting behavior. a, Two choice disparity discrimination task. After the animals maintained fixation for 0.5 s, the stimulus was shown for 1.5 s. The animals had to decide whether the stimulus was “far” or “near” by making a saccade to one of two targets after the stimulus offset and received a liquid reward for correct choices. b, Average psychophysical performance of Animal A (left) and Animal B (right) across all sessions, each fitted with a cumulative Gaussian function. The average psychophysical thresholds are 23% signal and 45% signal for Animal A and Animal B, respectively. c, The time course of the PKA (normalized) shows that the animals weight the stimulus more strongly early during the trial. Data were obtained from 0% signal trials and collapsed across animals (A: 55,570 trials in 213 sessions; B: 20,394 trials in 84 sessions). Error bars indicate SEM derived by resampling.

Figure 3.

Pupil size modulation with task covariates is consistent with pupil-linked arousal. a–c, Average z scores (across conditions) ± SEM of pupil size aligned on stimulus onset are shown for Monkey A (left) and Monkey B (right). Horizontal lines at the bottom of each panel indicate epochs of significant (p < 0.05, Bonferroni-corrected, 450 pupil size samples) pupil size modulation (by ANOVA in a, two sample t tests in b, c). a, Mean pupil size for five equally sized bins throughout each experimental session. Only small available reward 0% signal trials are used. Pupil size decreases throughout the session as expected for decreasing motivation (Monkey A: 6987 trials from 213 sessions; Monkey B: 2571 trials from 84 sessions). b, Average time courses of pupil size on 0% signal trials that followed a correct trial for large (red), intermediate (purple), and small (blue) available reward trials (Monkey A: 18,700 small available reward trials, 5468 intermediate available reward trials, and 13,035 large available reward trials from 213 sessions; Monkey B: 6897 small available reward trials, 2011 intermediate available reward trials, and 4843 large available reward trials from 84 sessions). c, Average time courses of pupil size on hard (<10%, excluding 0% signal, green) and easy (≥50% signal, yellow) trials. Only trials with small available reward that followed a correct trial were used (Monkey A: 39,390 hard trials and 8651 easy trials from 213 sessions; Monkey B: 10,813 hard trials and 14,020 easy trials from 84 sessions). d, Psychophysical thresholds on large available reward trials were significantly smaller than in small available reward trials (Monkey A: n = 213, p < 10⁻²²; Monkey B: n = 84, p < 0.01). e, Average pupil size during the 250 ms before the stimulus offset was significantly larger compared with small available reward trials (Monkey A: n = 213, p < 10⁻³¹; Monkey B: n = 84, p < 10⁻¹⁹, all paired t tests). f–h, Control sessions for which a black fixation marker was used were included when the number of trials exceeded 600 and the number of trials in each condition per session was at least 10 (9 and 12 sessions, for Animal A and Animal B, respectively). f–h, Colors same as in a–c. f, Monkey A: 139 trials in each time bin from 9 sessions; Monkey B: 221 trials in each time bin from 12 sessions. g, Monkey A: 411 small available reward trials, 102 intermediate available reward trials, and 403 large available reward trials from 9 sessions; Monkey B: 558 small available reward trials, 198 intermediate available reward trials, and 407 large available reward trials from 12 sessions. The pupil size averaged over 250 ms before stimulus offset of the stimulus presentation tended to be larger compared with small available reward trials (p = 0.12 for Animal A, p < 0.01 for Animal B, paired t tests). h, Monkey A: 775 hard trials and 465 easy trials from 9 sessions; Monkey B: 1347 hard trials and 1169 easy trials from 12 sessions. Similar to our results for white fixation markers, the pupil size averaged over the last 250 ms before stimulus offset on easy trials (yellow) significantly exceeded that for hard trials (p < 10⁻⁴ for Animal A and Animal B, respectively). Data are mean ± SEM.

Figure 4.

The signature of decision confidence requires good task performance. a, Discriminability between hard (<10%, excluding the 0% signal) and easy (≥50% signal) trials, quantified as aROC for each session (ordinate; 213 sessions from Animal A, 84 sessions from Animal B), plotted as a function of time (abscissa) in the trial after stimulus onset. The systematically larger pupil size for easy trials (bright colors) late in the trial emerges only after extensive training, particularly in Monkey B. b, The average aROC during the 250 ms before the stimulus offset is significantly correlated with the psychophysical threshold (A: n = 213, r = −0.48, p < 10⁻¹³, B: n = 84, r = −0.45, p < 10⁻⁵; Pearson's correlation coefficient).

Figure 5.

Pupil size shows signatures of decision confidence. a, Schematic of a drift-diffusion model in which the decision confidence depends on the distance of the decision variable to the category boundary. b, Signatures of statistical decision confidence. Left, Statistical decision confidence predicts accuracy. Middle, For high decision confidence, statistical decision confidence predicts steeper psychometric functions than for low decision confidence. Right, Decision confidence is predicted to increase with signal strength in correct trials and decrease with signal strength in error trials. c, d, Metric based on pupil size (mean pupil size during the 250 ms before stimulus offset for small (c) or large (d) available reward trials) shows characteristics of decision confidence. Left column, Mean pupil size increases monotonically with accuracy. Middle column, The monkeys' psychometric functions separated by mean pupil size are slightly steeper for large compared with small mean pupil size, as predicted for decision confidence. Right column, Mean pupil size increases for correct and slightly decreases on error trials (Monkey A), and for low signal strengths in Monkey B. Data points are slightly offset for better visualization. For Animal A, all 213 sessions were included. For Animal B, analyses are restricted to the last 40 sessions with good performance (compare Fig. 4). Data are mean ± SEM.

Figure 6.

Time window for signature of decision confidence in pupil size within the trial. a–d, p values for different analyses are shown for different times within the trial (x-axis) and lengths of the analysis window (y-axis) over which pupil size was averaged. Data for Animals A and B are shown in the left and right columns, respectively. Red star indicates the time window used for the analyses in this study. a, Bonferroni-corrected p values for comparison between pupil size in easy versus hard trials, as in Figure 3c. b, p values for the Spearman's correlation between accuracy and mean pupil size within each window, as in Fig. 5c (left column). c, p values derived by resampling for comparing psychometric thresholds for low- versus high-inferred confidence trials, as in Fig. 5c (middle column). d, p values for the Spearman's correlation between mean pupil size in the respective window and the predicted confidence, as in Fig. 5c (right column).

Figure 7.

The animals' psychophysical weighting on low- and high-confidence trials is compared with model predictions. a–d, Circles represent PKAs for high (yellow) and low (green) inferred confidence trials (median split) for Animal A (top row) and Animal B (bottom row), plotted as a function of time (A: 213 sessions; B: 40 sessions). To avoid confounding the pupil size modulation for available reward size with that for inferred decision confidence, the median split based on pupil size to assign trials to the high- or low-confidence bin was performed separately for small and large available reward trials. Error bars indicate SEM derived by resampling. a, The integration-to-bound model in which trials were separated based on decision confidence defined as |decision variable| (ITB) provides a reasonably good fit to the animals' data, including the characteristic higher PKA for lower confidence trials in the last time bin, resulting in a crossover of PKAs. b, The integration-to-bound model with decision confidence depended on both |decision variable| and the model's decision time on each trial yields improved fits, in particular for Animal A for which the crossover of PKA was more pronounced. Both the neural sampling-based probabilistic inference model for which decision confidence is defined by the Bayesian posterior probability (c) and the early sensory weighting model after Yates et al. (2017) based on a linear-nonlinear model reflecting the response dynamics (gain control) of sensory neurons (d) are unable to capture the crossover in PKA separated by confidence late in the trial resulting in worse fits. Model performance is compared using ΔAIC, the difference in AIC compared with the best performing model (ITB-dt) (e), and the normalized mean squared error (f).

Figure 8.

Exploring the parameter space of the models. Quantifying the PKA in the last time bin (PKA_{t_last}) for high- and low-confidence trials. Insets, PKAs separated by confidence (colors as in Figs. 1, 7) predicted by each model. Values for Animal A and B are included for comparison. a, Exploring parameters of the neural sampling-based probabilistic inference model (Haefner et al., 2016). Model parameters were chosen such that the average PKA decreased. We then explored PKA_{t_last} when systematically increasing the trial duration. While systematically decreasing with trial duration, for high-confidence trials, PKA_{t_last,high_confidence} > PKA_{t_last,low_confidence} across all parameters. b, Simplified model of evidence accumulation with confirmation bias (sigmoidal acceleration; see Materials and Methods), mimicking the behavior of a or of a choice attractor (Wimmer et al., 2015) and a bimodal distribution of the decision variable late in the trial (double-well energy landscape). Similar to a, PKA_{t_last,high_confidence} > PKA_{t_last,low_confidence}. Moreover, ΔPKA_{t_last} decreases with trial duration and with increasing the confirmation bias (parametrized by acceleration parameter α) but consistently remains positive, contrasting with the monkeys' data. c, Simplified model of evidence accumulation with confirmation bias (linear acceleration; see Materials and Methods) but a consistently unimodal distribution of the decision variable, in contrast to Wimmer et al. (2015) and Wong et al. (2007). When increasing α PKA_{t_last} approaches 0 for both high- and low-confidence trials, in contradiction with the animals' data. d, Exploring parameters of the early sensory weighting model after Yates et al. (2017). We systematically changed the relative weights and the width of the stimulus and contrast kernel (parameters a, b, t_max, τ), thereby varying the degree and time course of the adaptation. The level of adaptation was evaluated in response to the preferred stimulus and quantified as the response at the end of the stimulus presentation relative to the peak response. Negative values for adaptation correspond to adaptation below baseline. Vertical dashed line indicates the degree of adaptation observed by Yates et al. (2017) for MT neurons. Only simulations for which a decrease in the overall kernel amplitude over time is observed, and for which the PKA in high-confidence trials exceeds that for low-confidence trials in the first time bin were included. We plot ΔPKA_{t_last} (color code as defined in b, right) as a function of the degree of adaptation (abscissa) and the neuron's correlation with the choice of the model (choice correlation, quantified as defined by Pitkow et al., 2015). Choice correlation was evaluated for the entire trial (left) and the first (middle) and last (right) time bin. We found that ΔPKA_{t_last} < 0 (blue data points) only for sensory responses that were otherwise inconsistent with empirical data (i.e., suppression of the sensory response below baseline or negative correlation with choice early during the trial; compare middle panel).

Figure 9.

Exploring the cost of the decision bound on performance. a, Model psychophysical performance is shown for integration-to-bound models with different decision bounds (color coded as depicted in b). b, Plotting the model performance across all trials as a function of the decision bound. Because correct answers are assigned arbitrarily on 0% signal trials, the maximal performance is <100% correct. Vertical bar represents the range of values of the decision bound for model fits to the animals' data in Fig. 7a, b. It shows that their decision bound is close to where performance asymptotes, and supports the view that the cost of the decision bound on performance is small.