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. 2009 May 8;324(5928):759-64.
doi: 10.1126/science.1169405.

Representation of confidence associated with a decision by neurons in the parietal cortex

Roozbeh Kiani  1 , Michael N Shadlen
Affiliations

Representation of confidence associated with a decision by neurons in the parietal cortex

Roozbeh Kiani et al. Science. .

Abstract

The degree of confidence in a decision provides a graded and probabilistic assessment of expected outcome. Although neural mechanisms of perceptual decisions have been studied extensively in primates, little is known about the mechanisms underlying choice certainty. We have shown that the same neurons that represent formation of a decision encode certainty about the decision. Rhesus monkeys made decisions about the direction of moving random dots, spanning a range of difficulties. They were rewarded for correct decisions. On some trials, after viewing the stimulus, the monkeys could opt out of the direction decision for a small but certain reward. Monkeys exercised this option in a manner that revealed their degree of certainty. Neurons in parietal cortex represented formation of the direction decision and the degree of certainty underlying the decision to opt out.

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Figures

Figure 1
Figure 1
Post-decision wagering behavior in monkeys is indicative of choice certainty. (A) The sequence of events in the task. After acquiring a central fixation point (small red point), two “direction targets” (large red spots) appeared on the screen, one inside the neural response field (RF; gray shading), the other on the opposite side of the screen. The motion stimulus appeared after a short delay, remained visible for 100–900 ms, and was followed by another delay (1200–1800 ms). On half of the trials (lower branch) the delay persisted until the fixation point was turned off, which served as a Go signal that instructed the monkey to indicate the perceived direction of motion by a saccadic eye movement to one of the “direction targets.” A correct response led to a liquid reward; a wrong response led to no reward and a brief timeout. On the other half of the trials (upper branch) a third target was presented 500–750 ms after extinction of the motion. Choosing this “sure target” (Ts; blue spot) led to a smaller reward (~80% of correct reward). On these trials the monkey could choose Ts or a direction choice. The two trial types were randomly interleaved. (B) The frequency of choosing Ts was greater when the motion strength (%coherence) was weak or the duration brief. The points are data grouped in duration quantiles (deciles). Error bars (SE) are smaller than the symbols. (C) Decision accuracy when Ts option was waived. The graph compares performance on trials in which Ts was not shown (open symbols, dashed curves) with trials in which Ts was offered but waived (filled symbols, solid curves).
Figure 2
Figure 2
LIP activity predicts direction choices and the post-decision wager. (A) Responses from one neuron on trials in which Ts was not presented. Average firing rates for Tin (black) and Topp (gray) choices are shown for all correct choices (and the 0% coherent motion strength), during motion viewing and the delay period. Averages are aligned to motion onset (left part of graph) and saccade initiation (right). (B) Responses from the same neuron on trials in which Ts was presented. The dashed lines show neural activity on trials in which Ts was chosen (black and gray, motion toward Tin and Topp, respectively). The middle portion of the graph shows activity in the delay period, aligned to onset of Ts. (C–D) Population average responses of 70 LIP neurons from two monkeys. Same conventions as in A and B. Firing rates from each neuron were normalized to the mean level prior to onset of the motion stimulus. (E) The activity before Ts presentation was smaller for Ts choices than for Tin choices. Each data point represents the mean activity of an LIP neuron in the 200 ms before Ts presentation (hatched rectangle in D). Error bars represent SEM. Shading in the histogram shows significant cases (p<0.05). The arrow shows the mean difference of normalized activity across the population (mean±SEM, −0.20±0.03). (F) The activity before Ts presentation was larger for Ts choices than for Topp choices. Same conventions as E (mean difference=0.18±0.02).
Figure 3
Figure 3
Ts choices were correlated with trial-to-trial variation of neural activity. Responses from single trials were represented as the absolute deviation, in units of standard deviation, from the mean value using all the trials from a neuron (z-score). (A) The frequency of choosing Ts as a function of deviation from mean in the activity before Ts presentation. Curves are fits of Eq. 11 (25) to individual trials. The points illustrated on the graph were formed by grouping trials into 5 bins. (B) The frequency of choosing Ts as a function of deviations from the mean buildup rate of activity after motion onset. Same conventions as in A.
Figure 4
Figure 4
A simple bounded evidence accumulation model predicted both the behavioral results and the modulation of LIP responses. (A–C) The model. On each trial, the accumulation, v(t), diffuses to one of the decision bounds (gray lines). The process terminates when v(t) reaches a bound or the stream of motion evidence ceases. (A) Representation of v(t) as a propagating probability density, for all motion strengths, when the rewarded direction is rightward. Positive values for v(t) represent accumulated evidence in favor of rightward. At time zero, the distribution is a delta function at v=0. As time elapses, the range of v(t) expands to fill the space between the two bounds, and there is a drift toward positive values, as shown by the probability density of v at t=800ms (inset to the right of color map). The distribution associated with leftward motion (not shown) is the mirror symmetric graph reflected about v=0. (B) The log odds of a correct response based on the value of v(t) at decision time. Correct responses are associated with larger v, but the relationship between v and probability correct changes with decision time. (C) Ts is chosen when the probability of a correct response is less than a criterion level. (D–E) Model fits and predictions. The three model parameters (Table S1) were fit to the observed frequency of correct responses on trials in which Ts was not shown and the observed frequency of Ts choices on trials in which Ts was shown. These parameters predict the probability of a correct response on trials in which Ts was waived (solid curves in E). (F) Comparison of model predictions and neural data. The average trajectory of v(t) in the model was calculated for different coherence levels using the fit parameters. The calculation is based on the stimulus durations used in the experiment, and assumes that v is fixed from termination of accumulation process. The calculated trajectories (top) resemble the LIP responses (bottom). Neural responses were detrended by subtracting the mean response at each moment and shifted by the neural latency (200 ms).
Figure 5
Figure 5
Activity of LIP neurons when the location of Ts was in the RF. (A) Task design. For 19 neurons from two monkeys we placed Ts in the RF. The high-stakes direction targets were outside the RF. Task sequence was otherwise unchanged. (B) Responses on trials in which Ts was not offered. (C) Responses on trials in which Ts was presented. Firing rates were normalized to the visual activity in the 300 ms epoch following onset of Ts.
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