Representation of Confidence Associated with a Decision by Neurons in the Parietal Cortex

The monkeys opted for the sure target when the chance of making a correct decision about motion direction was small.

“The monkeys opted for the sure target when the chance of making a correct decision about motion direction was small.”

The monkeys exercised the sure-target option more frequently for weaker motion strengths and shorter stimulus durations.

“They exercised this option more frequently for the weaker motion strengths and for the shorter stimulus durations (p<10−8, Eq. 1, see (25); Fig. 1B)”

• cites [25] Materials and Methods are available as supporting online material.Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The improvement in choice accuracy when waiving the sure-target option was apparent at almost all motion strengths and stimulus durations.

“This improvement was apparent at almost all motion strengths and stimulus durations.”

For motion toward Tin, neural activity across the population was significantly smaller for Ts choices than for Tin choices.

“For motion toward Tin, the neural activity across the population was significantly smaller for Ts choices than for Tin choices (p=0.007, ANOVA; Fig. 2E).”

Similar divergence and persistence of activity for Tin and Topp choices occurred on trials in which Ts was presented but waived by the monkey.

“We observed a similar divergence and persistence of activity for Tin and Topp choices on the trials in which Ts was presented but was waived by the monkey (Fig. 2B, solid traces).”

LIP neurons exhibited spatially selective persistent activity that predicted whether an eye movement was planned into the response field on a memory guided saccade task.

“These neurons exhibited spatially selective persistent activity that predicted whether an eye movement was planned into the response field (RF) of the neuron on a memory guided saccade task(29–31).”

• cites [29] Colby CL Goldberg ME Annu Rev Neurosci 22 319 1999 10202542 sourceNot checked yet

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• cites [30] Gnadt JW Andersen RA Exp Brain Res 70 216 1988 3402565 sourceNot checked yet

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• cites [31] Platt ML Glimcher PW J Neurophysiol 78 1574 1997 9310444 sourceNot checked yet

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The buildup of firing rate reflected the stimulus strength.

“the buildup of firing rate reflected the stimulus strength (p=0.01, Eq. 10; Fig. S2)”

The same pattern of sure-target choices was observed on a subset of trials in which identical random dot patterns were repeated.

“This same pattern was observed on a subset of trials in which identical random dot patterns were repeated (p<0.025; Fig. S1)”

When the monkey chose Ts, the response gradually converged to the Topp level.

“When the monkey chose Ts the response gradually converged to the Topp level.”

When the monkeys waived the sure-target option, choice accuracy was better than on trials when they were not offered the post-decision wager.

“when the monkeys waived this option, the choice accuracy was better than on the trials when they were not offered the post-decision wager (p<10−3, Eq. 3; Fig. 1C).”

The intermediate activity pattern for Ts choices persisted into the delay period until Ts appeared.

“This pattern persisted into the delay period until Ts appeared (p<10−8, t-test).”

When the monkey chose Ts, the activity following motion changed more gradually and achieved intermediate values compared to Tin and Topp choices.

“when the monkey chose Ts, the activity following the motion changed more gradually and achieved intermediate values compared to the Tin and Topp choices.”

Across the population of 70 LIP neurons, intermediate firing rates during motion viewing and the early delay were associated with choosing the sure target later in the trial.

“Intermediate firing rates during motion viewing and the early delay were associated with choosing the sure target later in the trial, as shown by the population average firing rates (Fig. 2D).”

The finding that residual fluctuations had leverage on sure-target choice held for the subset of trials with identical random-dot motion stimuli.

“This finding also held for the subset of trials in which we used identical random-dot motion stimuli (p=0.015).”

The 'mixture of states' alternative prediction is not supported by the data.

“This ‘mixture of states’ alternative makes a clear prediction, which is not supported by the data.”

Residual fluctuations of LIP responses before sure target onset had significant leverage on the probability of choosing the sure target.

“These residual fluctuations before the sure target onset had significant leverage on the probability of choosing the sure target (p=4.0×10−5, Eq. 12).”

The variance associated with Ts choices was significantly smaller than the variance associated with mixtures of Tin and Topp choices.

“The variance associated with Ts choices was significantly smaller than the variance associated with the mixtures of Tin and Topp choices (p=4.7×10−5; F-test).”

For motion toward Topp, neural activity across the population was significantly larger for Ts choices than for Topp choices.

“For motion toward Topp, the activity was significantly larger for Ts choices than for Topp choices (p=0.001; Fig. 2F).”

For stronger stimuli, the buildup of LIP activity was steeper.

“For stronger stimuli, the buildup was steeper (p<10−8, Eq. 10)”

On single trials, the deviation of firing rate from an intermediate level just preceding Ts onset was inversely related to the probability that the monkey chose the sure bet option.

“The magnitude of this deviation was inversely related to the probability that the monkey chose the sure bet option (p=2.3×10−5, Eq. 11; Fig. 3A).”

The buildup rate of LIP activity after motion onset was related to the probability of choosing Ts later in the trial.

“The rate of change of LIP activity after motion onset, termed the buildup rate (36), was related to the probability of choosing Ts later in the trial.”

• cites [36] The buildup rate on each trial was calculated by fitting a line to the neural activity in a ~300 ms window starting at the dip of activity after motion onset (see Materials and Methods).Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Fluctuations in buildup rate and delay period activity were weakly correlated.

“although the fluctuations in buildup rate and delay period activity were weakly correlated (r=0.10, p<10−8)”

Each of buildup rate and delay period activity exerted independent leverage on the likelihood that the monkey would opt for the Ts wager.

“each exerted independent leverage on the likelihood that the monkey would opt for the Ts wager (p<0.03; Eq. 13).”

The link between buildup rate and choice certainty was not simply due to covariation of buildup rates and choice certainty with motion strength.

“Moreover, this link was not simply due to covariation of buildup rates and choice certainty with motion strength (p=0.0018, Eq. 12).”

Deviation of the buildup rate from intermediate values was associated with a lower probability of choosing the sure target.

“Deviation of the buildup rate from intermediate values was associated with a lower probability of choosing the sure target (p=0.017, Eq. 11; Fig. 3B).”

After the appearance of Ts, neurons with the sure target in their response field became predictive of the post-decision wager.

“However, after the appearance of Ts, these neurons with sure target in their RF became predictive of the post-decision wager.”

The model establishes a prediction, not a fit, for the probability correct on trials in which Ts was shown but waived.

“This establishes a prediction (not a fit) for the probability correct on the trials in which Ts was shown but waived (Fig. 4E, solid curves, R2=0.97).”

Neurons with Ts in the response field did not show significant modulation of activity during the motion stimulus or in the ensuing delay period.

“these neurons did not show a significant modulation of activity during the motion stimulus or in the ensuing delay period (42).”

• cites [42] The activity of each neuron was normalized by its (visual) response in the 300 ms after Ts onset.Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The weak activity present in neurons with Ts in the response field was uninformative about the choice to forego or choose the Ts option.

“Moreover, the weak activity that was present was uninformative about the choice to forego or choose the Ts option (Fig. 5B; p>0.1 for both directions of motion).”

The visual response in the first 200 ms was slightly larger when the monkey would choose Ts.

“the visual response in the first 200 ms was slightly larger when the monkey would choose Ts (p<0.01, ANOVA)”

As time elapsed during the remainder of the delay period, the firing rates gave a clear indication of whether the monkey would choose Ts.

“but as time elapsed during the remainder of the delay period the firing rates gave a clear indication of whether the monkey would choose the Ts.”

The effect of the visual response was weak, with a median difference of 7.7%.

“The effect was weak (median difference = 7.7%)”

Even before the onset of Ts, the neuron was informative about whether the monkey would choose or waive the sure-target option should it be offered.

“the profile of activity suggests that even before the onset of Ts, the neuron was informative about whether the monkey would choose or waive this option should it be offered.”

The source of information about difficulty is not governed solely by properties of the stimulus but also by internal variability that renders the evidence more or less reliable to the decision-maker.

“suggesting that the source of information about difficulty is not governed solely by properties of the stimulus but also by internal variability that renders the evidence more or less reliable to the decision-maker.”

The buildup of firing rate is compatible with the representation of accumulated evidence in favor of Tin.

“compatible with the representation of accumulated evidence in favor of Tin.”

Before Ts appeared, the monkey did not know whether the sure bet would be offered.

“Note that before Ts appeared, the monkey did not know whether the sure bet would be offered.”

• Also stated in: § Abstract · plain

  “During motion viewing, the monkey did not know whether the sure-bet option would arise.”

The monkeys did not choose the sure target on the basis of stimulus difficulty but instead based on a sense of uncertainty on each trial.

“It implies that the monkeys did not choose the sure target on the basis of stimulus difficulty but instead based on a sense of uncertainty on each trial.”

The variable discharge of LIP activity was related to the monkey's choice certainty, whether the variations were caused by experimental manipulations or random effects.

“We conclude from these analyses that the variable discharge of LIP activity was related to the monkey’s choice certainty, whether these variations were caused by experimental manipulations (i.e., motion strength and duration) or random effects (i.e., neural noise).”

The linkage of neural responses with sure target choices is not explained merely by their shared covariation with the stimulus.

“Therefore, the linkage of neural responses with sure target choices is not explained merely by their shared covariation with the stimulus.”

The significance of the single-trial effect is a strong indication that LIP responses represent choice certainty.

“Nonetheless, the significance of the effect is a strong indication that LIP responses represent the choice certainty.”

The monkey is more likely to opt for Ts when LIP activity achieves an intermediate level of firing rate.

“These observations demonstrate that the monkey is more likely to opt for Ts when the LIP activity achieves an intermediate level of firing rate.”

The intermediate levels of activity are not artifactual but represent a low state of certainty.

“We conclude that these intermediate levels of activity are not artifactual but represent a low state of certainty.”

The choice is determined by the sign of v.

“In both cases, the choice is determined by the sign of v.”

Left-right choices on this task are governed by the accumulation of evidence favoring one or the other option.

“As previously shown, the left-right choices on this task are governed by the accumulation of evidence favoring one or the other option (17).”

• cites [17] Gold JI Shadlen MN Annu Rev Neurosci 30 535 2007 17600525 sourceNot checked yet

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The decision variable v(t) is represented by the firing rates of LIP neurons.

“This accumulation, which we call a decision variable, v(t), is represented by the firing rates of LIP neurons.”

• cites [17] Gold JI Shadlen MN Annu Rev Neurosci 30 535 2007 17600525 sourceNot checked yet

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• cites [18] Shadlen MN Newsome WT J Neurophysiol 86 1916 2001 11600651 sourceNot checked yet

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• cites [19] Roitman JD Shadlen MN J Neurosci 22 9475 2002 12417672 PMC6758024 sourceNot checked yet

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A Bayesian framework that incorporates both evidence and decision time explains several aspects of the data.

“Indeed, a Bayesian framework that incorporates both evidence and decision time explains several aspects of the data.”

• AssumptionThe authors state this as an assumption: The prior probability that motion is left or right is equal.

Variation in the buildup rate affects the amount of time it takes to reach a decision.

“variation in the buildup rate also affects the amount of time it takes to reach a decision (19–21, 37, 38)”

• cites [19] Roitman JD Shadlen MN J Neurosci 22 9475 2002 12417672 PMC6758024 sourceNot checked yet

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• cites [20] Kiani R Hanks TD Shadlen MN J Neurosci 28 3017 2008 18354005 PMC6670720 sourceNot checked yet

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• cites [21] Churchland AK Kiani R Shadlen MN Nat Neurosci 11 693 2008 18488024 PMC2453226 sourceNot checked yet

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• cites [37] Cook EP Maunsell JH Nat Neurosci 5 985 2002 12244324 sourceNot checked yet

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• cites [38] Hanes DP Schall JD Science 274 427 1996 8832893 sourceNot checked yet

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A simple extension of the bounded evidence accumulation model explains the post-decision wagering.

“A simple extension of this bounded evidence accumulation model also explains the post-decision wagering.”

• AssumptionThe authors state this as an assumption: The prior probability that motion is left or right is equal.
• AssumptionThe authors state this as an assumption: Opting out of the direction decision happens when the expected chance of success based on v(t) at decision time is less than a criterion level.

Unlike neurons with a direction choice target in the response field, neurons that encode the location of Ts do not appear to represent choice certainty.

“Unlike the neurons with a direction choice target in the RF, the neurons that encode the location of Ts do not appear to represent choice certainty.”

The evolution of v(t) predicted by the model resembles qualitatively the responses of LIP neurons.

“Moreover, the evolution of v(t), predicted by the model resembles qualitatively the responses of LIP neurons (Fig. 4F and S4).”

• AssumptionThe authors state this as an assumption: The prior probability that motion is left or right is equal.

The model explains the saturating firing rate curves in Figure 2.

“It also explains the saturating firing rate curves in Figure 2.”

• AssumptionThe authors state this as an assumption: The prior probability that motion is left or right is equal.

It provides additional evidence that the monkey made a decision about the motion direction in the period preceding onset of Ts, even on trials when he opted out of the direction task.

“More generally, it provides additional evidence that the monkey made a decision about the motion direction in the period preceding onset of Ts, even on trials when he opted out of the direction task.”

This observation argues against an alternative explanation of the finding based on allocation of attention to the Ts location.

“This observation argues against an alternative explanation of our finding based on allocation of attention to the Ts location.”

There is no indication that the monkey approached the task as a choice between three alternatives, Tin, Topp and Ts.

“There is no indication that the monkey approached the task as a choice between three alternatives, Tin, Topp and Ts.”

The agreement between the simple model and the data affirms the plausibility of the Bayesian sequential sampling framework.

“The agreement between this simple model and the data affirms the plausibility of the “Bayesian sequential sampling” framework (41).”

• cites [41] Ma WJ Beck JM Latham PE Pouget A Nat Neurosci 9 1432 2006 17057707 sourceNot checked yet

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• AssumptionThe authors state this as an assumption: The prior probability that motion is left or right is equal.
• AssumptionThe authors state this as an assumption: Opting out of the direction decision happens when the expected chance of success based on v(t) at decision time is less than a criterion level.

The simple bounded evidence accumulation model explains the monkey's accuracy as a function of stimulus strength and viewing time.

“As previously shown, this simple model explains the monkey’s accuracy as a function of stimulus strength and viewing time.”

• AssumptionThe authors state this as an assumption: The prior probability that motion is left or right is equal.

The larger visual response suggests that Ts was more salient when there was greater choice uncertainty.

“suggesting that Ts was more salient when there was greater choice uncertainty (43).”

• cites [43] Bisley JW Goldberg ME Science 299 81 2003 12511644 sourceNot checked yet

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The mechanism underlying the representation of certainty in LIP is linked to the same evidence accumulation that underlies choice and decision time.

“The mechanism underlying the representation of certainty in LIP is linked to the same evidence accumulation that underlies choice and decision time (17, 20).”

• cites [17] Gold JI Shadlen MN Annu Rev Neurosci 30 535 2007 17600525 sourceNot checked yet

  Not checked in the free run.

• cites [20] Kiani R Hanks TD Shadlen MN J Neurosci 28 3017 2008 18354005 PMC6670720 sourceNot checked yet

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This accumulation is encoded in the firing rates of LIP neurons with response fields aligned to the choice targets representing the direction alternatives.

“This accumulation is encoded in the firing rates of LIP neurons with response fields aligned to the choice targets representing the direction alternatives (18, 55–57).”

• cites [18] Shadlen MN Newsome WT J Neurophysiol 86 1916 2001 11600651 sourceNot checked yet

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• cites [55] Hanks TD Ditterich J Shadlen MN Nat Neurosci 9 682 2006 16604069 PMC2770004 sourceNot checked yet

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• cites [56] Huk AC Shadlen MN J Neurosci 25 10420 2005 16280581 PMC6725829 sourceNot checked yet

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• cites [57] Law CT Gold JI Nat Neurosci 11 505 2008 18327253 PMC2424192 sourceNot checked yet

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The magnitude of the decision variable, combined with knowledge of elapsed time, maps directly to the probability of obtaining a reward.

“The magnitude of this decision variable, combined with knowledge of elapsed time, maps directly to the probability of obtaining a reward.”

The present results show that the same neurons that participate in decision formation carry the relevant signals for assigning the probability of obtaining a reward.

“The present results show that the same neurons that participate in decision formation (20, 55) carry the relevant signals for assigning the probability of obtaining a reward.”

• cites [20] Kiani R Hanks TD Shadlen MN J Neurosci 28 3017 2008 18354005 PMC6670720 sourceNot checked yet

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• cites [55] Hanks TD Ditterich J Shadlen MN Nat Neurosci 9 682 2006 16604069 PMC2770004 sourceNot checked yet

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An associative learning process based on LIP responses can therefore underlie the monkey's choice of Ts.

“An associative learning process based on LIP responses can therefore underlie the monkey’s choice of Ts.”

The ability to explain the rich pattern of behavioral results and the qualitative agreement between model and physiology favors the simple conceptual model.

“The ability to explain the rich pattern of behavioral results and the qualitative agreement between model and physiology favors the simple conceptual model.”

The intermediate levels of activity associated with less certain choices might be a sign of a more homogeneous level of activity across the population of neurons.

“Accordingly, the intermediate levels of activity associated with less certain choices might be a sign of a more homogeneous level of activity across the population of neurons.”

The task design ensured that the monkey made a decision about motion direction on each trial.

“The task design, a form of post-decision wagering (26–28), ensured that the monkey made a decision about motion direction on each trial.”

• cites [26] Persaud N McLeod P Cowey A Nat Neurosci 10 257 2007 17237774 sourceNot checked yet

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• cites [27] Shields WE Smith JD Washburn DA J Exp Psychol Gen 126 147 1997 9163934 sourceNot checked yet

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• cites [28] Kornell N Son LK Terrace HS Psychol Sci 18 64 2007 17362380 sourceNot checked yet

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The results advance understanding of the neural mechanisms underlying decision-making by coupling for the first time the mechanisms leading to decision formation and the establishment of a degree of confidence.

“Fundamentally, our results advance understanding of the neural mechanisms that underlie decision-making by coupling for the first time the mechanisms leading to decision formation and the establishment of a degree of confidence.”

The finding suggests that when the brain embraces a truth, it does so in a graded way so that even a binary choice leaves in its wake a quantity that represents degree of belief.

“Our finding suggests that when the brain embraces a truth, it does so in a graded way so that even a binary choice leaves in its wake a quantity that represents degree of belief.”