Dynamic interplay of value and sensory information in high-speed decision making

Summary

In dynamic environments, split-second sensorimotor decisions must be prioritized according to potential payoffs to maximize overall rewards. The impact of relative value on deliberative perceptual judgments has been examined extensively [1–6], but relatively little is known about value-biasing mechanisms in the common situation where physical evidence is strong but the time to act is severely limited. In prominent decision models, a noisy but statistically stationary representation of sensory evidence is integrated over time to an action-triggering bound, and value-biases are effected by starting the integrator closer to the more valuable bound. Here we show significant departures from this account for humans making rapid sensory-instructed action choices. Behavior was best explained by a simple model in which the evidence representation, and hence rate of accumulation, is itself biased by value and is non-stationary, increasing over the short decision timeframe. Because the value bias initially dominates, the model uniquely predicts a dynamic “turn-around” effect on low-value cues, where the accumulator first launches towards the incorrect action but is then re-routed to the correct one. This was clearly exhibited in electrophysiological signals reflecting motor preparation and evidence accumulation. Finally, we construct an extended model that implements this dynamic effect through plausible sensory neural response modulations, and demonstrate the correspondence between decision signal dynamics simulated from a behavioral fit of that model and the empirical decision signals. Our findings suggest that value and sensory information can exert simultaneous and dynamically countervailing influences on the trajectory of the accumulation-to-bound process driving rapid, sensory-guided actions.

Results

In many real-life contexts such as fast-moving sports or traveling in traffic, sensory cues often occur which are physically strong but demand a motor response so immediate that their representation in the brain has barely had a chance to stabilize. Such tight time constraints bring a high risk of errors and necessitate that sensorimotor decision processes be prioritized according to anticipated costs and benefits to maximize expected gain. Although haste is as prevalent a limiting factor to making timely and accurate action choices as sensory ambiguity, the field has largely focused on deliberative, protracted decisions in the latter scenario. The mechanisms of value-based prioritization in severely time-constrained situations remain unclear, representing a significant gap in our current understanding of the normal repertoire of decision mechanisms. To examine this, we recorded behavioral and electrophysiological indices of decision formation from 15 human subjects tasked with discriminating a color change (green/cyan) at fixation and making a corresponding action (left-/right-hand button-click) within a strict deadline of 325ms (Figure 1A). Importantly, subjects earned more points (40) for correctly discriminating one color than the other (5 points), with incorrect or post-deadline responses earning 0 points (Figure 1A).

Figure 1. Behavioral task and data.

(A) Upon achieving fixation, subjects first viewed two peripheral, equiluminant green and cyan discs (“targets”) indicating which color alternative maps to which response hand on the current trial. After a 777–824 ms delay, the fixation point abruptly changed its color with equal probability to one of the target colors, demanding immediate execution of the corresponding response within a strict deadline of 325 ms. Depending on the cued color, a correct response earned the subject five or forty points. Here, a low-value correct trial is illustrated. Within each 120-trial block, the color-to-value association remained fixed but the mapping of color to response changed pseudorandomly on a trial-by-trial basis.

(B) Upper panel: Reaction time (RT) distributions for both correct (thick lines) and error responses (thin lines) on trials with high-value cues (red) and low-value cues (green). The 325-ms deadline is indicated by the vertical gray line. Mean RTs are indicated by symbols placed over the respective RT distributions. Error bars indicate S.E.M., which extends little beyond the symbol sizes. Lower panel: Conditional accuracy functions quantifying accuracy as a function of RT. Action choices were strongly value-biased for fast responses but became increasingly sensory-based with increasing RT, eventually converging on almost perfect accuracy.

As is typically observed for payoff-biased decisions [2,4,5,7–10], errors were more frequent on low-value cues (i.e., erring toward the high-value option; 28% vs 12%, t(13)=5.55, p<10⁻⁴), and correct responses to low-value cues (mean=335ms) were slower than to high-value cues (mean=280ms; t(13)=9.29, p<10⁻⁶). Strikingly, error reaction times (RT) were significantly faster than correct RTs not only for low-value cues (t(13)=18.14; p<10⁻⁹), but also for high-value cues (t(13)=4.25; p<0.001). Plotting accuracy over ascending RT revealed a dynamic shift from almost purely value-based choices to fully sensory-based, correct responses (Figure 1B).

In the most prominent sensorimotor decision models, noisy but stationary (statistically non-time-dependent) “evidence” samples are sequentially integrated over time into a “decision variable” (DV) which triggers a correct or incorrect action upon reaching an upper or lower bound, respectively [11,12]. According to the dominant accounts, decision makers set a lower criterion on the cumulative evidence required for choosing higher-value than for lower-value options. Models implement this as a “starting-point bias” between two fixed bounds [2,13] (Figure 2A), direct evidence for which has been found in sensorimotor neurons of monkeys [3]. An alternative biasing mechanism is to modulate the sensory representations themselves or their weighting in the accumulation process, resulting in a “drift rate bias” (Figure 2B). Although it is known from research on attention [14,15], expectation [16] and reward [17,18] that the brain is generally capable of exerting such sensory-level modulations, starting-point biases have been found to greatly dominate over drift rate biases in accounting for sensorimotor decision behavior biased by either value or prior probability [4–6,19–21].

Figure 2. Comparison of alternative accumulation-to-bound models.

(A–D) Schematics illustrating the four alternative, simplified models for capturing the value biases and relatively fast error RTs observed in our behavioral data. In the standard models typically examined (A and B), sensory evidence (SE) is stationary (additive noise not shown) and thus the decision variable (DV) on average increases linearly with time. In the models with increasing evidence (C and D), drift rate (represented directly as mean sensory evidence here for clarity of presentation) increases linearly over time, so that the DV grows with a curved (quadratic) path, and had no starting point variability. In the starting point bias models, the initial DV value is shifted towards the high-value bound with no change to the evidence (A and C). In the drift rate bias models, the sensory evidence driving the accumulation process is offset in the direction of the higher value (B and D).

(E) Mean Bayes Information Criterion (BIC) values quantifying goodness of fit for the four alternative models, arranged in the same order as panels A–D. The smallest BIC values for the drift rate bias model with increasing evidence signifies that it provides the best fit to behavior. Average parameter values are listed in Table S1 and simulated RT distributions and conditional accuracy functions in Figure S2. Adding either a difference in non-decision time between high- and low-value responses or drift rate variability to the standard stationary-evidence models did not change these results (see Figure S1).

(F–I) Simulated decision variable dynamics over time starting from the onset of accumulation for correct high-value-cued trials, correct low-value-cued trials with relatively fast and relatively slow RT, and incorrect low-value-cued trials, using parameters estimated from the behavioral fit of each competing model (E). Starting point biases were reflected in positive and negative shifts in DV starting level for high- and low-value cues, respectively (‘1’, F,H). Starting point variability was reflected in error trials being associated with a starting level closer to the error bound, and higher starting levels for faster correct trials (‘2’, F,G). A biased and increasing drift rate was uniquely associated with a “turn-around” effect on slower, correct responses to low-value cues due to drift rate shifting from an initially negative to a positive value due to the growing sensory influence. With stochastic variation, this initial downward trajectory often goes far enough to cross the lower bound, resulting in an error. SPB-VS: starting point bias model with variable starting point; DRB-VS: drift rate bias model with variable starting point; SPB-IE: starting point bias model with increasing evidence; DRB-IE: drift rate bias model with increasing evidence.

See also Figure S1, Figure S2 and Table S1.

Fast errors, a common feature of time-constrained decision tasks [22], are captured in standard, stationary-evidence models by adding random trial-to-trial variability in starting point [13]. An alternative explanation, however, is that accuracy increases as a function of RT simply because sensory evidence strength (hence drift rate [23]) increases over time while being accumulated (Figure 2C,D). This is based on the premise that even for physically strong, abruptly-onsetting sensory events, feature-selective sensory neural representations do not emerge in a discrete instant but rather emerge gradually [24,25] when viewed on the narrow timescale of rapid decisions.

To examine these alternative mechanisms for generating value biases (starting point bias (SPB) versus drift rate bias (DRB)) and for producing fast errors (starting point variability (VS) versus increasing evidence (IE)), we constructed four (2×2) simplified bounded diffusion models (Figure 2A–D) and fit them to individual subject RT distributions (Figure S1). Models with increasing evidence produced better fits (lower BIC) than models with starting point variability (main effect of fast-error mechanism: F(1,13)=30.2, p<10⁻³; Figure 2E). Further, we found an interaction (F(1,13)=19.5, p<0.01), whereby a starting point bias provided a better fit for stationary-evidence models with starting point variability as is typically observed (t(13)=4.26, p<0.001), but a drift rate bias provided the better fit among models with increasing evidence (t(13)=2.42, p<0.05).

By their nature, these alternative models predict qualitatively distinct initial decision variable (DV) dynamics when comparing across value conditions (high- vs. low-value cues) and behavioral outcomes (low-value cued trials with relatively fast correct vs. slow correct vs. error responses; Figure 2F–I). By simulating average DV trajectories from the timepoint of accumulation onset using parameters from the behavioral fits, we observed that while bias (labelled ‘1’) and/or variability (‘2’) in start point were expressed in the expected differences in starting level, a dynamic “turn-around” effect was uniquely exhibited in the DRB-IE model (‘3’). For low-value cues in this model, drift rate starts out negative and systematically shifts to positive values over time (Figure 2D). With trial-to-trial variability due to noise, the DV often crosses the incorrect bound before being re-routed by the growing sensory influence, but on trials where it comes close but is “rescued” just in time, there is a distinct turn-around in its trajectory, accompanied by a relatively slow but correct ultimate action choice.

To empirically test for these value-biasing signatures, we traced the trajectories of two electroencephalographic (EEG) signals known to reflect evidence accumulation dynamics. We first examined the lateralized readiness potential (LRP), which continuously traces the relative degree of motor preparation for the correct (positive values in Figure 3A) versus incorrect (negative values) action as the decision unfolds, and thereby reflects differential decision variable dynamics [10,26,27]. Signatures of all models were exhibited to varying degrees in the LRP waveforms (Figure 3A). Most strikingly, a clear turn-around effect was observed for slow, correct low-value-cued trials (time interval 170–200ms compared to 0–30ms; t(13)=−5.79, p<10⁻⁴), as uniquely predicted by the biased, dynamic drift rate (DRB-IE) model. Starting levels around cue onset (−50 to 50ms) also reflected a starting-point bias (high-versus low-value cues: t(13)=2.70, p<0.02), and starting-point variability (one-way ANOVA for low-value fast, slow, error: F(2,26)=4.56, p=0.02). While these starting-level effects were smaller in magnitude than those predicted by the models allowing for them (Figure 2F–H), the turn-around effect was more pronounced in the LRP waveforms than predicted by the DRB-IE model simulation (Figure 3A; see also Figure S3 for gradation across more RT bins).

Figure 3. Electrophysiological signals reflecting relative motor preparation and evidence accumulation.

(A) Empirically measured differential motor preparation reflected in the lateralized readiness potential (LRP), for the same 4 trial conditions as simulated in Figure 2F–I. Upward deflections reflect preparation towards the correct response. Key signatures of all four simplified models (Figure 2) are exhibited. Right: scalp potential distribution of the difference between left-response and right-response trials, illustrating the LRP topography.

(B) The centro-parietal positivity (CPP), which reflects a motor-independent representation of cumulative evidence at a more abstract level, plotted for the same conditions. Consistent with initial accumulation of ‘wrong’ evidence followed by a gradual take-over of correct evidence (reflected in the turn-around in LRP), the CPP exhibited an initial buildup, then a momentary lull (roughly coincident with LRP crossing back over its baseline level), and resumed buildup particularly for the conditions of incorrect and slow correct low-value cues. In the case of errors, the initial buildup of “wrong” evidence was enough to cross the error bound. Note that the fact that the dip is most strongly exhibited for slower correct and fast incorrect low-value cued trials – the two conditions with longest and shortest RT, respectively – rules out the possibility that these patterns arise from differences in the temporal overlap of non-decision related stimulus- and response-locked processes due to RT differences. Figure S3 repeats this analysis for more RT bins to highlight graded nature of effects.

We next examined the centro-parietal positivity (CPP), which has been shown to reflect accumulation-to-bound dynamics independent of sensory modality or response requirements, consistent with an abstract decision variable computed upstream from effector-specific motor preparation circuits [28,29]. In contrast to the differential LRP signal, the CPP manifests with a positive polarity at midline scalp sites regardless of the sensory alternative presented [27], or whether the response is ultimately correct or incorrect, suggesting that it reflects the absolute value of cumulative, differential evidence ([30]; see Methods). It would follow that on slow, correct low-value-cued trials exhibiting a strong turn-around effect, the CPP should first rise with the initial accumulation of “wrong” evidence, drop or plateau momentarily when this initial evidence is nullified by growing, correct sensory evidence, and rise again with the accumulation of further correct evidence. The CPP exhibited this very pattern (Figure 3B; t(13)=4.92, p=0.0003, difference in amplitude between 240–270ms and 170–200ms greater than that expected for monotonic buildup). Thus, the turn-around effect is not specific to, or introduced at, the level of motor preparation, and is manifest in upstream, motor-independent processing levels, consistent with modulations of the accumulator input.

The essential ingredient of the best-fitting DRB-IE model is a temporally increasing drift rate that is offset towards the higher-value option (Figure 2D), implemented as simple linear affine functions. In practice, however, neural feature selectivity does not continue to grow to infinity, and how drift rate can initialize with a negative value for low-value cues is not immediately obvious. We thus developed an explanatory account in terms of idealized but plausible, aggregate responses for two sensory neuronal populations, each with a tuning preference for one of the two color alternatives (Figure 4A). Mimicking motion direction-selective neurons of the monkey middle temporal area (MT; [31], data of [32]; see Figure S4) both populations initially respond non-selectively under neutral conditions, but thereafter gradually become fully feature-selective (Figure 4A, left). If a value bias is exerted by amplifying the responses of higher-value color-coding population and/or attenuating the low-value population, then for low-value cues the differential sensory evidence (“correct” minus “incorrect” population) assumed to feed the accumulator process would start out negative but immediately grow towards a positive value (Figure 4A, right), producing the characteristic turn-around effect in the accumulator. We constructed a “Value-Modulated Sensory Response” (VMSR) model by parameterizing value-based modulation of these sensory responses and adding starting point bias and variability to allow for the observed effects on LRP starting level (see Methods). For comparison we constructed a strong “standard” model with stationary evidence that also had both bias types, based on recent findings that models allowing for drift rate biases in addition to the dominant starting-point biases capture prior-biased decision behavior better than models with only a starting-point bias [33,34]. We also allowed for the fact that non-decision delays may be shorter for executing high-value than low-value motor responses, and trial-to-trial drift rate variability to potentially produce negative drift rates on some low-value trials and hence an initial launch in the incorrect direction as observed. The VMSR model provided a significantly better behavioral fit (Figure S2C) than the Standard Dual-bias model (t(13)=5.04, p=0.0002; Figure S3G). We again simulated average decision variable waveforms, this time both stimulus- and response-aligned and with the CPP simulated as the absolute value of cumulative evidence. This revealed a strong similarity between the real and VMSR-simulated waveforms (Figure 4B,C; Figure S3), including a moderate degree of bias and variability in LRP starting level and strong turn-around effect in both the LRP and CPP. In contrast, the Standard Dual-bias model overestimated the starting level effects and did not produce turn-around dynamics. Accordingly, correlations between real and simulated waveforms were significantly greater for the VMSR model (LRP: t(13)=3.28, p=0.006; CPP: t(13)=2.48, p=0.028).

Figure 4. Value-Modulated Sensory Response (VMSR) model.

(A) Idealized sensory responses of two neural populations with a tuning preference for each color alternative, forming the basis of the VMSR model. Response profiles trace the expectation (i.e., trial-average) of activity over time, and additive noise is applied on each single trial. Taking the example of a presented cyan cue, the “preferred” (cyan neurons) and “unpreferred” (green neurons) sensory populations are initially excited equally strongly under value-neutral conditions (left), but selectivity gradually develops as the “unpreferred” population activity drops away. The differential evidence (gray trace) thus increases from zero to a stable positive level. When cyan is the higher-value color (middle), the cyan neurons’ response is enhanced and the green neurons’ response attenuated, which results in a positive offset in the differential evidence (red trace). Meanwhile when cyan is the lower-value color (right), the modulations are reversed so that the differential evidence is offset negatively (green trace) as in the abstract version of the model (Figure 2D).

(B) Simulation of average Decision Variable (DV) trajectories for the VMSR model using parameters from fits to the behavioral data (see Methods). Both cue-locked and response-locked DV waveforms, simulated for each individual and then averaged, match the empirically observed dynamics of the LRP (Figure 3A) including the distinctive “turn-around” effect.

(C) The motor-independent accumulator signal (CPP) was simulated from the same behavioral fit of the VMSR model by taking the absolute value of the cumulative differential sensory evidence (|ΣSE|) on each single trial. Like the empirical CPP (Figure 3B), the simulated CPP trace for incorrect and slow correct low-value cues undergoes an initial buildup followed by a lull and then a second phase of buildup. Note that although the simulated CPP traces on single trials with turn-around effects dip down to zero at the time point where differential cumulative evidence passes from negative to positive, averaging across trials and subjects significantly blunts this dip in the average simulated traces (see also Figures S2, S3 and S4).

Discussion

Even for perceptually obvious events, selecting and executing the response that maximizes the likely payoff is a significant challenge when time is limited, yet this common scenario has received little attention in decision neuroscience. Here we showed that the mechanisms underlying such behavior significantly depart from standard models of simple perceptual judgments. In keeping with all previous studies of biased decisions, standard, stationary-evidence model fits suggested that starting-point biases were strongly dominant over drift rate biases in accounting for behavior. However, simply by incorporating a temporal increase in evidence strength mimicking real sensory neural response dynamics over such short timeframes, not only were fits generally superior but this dominance in biasing mechanisms was reversed. Further, we showed that compared to a model implementing both starting-point and drift rate biases in the standard way ([33–35]), a model that implements the biased, increasing drift rate effect through plausible sensory response modulations alongside starting point biases provides a significantly better account of both behavior and the temporal dynamics of neurophysiological decision signals at two sensorimotor processing levels, across the entire timeframe of the decision. This not only provides novel insights into decision mechanisms in time-constrained scenarios but, more broadly, underscores the fact that the role of certain mechanisms in any decision model can be misinterpreted when other core aspects of the brain’s decision processes are mischaracterized.

The crucial signature of our model was a “turn-around” effect on low-value cues, whereby the differential evidence accumulator is initially launched towards the higher-value action but then dynamically re-routed towards the correct action. Our observation of this effect in the dynamics of relative motor preparation is unprecedented for a decision of this nature. Dynamic shifts in dominance of two competing alternative motor plans have been observed in situations where multiple, conflicting sensory stimuli are presented, either together (e.g. in the Flanker task [26] or value-based choice tasks [36]), or sequentially (e.g. the “compelled response task” [37]), but here we observe the effect for a single, discrete sensory feature change due to the purely internal conflict between value and sensory information. Further, that the effect was observed for correct low-value trials considered alone (not averaged with errors [10]) demonstrates its role in “rescuing” the decision from value-biased errors almost committed. These turn-around dynamics have the appearance of “changes of mind” reported to occur spontaneously for difficult decisions [38], the major distinction being that here they are driven systematically by the gradual shift of balance from value-driven to sensory-driven accumulation.

Our observation of the “turn-around” perturbation in abstract-level evidence accumulation reflected in the CPP supports the idea that value directly influences the input of the accumulation process. This could occur through modulation of the sensory representations themselves, similar to neuronal response modulations observed due to feature-based attention [15,39–42] and expectation [16] and consistent with reward-sensitivity reported for early visual activity [17,18]. Alternatively, value may produce drift rate biases by shifting the weighting or reference values used in the readout of sensory representations fed into the accumulator, without altering the sensory representations directly. The computational implementation of our models is compatible with either alternative, and thus future work must employ direct measures of early sensory responses to resolve this. Future work must also address how subjects learn to employ one or the other bias type depending on the temporal, sensory and value settings of a given situation.

Other novel models have previously produced fits to value-biased behavior superior to the standard starting-point or drift bias models [7,10], but in contrast to our account, they assume nonoverlapping influences of value and sensory information on the decision process. The “two-stage-processing” hypothesis [7] is based on the idea of a discrete attention switch from value to sensory information. Though conceptually distinct, this bears a practical similarity to our model in that the decision variable is first driven by value, then sensory information, and our VMSR model effectively offers a plausible implementation of a more graded version of this shift. In another model, a value-biased, short-latency “fast guess” process sometimes enters the race between two sensory accumulators [10]. Although originally conceived to account for accuracy costs due to speed pressure [43,44], more recent research tends to categorize fast guesses as “contaminant” events [45]. Our VMSR model provides a plausible mechanism for generating “fast guess” behaviors without recourse to the idea of a separate, non-integrative [2] “fast guess” process in the brain. It further can specify, through an extremely simple mapping, how the computational process of decision formation translates to the observed dynamics of evidence accumulation and motor preparation measured electrophysiologically.

Time-dependent biases in decision signal buildup have been reported for decisions benefiting from prior information in tasks where stimulus strength varies randomly across trials [46], a scenario in which this biasing mechanism is optimal [35]. These bias components are conceived as buildup components added to cumulative evidence rather than alterations directly to drift rate or the sensory inputs being integrated, and lead to an increasing expression of bias with increasing RT in mixed-difficulty conditions, as opposed to a decreasing influence as observed here. Dynamic shifts in drift rate in the course of a single decision have previously been employed to model behavior when the physical stimulus itself changes by disappearing, being backward-masked [47,48] or switching mid-trial [49–52], during shifts of attention among display items [53–55] or visual memory trace formation [56]. Our findings highlight the potential importance of time-dependent drift rate for even unitary, simple discrimination decisions, and that although the stationary evidence assumption provides good quantitative behavioral fits for temporally-extended judgments [12,57], it may overlook a critical dynamic feature in rapid, time-constrained sensorimotor decisions.

STAR Methods

CONTACT FOR RESOURCE SHARING

Further information and requests for resources should be directed to and will be fulfilled by the Lead Contact, Simon P. Kelly (simon.kelly@ucd.ie).

EXPERIMENTAL SUBJECT DETAILS

Participants

Fifteen subjects (7 female), ranging in age from 21 to 35 years old (mean=25 years), participated in this study. All subjects had normal or corrected-to-normal vision. Subjects gave written informed consent and all experimental procedures were approved by the Institutional Review Board of the City College of New York. $12 per hour compensation was given to the subjects and they could earn up to $12 additionally depending on their performance.

METHOD DETAILS

Task and Stimuli

The experiments took place in a dark, sound-attenuated booth. Participants were seated 57 cm from a CRT monitor with a refresh rate of 85 Hz and resolution of 600 × 800. Participants were instructed to maintain fixation on a small square (0.5° of visual angle) in the center of the screen for the duration of each trial, and eye position was monitored with a remote eye tracker (EyeLink 1000, SR Research, 1000Hz). The visual stimuli were generated using PsychToolbox [58,59] running in MATLAB (version 7.11, MathWorks).

In the rapid color-discrimination task, each trial began with a centrally placed, light gray fixation square (89 cd/m²) presented on a darker gray background (29 cd/m²; Fig. 1A). Once fixation was maintained for 400–450ms, equiluminant green and cyan “targets” (filled circles with a diameter of 2°, 89 cd/m²) were presented 8° directly to the right and left of fixation. The placement of colors indicated the stimulus-action mapping for the upcoming sensorimotor decision, and was pseudorandomized across trials. After 777 or 824 ms (randomly interleaved to reduce 10-Hz alpha-ringing from preceding target onset), the fixation square changed its color to match one of the two targets. To obtain a reward, subjects had to press a button with the index finger of the hand corresponding to the location of the cued target color within a strict deadline of 325 ms. The two color alternatives were associated with different reward amounts received if correctly responded to on time. Participants were instructed about the color-to-value associations (cyan=40 pts (high) and green=5 pts (low), or cyan=5 pts (low) and green=40 pts (high)) at the beginning of each block. Participants each completed 6 blocks of 120 trials of this task. The color-to-value mapping remained constant within each block, and was switched after three blocks with the initial mapping counterbalanced across subjects. If subjects broke fixation at any time between initial fixation and the response, the trial was aborted and a message, “Keep your eyes on fixation!” was printed on the screen. At the end of the trial, a short feedback message was displayed indicating either that the subject was correct (‘Nice!’) along with the points gained, or that no points were rewarded, either because the response was initiated before the cue (‘Too early, wait for cue’), was on-time but incorrect (‘Wrong way’), missed the 325-ms deadline (‘Too slow’), or because no response was made before the trial ended 550 ms after the cue (‘Way too slow’). Before recording, participants practiced the task for 4 blocks of 120 trials, with the response deadline starting at 450ms and decreasing to 325 ms by the fourth block.

Behavioral data analysis

We measured reaction times (RT) relative to cue onset and response accuracy for the two conditions of high- and low-value cues. One of the 15 subjects took a qualitatively different approach to the task than the others, almost completely ignoring the sensory information in the cue. This was reflected in an extremely high low-value error rate (72%), extremely low median reaction time (215 ms), and extremely high number of anticipatory movements (RT<50 ms on 56 out of 720 trials), each of which was classed as an outlier by the criterion of falling more than two inter-quartile ranges beyond the upper/lower quartile. This subject was therefore excluded from further analysis. For the remaining 14 subjects, anticipatory actions (RT<50 ms) were made on 1.0 ± 2.0 % of trials and response omissions (no response by 550 ms) on a further 1.2 ± 1.0 % of trials. These trials were excluded from analysis. Trials on which the deadline for obtaining rewards was missed but a response was made before the trial’s end at 550 ms were included, because these represent an integral part of the full pattern of responding in the task and no physical change occurred on screen before trial end. To compute RT distributions for plotting (Figure 1B, S2), we divided trials into non-overlapping RT bins of width 23.5-ms ranging from 50–550 ms). For conditional accuracy functions (CAF) we calculated the proportion of correct trials within each of these RT bins and plotted response accuracy over the bins’ mean RTs (Figure 1B).

Modeling

In the first behavioral modeling analysis, we compared 4 bounded diffusion models, a 2×2 set where we crossed the two alternative mechanisms for value biasing (starting-point versus drift rate bias) with two alternative mechanisms for producing incorrect responses of shorter RT than correct ones (“fast errors”; starting point variability and increasing evidence strength). All models shared the basic principle of bounded accumulation of noisy evidence, with the dynamics of the one-dimensional decision variable (DV), x, described by the discrete difference equation:

$$\mathrm{x}(\mathrm{t})=\mathrm{x}(\mathrm{t}-1)+\mathrm{E}(\mathrm{t})\ast \text{dt}+\mathrm{N}(0,\mathrm{s}\ast \text{sqrt}(\text{dt}))$$

where dt is the discrete time increment,, E(t) specifies the expectation of the differential evidence and thus the momentary drift rate of the DV at time step t, and N(0, s*sqrt(dt)) refers to Gaussian noise with zero mean and variance s²dt [60]. All four models had a single “non-decision time” parameter to account for additive delays due to processes other than the accumulation-to-bound process and a single bound parameter, with the noise level anchored at s=0.1, relative to which all other parameters are scaled.

In the Starting Point Bias model with variable starting point (SPB-VS), and the Drift Rate Bias model with variable starting point (DRB-VS), the evidence function E(t) was a step function, whose height for a given condition equated to the stationary drift rate. In the Starting Point Bias model with increasing evidence (SPB-IE), and the Drift Rate Bias model with increasing evidence (DRB-IE), the evidence function E(t) was a linear function with positive slope, corresponding to non-stationary, growing drift rate, and these models had no starting point variability. In the SPB models, the starting point of accumulation was shifted closer to the bound of the higher paying option and drift rate was constrained to be equal across value conditions. In the DRB models, the two value conditions were allowed to have different drift rates, and the starting point was constrained to be zero on average. The SPB-VS model was governed by:

$$\begin{array}{lll}\mathrm{x}(\mathrm{t})=\mathrm{x}(\mathrm{t}-1)+\mathbf{d}\ast \text{dt}+\mathrm{N}(0,\mathbf{s}\ast \text{sqrt}(\text{dt})),\hfill & \mathrm{x}(0)={\mathbf{z}}_{\mathbf{B}}+\text{rand}1\ast \mathbf{sz};\hfill & (\text{High-value}\text{cue})\hfill \\ \mathrm{x}(\mathrm{t})=\mathrm{x}(\mathrm{t}-1)+\mathbf{d}\ast \text{dt}+\mathrm{N}(0,\mathbf{s}\ast \text{sqrt}(\text{dt})),\hfill & \mathrm{x}(0)=-{\mathbf{z}}_{\mathbf{B}}+\text{rand}1\ast \mathbf{sz};\hfill & (\text{Low-value}\text{cue})\hfill \end{array}$$

which proceeded until either bound b (correct) or −b (error) was crossed, at which point non-decision time tnd was added to compute the full RT for the trial. Adding tnd at the end of the decision process is no different than interposing it between cue onset and the beginning of decision formation in terms of behavioral fitting, but it conveniently allows us to refer to time t as starting from accumulation onset (t=0) in the present model descriptions. This same stopping rule and additive non-decision time component were implemented identically in all models, and the simulation time resolution was fixed at dt=1 ms. For convenience we use the term ‘rand1’ to denote a uniform random variable over the range {−1,1}. The starting point bias z_B was implemented as a symmetric shift upwards (+ z_B) and downwards (− z_B) from the midpoint between bounds (x=0) for high and low value cues, respectively. The SPB-VS model thus had 5 free parameters: tnd, b, z_B, starting point variability half-range sz, and a constant drift rate E(t) = d.

The DRB-VS model was governed by:

$$\begin{array}{lll}\mathrm{x}(\mathrm{t})=\mathrm{x}(\mathrm{t}-1)+(\mathbf{d}+{\mathbf{d}}_{\mathbf{B}})\ast \text{dt}+\mathrm{N}(0,\mathbf{s}\ast \text{sqrt}(\text{dt})),\hfill & \mathrm{x}(0)=0+\text{rand}1\ast \mathbf{sz};\hfill & (\text{High-value}\text{cue})\hfill \\ \mathrm{x}(\mathrm{t})=\mathrm{x}(\mathrm{t}-1)+(\mathbf{d}-{\mathbf{d}}_{\mathbf{B}})\ast \text{dt}+\mathrm{N}(0,\mathbf{s}\ast \text{sqrt}(\text{dt})),\hfill & \mathrm{x}(0)=0+\text{rand}1\ast \mathbf{sz};\hfill & (\text{Low-value}\text{cue})\hfill \end{array}$$

Here, the starting point was on average midway between the bounds but variable across trials, and high and low value cues had different drift rates given by d + d_B and d − d_B respectively, such that d is the midpoint between the two and d_B relates to a symmetric bias from that midpoint. [Note the fit was conducted with two separate drift rates dH and dL which later were translated to these midpoint and bias drift rate parameters for clarity of exposition]. This model thus had 5 free parameters: tnd, b, sz, d, and d_B.

The SPB-IE model was governed by:

$$\begin{array}{lll}\mathrm{x}(\mathrm{t})=\mathrm{x}(\mathrm{t}-1)+\mathbf{c}\ast \mathrm{t}\ast \text{dt}+\mathrm{N}(0,\mathbf{s}\ast \text{sqrt}(\text{dt})),& \mathrm{x}(0)={\mathbf{z}}_{\mathbf{B}};& (\text{High-value}\text{cue})\\ \mathrm{x}(\mathrm{t})=\mathrm{x}(\mathrm{t}-1)+\mathbf{c}\ast \mathrm{t}\ast \text{dt}+\mathrm{N}(0,\mathbf{s}\ast \text{sqrt}(\text{dt})),& \mathrm{x}(0)=-{\mathbf{z}}_{\mathbf{B}};& (\text{Low-value}\text{cue})\end{array}$$

so that drift rate increased linearly with positive slope c over time, i.e., E(t) = c*t. z_B again quantified the symmetric starting point bias from x=0. This model had 4 free parameters: tnd, b, z_B, and drift rate growth rate c.

Finally, The DRB-IE model was governed by:

$$\begin{array}{ccc}\mathrm{x}(\mathrm{t})=\mathrm{x}(\mathrm{t}-1)+({\mathbf{d}}_{\mathbf{B}}+\mathbf{c}\ast \text{t)}\ast \text{dt}+\mathrm{N}(0,\mathbf{s}\ast \text{sqrt}(\text{dt})),& \mathrm{x}(0)=0;& (\text{High-value}\text{cue})\\ \mathrm{x}(\mathrm{t})=\mathrm{x}(\mathrm{t}-1)+(-{\mathbf{d}}_{\mathbf{B}}+\mathbf{c}\ast \text{t)}\ast \text{dt}+\mathrm{N}(0,\mathbf{s}\ast \text{sqrt}(\text{dt})),& \mathrm{x}(0)=0;& (\text{Low-value}\text{cue})\end{array}$$

so that the linearly increasing drift rate additionally had an offset d_B in the direction of higher value, i.e., E(t) = ±d_B + c*t. This model thus also had 4 free parameters: tnd, b, c, and d_B. This DRB-IE model has the unique feature that the decision variable tends initially to be launched towards the choice bound of the high-value option, and as time passes is increasingly driven by the growing sensory evidence influence captured in c*t, which eventually comes to dominate. The strength of the payoff bias d_B relative to the evidence growth rate c and bound b governs when and in what proportion of trials the decision variable hits one of the two bounds before this shift in influence can occur.

A neurally plausible basis for a biased and dynamically changing drift rate is the value-based modulation of sensory responses of neurons tuned to the color alternatives, which respond initially non-selectively but with increasing color-selectivity over time (Figure 4A). We implemented this in the Value Modulated Sensory Response (VMSR) model, whose DV dynamics are governed by:

$$\begin{array}{lll}\mathrm{x}(\mathrm{t})=\mathrm{x}(\mathrm{t}-1)+\mathrm{E}(\text{t)}\ast \text{dt}+\mathrm{N}(0,\mathbf{s}\ast \text{sqrt}(\text{dt})),& \mathrm{x}(0)={\mathbf{z}}_{\mathbf{B}}+\text{rand}1\ast \mathbf{sz};& (\text{High-value}\text{cue})\\ \mathrm{x}(\mathrm{t})=\mathrm{x}(\mathrm{t}-1)+\mathrm{E}(\text{t)}\ast \text{dt}+\mathrm{N}(0,\mathbf{s}\ast \text{sqrt}(\text{dt})),& \mathrm{x}(0)=-{\mathbf{z}}_{\mathbf{B}}+\text{rand}1\ast \mathbf{sz};& (\text{Low-value}\text{cue})\end{array}$$

where in this case the evidence E(t) is the difference in activity between the neural population coding for the presented cue color (“preferred” response Rp), and the population coding for the color not presented (“unpreferred” response Ru):

$$\mathrm{E}(\mathrm{t})=(1+\mathrm{B})\ast \text{Rp}(\mathrm{t})-(1-\mathrm{B})\ast \text{Ru}(\mathrm{t}).$$

Here, a modulatory bias B is applied which is positive for high-value cues (B = M_B) and negative for low-value cues (B = −M_B). For parsimony, we take the preferred response under neutral conditions to be a step function,

$$\begin{array}{cc}\text{Rp}(\mathrm{t})=\mathbf{Rm},& \mathrm{t}>=0\\ \text{Rp}(\mathrm{t})=0,& \mathrm{t}<0\end{array}$$

and the unpreferred response to be an equal-sized step-up followed by a decrease to zero according to a cumulative Weibull function,

$$\begin{array}{ll}\text{Ru}(\mathrm{t})=\mathbf{Rm}\ast \exp (-(\mathrm{t}/\mathbf{tau})^\mathbf{k}),\hfill & \mathrm{t}>=0\hfill \\ \text{Ru}(\mathrm{t})=0,\hfill & \mathrm{t}<0\hfill \end{array}$$

where Rm is the response magnitude and tau and k dictate the timing and shape of the drop-off to zero. We chose a cumulative Weibull function here so that both the duration of the initial non-color-selective phase of the response and the steepness with which selectivity then develops are free to be determined by the behavioral fit. Because Rp(t) and Ru(t) are initially commensurate when they begin, with the unpreferred response falling after a short time, when biased with a negative B<0, the differential evidence E(t) will initially start out negative and gradually increase and switch to positive values, thus generating the dynamic shift of influence and characteristic “turn-around” effect associated with our biased, increasing evidence model (DRB-IE; Figure 2D). The VMSR model thus has 8 parameters in total: non-decision time tnd, bound b, Response magnitude Rm, Weibull parameters tau and k, modulatory bias M_B, and starting point bias z_B, and variability sz.

Finally, we constructed a “Standard Dual-bias” model for a fair comparison against the VMSR model in terms of capturing both behavior and neural decision signal dynamics, using a combination of mechanisms included in previous work using conventional, stationary-evidence diffusion models. The DV dynamics for this model was governed by:

$$\begin{array}{lll}\mathrm{x}(\mathrm{t})=\mathrm{x}(\mathrm{t}-1)+(\mathbf{di}+{\mathbf{d}}_{\mathbf{B}})\ast \text{dt}+\mathrm{N}(0,\mathbf{s}\ast \text{sqrt}(\text{dt})),\hfill & \mathrm{x}(0)={\mathbf{z}}_{\mathbf{B}}+\text{rand}1\ast \mathbf{sz};\hfill & (\text{High-value}\text{cue})\hfill \\ \mathrm{x}(\mathrm{t})=\mathrm{x}(\mathrm{t}-1)+(\mathbf{di}-{\mathbf{d}}_{\mathbf{B}})\ast \text{dt}+\mathrm{N}(0,\mathbf{s}\ast \text{sqrt}(\text{dt})),\hfill & \mathrm{x}(0)=-{\mathbf{z}}_{\mathbf{B}}+\text{rand}1\ast \mathbf{sz};\hfill & (\text{Low-value}\text{cue})\hfill \end{array}$$

where in this case on any given trial the drift rate di, which is constant over time within that trial, is taken from a normal distribution di = N(d, sd), and the non-decision time takes on a different value for high-value responses, tndH, than for low-value responses, tndL. The Standard Dual-bias model thus had 8 free parameters: tndH, tndL, b, z_B, sz, mean drift rate d, bias in drift rate d_B and across-trial variability in drift rate sd.

Model fitting and Comparison

All of the above models were fit to the behavioral data by Monte-Carlo simulation methods on a subject by subject basis, using a SIMPLEX routine [61] implemented in the Matlab function fminsearchbnd with a G² likelihood ratio statistic as the cost function [62]. The G² value of each model indicates the goodness of fit between simulated and actual behavioral data for each model. It is calculated as

$$G^2=2\left({\displaystyle \sum _{v=1}^2{n}_v{\displaystyle \sum _{o=1}^2{\displaystyle \sum _{q=1}^6{p}_{\mathit{voq}}\log \frac{p_{\mathit{v},\mathit{o},\mathit{q}}}{{\pi }_{\mathit{v},\mathit{o},\mathit{q}}}}}}\right)$$

where p_v,o,q and π_v,o,q are the observed and predicted proportions of responses in bin q of outcome o (correct/error) of condition v (high-value/low-value cue), respectively. n_v is the number of valid trials per value condition. q indexes six RT bins divided by the quantiles [0.1 0.3 0.5 0.7 0.9]. Thus, the model fit aims to account for RT distributions and choice probabilities simultaneously. Models with a lower G² value fit the data more accurately. We achieved the fit of each model via a 2-step process, in the first of which we used a version of the model with the bound b fixed to a value of 1 and the within-trial noise s free to vary, for the reason that several parameters such as starting point bias z_B and variability sz have obvious natural limits determined by this bound, thus facilitating choice of parameter limits for the bounded SIMPLEX algorithm. For this first step we generated a large number of random points in a wide parameter space and saved the first 100 of them that when simulated produced mean RT and accuracies somewhere in the rough vicinity of pooled empirical ones, and carried out an fminsearch with a large tolerance (20) and few iterations (max 500) for each of these 100 starting vectors. In the second step we identified the parameters of the best fitting model among those 100, translated them to a model version in which s was fixed to 0.1 and b free to vary - the most common choice in the literature - by applying the appropriate scaling factors, and then refined the fit using a further fminsearch run with smaller tolerance (10) and more iterations (5000).

Model comparison across the four reduced-parameter models and between the VMSR and Standard Dual-bias models was carried out by computing Bayesian information criterion (BIC) which can be derived from G² and penalizes against greater numbers of free parameters:

$$\mathit{BIC}=G^2+f\log (\mathrm{n})$$

where f is the number of free parameters and n is the total number of trials. BIC values are plotted for each subject and each of the simplified models in Figure S1, and for the VMSR versus Standard Dual-bias models in Figure S3.

Decision signal simulations from model fits

Once the best-fitting parameters were determined for each behavioral model, we simulated 1000 trials for each condition and each subject using identical processes as detailed above in order to generate simulated average DV trajectories for an illustrative set of conditions/outcomes for each of the four simplified models (Figure 2F–I) and for the VMSR and Standard Dual-bias models (Figure 4, Figure S3). The purpose of the waveform simulations of Figure 2F–I was to provide a concrete demonstration of the qualitative differences between the predictions of the 4 simplified models, explicating the dynamic features that should be present at the onset of accumulation in the real decision signals given the presence of starting point bias (difference in starting level across cues of different value); starting point variability (differences in starting level across low-value cued trials resulting in fast/slow correct responses versus errors); and biased, increasing evidence (turn-around effect in low-value cues with slow, correct responses). For this purpose it was sufficient to time-lock the simulated decision variable to the onset of accumulation and disregard non-decision time. We simulated DV trajectories for the four conditions of correct high-value-cued trials, correct low-value-cued trials with relatively fast and relatively slow RT, and incorrect low-value-cued trials, because it was in the low-value trials that behavioral outcome varied most in speed and accuracy. By design, error trials were those in which the DV reached the lower bound. For each trial, the decision variable signal was made to linearly drop back to zero over a 60 msec time period following the crossing of a bound, thus complying with what is known to occur for real signatures of differential motor preparation (LRP), though this isn’t strictly necessary for this examination of initial DV starting-level and deflection dynamics. After sorting trials of each simulation into four categories (high-value correct, low-value correct fast, low-value correct slow and low-value error), we averaged them across subjects.

To more comprehensively simulate decision signal waveforms representing differential motor preparation (LRP) and motor-independent evidence accumulation (CPP) from the more complex VMSR and Standard Dual-bias models we took the additional step of allocating a portion of the non-decision time for each subject to the period intervening between threshold crossing and response according to the peak latency of the response-locked LRP (−52.4 ± 19.3 ms). The remaining portion of non-decision time was interposed between cue onset and the start of the accumulation process. In the case of the VMSR model, this coincided with the start of the idealized sensory responses. Each trial’s baseline level of differential motor preparation was determined by the starting point of the DV on that trial, arising from the value bias plus variability in starting point. We simulated CPP waveforms by tracing the absolute value of the cumulative sensory evidence, without regard to starting point shifts due to value or random biases, which we assume enter at the motor preparation level [63]. This is based on the fact that the CPP builds with positive polarity regardless of which of the two competing decision alternatives is chosen or which is correct, and the consequent suggestion that it reflects the activity of two neural populations encoding cumulative evidence for the competing alternatives, which each project positive-polarity potentials on the scalp [30]. Since, despite this assumed summation of two accumulator processes, the CPP reaches a stereotyped threshold level at response for urgency-free, continuous monitoring decisions [27,28], the most parsimonious account of its generating mechanisms is that when one population has accumulated evidence, the other remains silent, in which case the CPP measured on the scalp would simply reflect the absolute value of differential cumulative evidence. In this scheme, the two populations together encode a single, signed quantity of cumulative differential evidence, similar to the way each Cartesian axis of a vector representation (e.g. wind velocity) has been proposed to be encoded by two neural populations in simple population coding schemes [67,68]. Whereas we made the LRP fall to zero upon the action-initiating threshold crossing, we allowed the CPP to continue reflecting cumulative evidence, based on the assumption that responses in this task are often made considerably earlier than the time at which subjects can confidently judge the stimulus, thus encouraging continued stimulus evaluation, and that the ultimate threshold is set at the motor level rather than directly at the intermediate level of evidence accumulation [63]. This continued evidence accumulation was simulated in the same way regardless of response correctness.

All of these assumptions were implemented identically for the VMSR and Standard Dual-bias models.

In order to quantitatively compare the VMSR and Standard Dual-bias models in terms of how well they captured empirical decision signal dynamics, we computed a correlation coefficient for each signal (LRP and CPP) and each individual subject between the real and simulated waveforms, concatenating the cue-locked time range of −50 to 350 msec with the response-locked time range of −250 to 0 msec. We then simply used a paired t-test for each signal to test whether the differences in correlation between the two models was significantly different than zero.

It is important to note that all assumptions for the model simulations were based on prior proposals regarding how evidence accumulation and/or bias are represented in the LRP and CPP. The choice of a cumulative Weibull function for the unpreferred neural response was based on the desire to have a short but non-zero time period during which the neural populations respond equivalently under neutral conditions, after which the unpreferred response decays smoothly to baseline levels (given a value of zero without loss of generality). Our aim was to test correspondence in qualitative patterns reflecting value biases and increasing evidence and we did not make adjustments to fit the simulated traces to the empirical ones with the one exception of apportionment of non-decision time to before and after the accumulation process based on individual LRP peak latencies. Thus, the closeness of the match between real and simulated LRP and CPP waveforms for the VMSR model was not expected based only on the method of simulation, and indeed was significantly worse for the Standard Dual-bias model.

Electrophysiological data processing and analysis

Continuous electrophysiological data were recorded in DC mode from 97 scalp electrodes with a sampling rate of 500 Hz and an online reference at site FCz (ActiCap, Brain Products). All offline analysis was performed using in-house scripts written in Matlab (MathWorks, Natick, MA) with raw data-reading, channel interpolation and topographic plot functions from the EEGLAB toolbox [64]. In offline analysis, continuous data were first linearly detrended and low-pass filtered by convolution with a 58-tap hanning-windowed sinc function designed to provide a 3-dB corner frequency of 41.5 Hz and a local extremum of attenuation coinciding with the mains frequency (60 Hz), while also avoiding phase distortion and ringing artifacts [65]. Data were epoched from −500ms to 1400ms relative to target onset and baseline-corrected with respect to the pre-target interval −100ms to 0ms. Channels with excessively high variance with respect to neighboring channels and channels that saturated during the task were identified by visual inspection of channel variances and interpolated (spherical splines). Epoched data were then re-referenced to the average of all channels. Trials on which the maximum absolute potential exceeded 60 u μV were rejected from the analysis.

The lateralized readiness potential (LRP) was measured as the difference in event-related potential (ERP) between electrodes at standard 10–20 sites C3 and C4 [26]. Specifically, the ERP waveform ipsilateral to the correct response-hand was subtracted from the contralateral waveform so that the upward positive direction signified motor preparation favoring the correct, sensory-cued response alternative. Signals were baseline-corrected with respect to a time period just prior to target presentation, when value was not yet mapped to actions. The centro-parietal positivity (CPP) was measured directly from electrode site CPz [28], with baseline correction relative to a 100-ms interval at cue onset. Cue-locked (−200 to 500 ms with respect to the color-change of the fixation square) and response-locked (−400 to 50 ms with respect to the button press) ERPs were extracted from these longer single-trial epochs, and an additional offline low-pass filter up to 10 Hz (4th-order Butterworth) was applied prior to plotting in the intervals 0 to 380 ms and −280 to 30 ms, respectively (Figure 3). In order to test for the qualitative predictions of the alternative models, we plotted the LRP for four separate behavioral conditions: incorrect responses to low-value cues, correct responses to high-value cues and fast and slow correct responses to low-value cues (split by median reaction time). High-value error trials were not analyzed further due to low trial numbers (43.8 ± 27.1 per subject). The same procedure was used for supplementary Figure S3 except that the correct low-value cue trials were divided into 4 RT bins.

QUANTIFICATION AND STATISTICAL ANALYSIS

Statistical analyses

To test for trends across subjects in the quality of quantitative behavioral fits of the competing models, we carried out a 2 × 2 repeated-measures ANOVA with the factors of bias type (Starting point bias vs drift rate bias) and fast-error mechanism (starting point variability vs increasing evidence). Repeated-measures t-tests and one-way ANOVAs were employed as appropriate to test for the presence of starting point bias, variability and turn-around effect in the LRP waveforms. Significance was defined as p<0.05.

For all error bars and waveform error-bar shading, between-subject variability has been factored out so that only variance relevant to a repeated-measures experimental design remains. Note that for the VMSR model, error shading is not directly comparable to real LRP waveform error shading as it does not include systematic noise that is present in EEG recording (Figures 3 and 4).

In order to test for the presence of the expected signature of the “turn-around” effect on slow, correct, low-value trials, we conducted t-tests between the amplitude in a time period in which the signature was expected to occur (in line with model simulations) to an appropriate preceding timeframe within that same single condition. For the LRP, we tested the interval 170–200 ms against the preceding interval 0–30 ms. Importantly, the expected signature is different for the CPP because whereas the LRP reflects a signed, differential index of the decision process, the CPP climbs positively for cumulative evidence for either alternative (correct or incorrect), thus instead reflecting the absolute value of differential cumulative evidence. This means that whereas initial accumulation of wrong evidence is unmistakable in the negative-going deflections in the LRP, in the CPP these register as positive, just like correct evidence, and the critical signature of the turn-around is actually the dip it undergoes after the correct evidence has begun to exceed the wrong evidence, bringing cumulative differential evidence back to baseline levels. Though the CPP undergoes this characteristic dip on each single trial, due to its narrow extent and temporal jitter this comes out more like a plateau in average decision variable simulations of the VMSR model (see Figure 4C in main text). Thus, in order to test for either a dip or plateau, we tested against the null hypothesis that the CPP rises from start to finish monotonically without such a dip or plateau. For each subject a straight line was first computed by connecting the onset (taken as 100 ms for all subjects) to the individual peak in the stimulus-locked CPP and we tested for a difference in amplitude in the interval 240–270 ms (where the dip/plateau is expected to occur) compared to the interval 170–200 ms (where buildup has stopped for wrong evidence and the turn-around starts in the LRP) after subtracting away this line.

DATA AND SOFTWARE AVAILABILITY

The data and algorithms used for the analysis and modeling are available under DOI:10.17605/OSF.IO/BG8S4 (ARK c7605/osf.io/bg8s4)