Abstract
An important open question in neuroeconomics is how the brain represents the value of offers in a way that is both abstract (allowing for comparison) and concrete (preserving the details of the factors that influence value). Here, we examine neuronal responses to risky and safe options in five brain regions that putatively encode value in male macaques. Surprisingly, we find no detectable overlap in the neural codes used for risky and safe options, even when the options have identical subjective values (as revealed by preference) in any of the regions. Indeed, responses are weakly correlated and occupy distinct (semi-orthogonal) encoding subspaces. Notably, however, these subspaces are linked through a linear transform of their constituent encodings, a property that allows for comparison of dissimilar option types. This encoding scheme allows these regions to multiplex decision related processes: they can encode the detailed factors that influence offer value (here, risky and safety) but also directly compare dissimilar offer types. Together these results suggest a neuronal basis for the qualitatively different psychological properties of risky and safe options and highlight the power of population geometry to resolve outstanding problems in neural coding.
SIGNIFICANCE STATEMENT To make economic choices, we must have some mechanism for comparing dissimilar offers. We propose that the brain uses distinct neural codes for risky and safe offers, but that these codes are linearly transformable. This encoding scheme has the dual advantage of allowing for comparison across offer types while preserving information about offer type, which in turn allows for flexibility in changing circumstances. We show that responses to risky and safe offers exhibit these predicted properties in five different reward-sensitive regions. Together, these results highlight the power of population coding principles for solving representation problems in economic choice.
Introduction
We are often faced with the need to choose between options that differ qualitatively. To make such choices, it is helpful to have access to an abstract representation of the value of each option. Much of neuroeconomics is predicated on the assumption that such representations must exist and, in particular, that they exist in the form of specialized abstract value neurons (Platt and Glimcher, 1999; Padoa-Schioppa and Assad, 2006; Lau and Glimcher, 2008; Kennerley et al., 2009; Peters and Büchel, 2010; Kolling et al., 2016). Such neurons would, by definition, have firing rates that covary monotonically with the values of offers regardless of their other qualities. That is, two options with identical subjective values would elicit the same firing rate response in an abstract value neuron even if they differed in other ways. For example, if asked to evaluate a Ferris wheel ride and an equally valued cupcake, a value neuron will necessarily have the same response to both. One advantage of the abstract neuron representational system is that a downstream decoder can produce good choices simply by identifying the neuron or neurons that encode the highest value and selecting the appropriate choice. However, while such an encoding scheme has its advantages, it has a major weakness, it is inflexible in situations where the relative importance of these features changes.
More broadly, the abstract value neuron idea is out of step with modern thinking on how information is coded in populations of neurons. While the “neuron doctrine” is focused on the idea that information explicitly encoded in the firing rates of single neurons, the “population doctrine” emphasizes the flexible and expressive power of neuronal populations (Saxena and Cunningham, 2019; Ebitz and Hayden, 2021). From the perspective of populations, abstraction can come from geometry; specifically, from transformable subspaces (Elsayed et al., 2016; Tang et al., 2020; Yoo and Hayden, 2020; Libby and Buschman, 2021). This way of generating abstraction has the major advantage of allowing a population of neurons to simultaneously carry details about the features of the offers and to have an abstract representation of value.
We hypothesized that neurons in core value regions use the population approach to encode a value signal. To test this hypothesis, we studied encoding of risky and safe options in a two-option risky choice task. Psychologists have established that risky and safe options are treated differently. We have a strong preference for safe options (Holt and Laury, 2002; Heilbronner, 2017), risky options differentially activate motivational and emotional factors (Loewenstein et al., 2001; Slovic et al., 2004, 2007; Lerner et al., 2015), and risk differs qualitatively from certainty among dimensions like the prospect of learning and satisfaction of curiosity (Binde, 2013; Heilbronner and Hayden, 2013; Wang and Hayden, 2021). Population geometric encoding would allow for value comparison while also maintaining information that allows risk and surety to be treated differently. It is well established that neural responses in core value regions scale with the probability (and thus the subjective value) of risky offers (McCoy and Platt, 2005; Kennerley et al., 2009; So and Stuphorn, 2010; Raghuraman and Padoa-Schioppa, 2014; Strait et al., 2014; Azab and Hayden, 2017). Perhaps surprisingly, little of this research has addressed the critical question of whether risky and safe offers use the same coding scale, and none of it has used a dense sampling of probability space needed to retrospectively identify equally valued risky and safe offers and test how their codes are related.
We examined responses of neurons in five core reward areas in a gambling task (Fig. 1A). We found that responses of single neurons to safe offers are not just distinct but are unrelated to responses evoked by risky offers. Instead, risky and safe offers are encoded by overlapping sets of neurons using distinct and semi-orthogonal subspaces. At the same time, these subspaces are linkable through simple, linear transformations. These results are consistent with the hypothesis that the brain's core value regions strategically use subspace orthogonalization to flexibly partition different offer types in a way that allows for value comparison. More generally, these results endorse the utility of population perspectives in tackling classic problems in neuroscience.
Materials and Methods
Surgical procedures
Subjects were male macaques. All procedures were approved by either the University Committee on Animal Resources at the University of Rochester or the institutional animal care and use committee (IACUC) at the University of Minnesota. Animal procedures were also designed and conducted in compliance with the Public Health Service's Guide for the Care and Use of Animals. All of the animals were handled according to approved institutional animal care and use committee (IACUC) protocols (#2005-61938127A) of the University of Minnesota. The protocol was approved by the Committee on the Ethics of Animal Experiments of the University of Minnesota (NIH permit number: A3456-01). All surgery was performed under controlled anesthesia. Six male rhesus macaques (Macaca mulatta) served as subjects. A small prosthesis for head fixation was used. Subjects were habituated to laboratory conditions and then trained to perform oculomotor tasks for liquid rewards. We place a Cilux recording chamber (Crist Instruments) over the area of interest (for breakdown, see below, Behavioral tasks). We verified positioning by magnetic resonance imaging with the aid of a Brainsight system (Rogue Research). Animals received appropriate analgesics and antibiotics after all procedures. Throughout both behavioral and physiological recording sessions, we kept the chamber clean with regular antibiotic washes, and we sealed them with sterile caps.
Recording sites
We approached our brain regions through standard recording grids (Crist Instruments) guided by a micromanipulator (NAN Instruments). All recording sites were selected based on the boundaries given in the Paxinos atlas (Paxinos et al., 2000). In all cases we sampled evenly across the regions. Neuronal recordings in Orbitofrontal cortex (OFC) were collected from subjects P and S (Yoo and Hayden, 2020); recordings in Ventromedial prefrontal cortex (vmPFC) were collected from subjects B and H (Strait et al., 2014); recordings in Perigenual anterior cingulate cortex (pgACC) were collected from subject B and V (Maisson et al., 2021); recordings from posterior cingulate cortex (PCC) were collected from subject P and S (Wang et al., 2022); and recording in ventral striatum (VS) were collected from subject B and C (Strait et al., 2016). For details, see Figure 1B.
We defined OFC 13 as lying within the coronal planes situated between 28.65 and 34.05 mm rostral to the interaural plane, the horizontal planes situated between 3 and 6.5 mm from the brain's ventral surface, and the sagittal planes between 5 and 14 mm from the medial wall. The coordinates correspond to area 13m in Paxinos et al. (2000).
We defined vmPFC 14 as lying within the coronal planes situated between 29 and 44 mm rostral to the interaural plane, the horizontal planes situated between 0 and 9 mm from the brain's ventral surface, and the sagittal planes between 0 and 8 mm from the medial wall. These coordinates correspond to area 14m in Paxinos et al. (2000).
We defined pgACC 32 as lying with the coronal planes situated between 30.90 and 40.10 mm rostral to the interaural plane, the horizontal planes situated between 7.30 and 15.50 mm from the brain's dorsal surface, and the sagittal planes between 0 and 4.5 mm from the medial wall (Fig. 1B). Our recordings were made from central regions within these zones, which correspond to area 32 in Paxinos et al. (2000).
We defined PCC 29/31 as lying within the coronal planes situated between 2.88 mm caudal and 15.6 mm rostral to the interaural plane, the horizontal planes situated between 16.5 and 22.5 mm from the brain's dorsal surface, and the sagittal planes between 0 and 6 mm from the medial wall. The coordinates correspond to area 29/31 in Paxinos et al. (2000).
We defined VS as lying within the coronal planes situated between 20.66 and 28.02 mm rostral to the interaural plane, the horizontal planes situated between 0 and 8.01 mm from the ventral surface of the striatum, and the sagittal planes between 0 and 8.69 mm from the medial wall. Note that our recording sites were targeted toward the nucleus accumbens core region of the VS.
We confirmed recording location before each recording session using our Brainsight system with structural magnetic resonance images taken before the experiment (0.5 voxels). We confirmed recording locations by listening for characteristic sounds of white and gray matter during recording, which in all cases matched the loci indicated by the Brainsight system with an error of ∼1 mm in the horizontal plane and ∼2 mm in the z-direction.
Electrophysiological techniques
Either single (FHC) or multicontact electrodes (V-Probe, Plexon) were lowered using a microdrive (NAN Instruments). Individual action potentials were isolated on a Plexon or Ripple. Neurons were selected for study solely based on quality of isolation; we never preselected based on task-related response properties. All collected neurons for which we managed to obtain at least 300 trials were analyzed; no neurons that surpassed our isolation criteria were excluded from analysis.
Eye-tracking and reward delivery
Eye position was sampled at 1000 Hz by an infrared eye-monitoring camera system (SR Research). Stimuli were controlled by a computer running MATLAB (MathWorks) with Psychtoolbox and Eyelink Toolbox. Visual stimuli were colored rectangles on a computer monitor placed 57 cm from the animal and centered on its eyes (Fig. 1A). A standard solenoid valve controlled the duration of juice delivery. Solenoid calibration was performed daily.
Behavioral tasks
Six macaques performed in the risky choice task. Both tasks made use of vertical rectangles indicating reward amount and probability. We have shown in a variety of contexts that this method provides reliable communication of abstract concepts such as reward, probability, delay, and rule to monkeys (Hayden et al., 2010; Blanchard et al., 2014).
Risky choice task
The task presented two offers on each trial. A rectangle 300 pixels tall and 80 pixels wide represented each offer (11.35° of visual angle tall and 4.08° of visual angle wide; Fig. 2A). Two parameters defined gamble offers, stakes and probability. Each gamble rectangle was divided into two portions, one red and the other either gray, blue, or green. The size of the color portions signified the probability of winning a small (125 μl, gray), medium (165 μl, blue), or large reward (240 μl, green), respectively. We used a uniform distribution between 0 and 100% for probabilities. The size of the red portion indicated the probability of no reward. Offer types were selected at random with a 43.75% probability of blue (medium-stakes) gamble, a 43.75% probability of green (high-stakes) gambles, and a 12.5% probability of gray options (safe offers).
On each trial, one offer appeared on the left side of the screen and the other appeared on the right. We randomized the sides of the first and second offer. Both offers appeared for 400 ms and were followed by a 600-ms blank period. After the offers were presented separately, a central fixation spot appeared, and the subject fixated on it for 100 ms. Next, both offers appeared simultaneously and the animal indicated its choice by shifting gaze to its preferred offer and maintaining fixation on it for 200 ms. Failure to maintain gaze for 200 ms did not lead to the end of the trial but instead returned the monkey to a choice state; thus, subjects were free to change their mind if they did so within 200 ms (although in our observations, they seldom did so). Following a successful 200-ms fixation, the gamble was resolved, and the reward was delivered. We defined trials that took >7 s as inattentive trials and we did not include them in the analyses (this removed ∼1% of trials). Outcomes that yielded rewards were accompanied by a visual cue: a white circle in the center of the chosen offer. All trials were followed by an 800-ms intertrial interval with a blank screen.
Estimation of subjective value equivalence
We calculated the indifference point between safe and risky offers. For each subject, independently, we fitted a sigmoidal function to the distribution of choices (safe or risky) across the full range of risky offer probabilities:
Statistical methods
We constructed peristimulus time histograms by aligning spike rasters to the presentation of the first offer and averaging firing rates across multiple trials. We calculated firing rates in 20-ms bins, but we analyzed them in longer (500 ms) epochs. Some statistical tests of neuronal activity were only appropriate when applied to single neurons because of variations in response properties across the population. We have used this epoch in all our past research on this and similar tasks (Strait et al., 2014, 2015, 2016; Azab and Hayden, 2017, 2018, 2020). We have found that this epoch provides a good characterization of functional responses and allows for fair comparison across brain regions. We used it here for those reasons and because adherence to a single preplanned epoch of interest reduces the likelihood of inadvertent “p-hacking.”
Shuffle analysis
to understand the values of correlations that we would obtain by chance, in the absence of a true effect, is it useful to repeat our analysis on dummy data. To do so, we performed a specific control procedure developed by Elsayed et al. (2016). In this analysis, we wished to preserve the features of each neuron without removing that information, so we shuffled across time, meaning that we randomly sorted the spikes to occur at random times, but maintained their linkage to the neuron that generated them. This procedure then gave dummy data that we performed our correlation analyses on. More specifically, we shuffled the data from across all three of the previously computed response matrices (safe, matched-medium, and matched-large) and computed the alignment index between pairs of shuffled sets. Because the data are randomized, any alignment index at or below this dummy threshold would be considered at least semi-orthogonal. We then, following standard logic of bootstrap analyses, repeated this process over 1000 randomizations. Then, to test for significance, we computed the 99% confidence interval across iterations; a value outside of this range can therefore be said to be significant at p < 0.005 (given that our t test is assumed to be one-tailed).
Population overlap
We adapted a previously published procedure (Azab and Hayden, 2017). For each neuron, we isolated both medium-stakes and high-stakes risky offers with subjectively equal values to the respective subject. For each trial, we computed the average firing rate across a 500-ms window, starting from 100 ms after the appearance of the first offer (see above). We then regressed the firing rates on the corresponding offer probability on each trial to produce a β weight representing that neurons degree of linear encoding of offer probability. For safe offers, we were limited by the fact that there is only a single probability value (100%) for safe offers. Therefore, we also computed the average firing rate from a 500-ms window that preceded the start of the trial by 100 ms. For each trial, we computed the difference between the offer response and the pretrial response, to represent the degree of linear encoding for the safe offer type. Finally, we performed a correlation between the absolute value of the safe offer encoding and the absolute value of the risky offer β weights. We plotted the two encoding weights against each other and computed the line of best fit, given the correlation coefficient.
Decoding analysis
We built a pseudo-population of pseudo-trials. First, we isolated neural responses to the safe offers and the equivalent risky offers. Then, we collapsed the firing rates for each trial into an average for the 500-ms offer 1 epoch. We randomly selected 1000 samples for each neuron, under both risk conditions, resulting in two n X 1000 matrices (one for each offer type; safe vs risky), where n represents the number of neurons recorded from each region. We used an elastic-net logistic GLM to decode safe versus risky trials. Elastic-net offers regularization over the decoding weights, including both L1 and L2-norms of both Lasso and Ridge regression, respectively. Elastic-net GLMs can provide parameter estimates with reduced bias and variance when there is collinearity in the predictors (Zou and Hastie, 2005). Specifically, the Lasso regularization has the effect of shrinking weakly contributing predictors to 0. The ridge regularization has the effect of reducing the size of all predictors. The elastic-net represents a mixture of both these costs in determining GLM parameters. We fit the GLM across 1000 within-sample bootstraps. On each iteration, a randomly selected subset, constituting half of each original safe versus risky offer type pseudo-population, was used to fit the model and the other half was used for cross-validation. The resulting cross validation provided a measure of accuracy with which the elastic-net logistic regression model was able to decode safe versus risky offer types from the cross-validation set of firing rates.
We performed this entire procedure on 1000 bootstrapped iterations of randomly constructed pseudo-populations. We averaged the accuracy across these out-of-sample bootstrapped cross-validations and calculated the standard error across iterations. This procedure was performed independently for safe versus medium-risky and safe versus high-risky, and was performed independently for each subject. Finally, the entire procedure was performed on shuffled data, to confirm that the expected prediction accuracy for a binary decoder of randomized data would be 50%. To do this, each original pseudo-population was instead comprised of a randomly selected trial, regardless of the offer type. Additionally, each pseudo-trial was randomly assigned a label as one of the possible offer types. We then compared the average decoding accuracy between safe-risky and the shuffled data, using a standard two-sample t test, with Bonferroni corrections.
Subspace alignment
We followed the procedure described previously by Elsayed et al. (2016). Specifically, for each structure, we separated offers and neural responses by their risk profile (safe and equivalent risky offer of medium-stakes and high-stakes), as described previously. For each neuron, we identified two factors to incorporate into a single condition: time and offer position. Time included the same 500-ms period following the onset of offer 1 and preceding the onset of offer 2. Time was segmented into 20-ms bins. For each 20-ms bin, we computed the mean firing rate across trials on which the offer was positioned on either the left or right of the screen. Thus, we constructed a condition (time X offer position) X neuron matrix of mean firing rates; that is, a 50 × n-neurons matrix. One such matrix was constructed for safe offers, one for medium, and one for high-stakes risky offers of equivalent value. Firing rates in prefrontal areas of macaques tend to be sparse. So, we smoothed these matrices using a Gaussian filter, with a σ equal to one. We smoothed across columns in the matrix; in other words, we smoothed each neuron individually. We then normalized the smoothed matrices, by computing the z score within each cell, to account for differences in encoding scaling between neurons.
Next, we performed a principal component analysis, using eigenvalue decomposition, on the safe response matrix, providing a transformation matrix into which we projected both the safe response matrix and each of the risky response matrices. We computed the explained variance because of each of the principal components. We performed the same process of dimensionality reduction for each of the risky offers, projecting both the safe response and corresponding risky response data into the resulting principal component spaces (medium-stakes and high-stakes risky response each into their own principal component spaces). To determine whether the subspaces were aligned, we computed an alignment index:
In Results, we described the difficulty associated with interpreting alignment indices given the structure of the data, and the corresponding need to use shuffling procedures to determine the effective upper and lower limits of measured alignment. To implement this procedure, we tested whether the safe and risky subspaces were more or less orthogonal, relative to randomly sampling within the space of this fixed correlation structure. We concatenated all safe and risky offer data into a single matrix. We then computed the covariance matrix and performed an eigenvalue decomposition for the covariance matrix. We then randomly sampled subspaces that were aligned to the fixed correlation structure of the response space, as follows:
Data and materials availability
All analyses were performed using stock MATLAB functions, and no custom code was generated. Data used for all reported analyses are available on Dryad (https://doi.org/10.5061/dryad.ttdz08kx9).
Results
Behavior
On each trial of the risky choice task, a macaque (M. mulatta) subject chose between two offers that varied in magnitude and probability (Fig. 1A; Strait et al., 2014; see Materials and Methods). Safe offers (12.5% of offers) provided a small volume of juice (125 μl) with 100% certainty. Risky offers provided either a medium (165 μl, 43.75% of offers) or large (240 μl, 43.75% of offers) volume of juice with a defined probability (0–100%, 1% increments). The offer types for the two offers were generated at random and independently on each trial. Our dataset consists of responses from six subjects in 315 recording sessions and consists of 211,884 trials (average 672.6 trials per session). Target regions for neural recordings are illustrated in Figure 1B and anatomic boundaries are provided in the Materials and Methods.
Task, targeted structures, behavior, and calculation of equivalent risky and safe values. A, Structure of our risky choice task (Strait et al., 2014). Task consists of 400-ms offer 1 presentation, a 600-ms blank period, a 400-ms offer 2 presentation, another 600-ms blank period, then a fixation spot and, on fixation, reappearance of both offers and choice (indicated by saccade). For each offer, the magnitude of the associated reward (stakes) is indicated by the bottom color (green, high or blue, medium) of the stimulus. The probability of being rewarded is indicated by its size. B, Anatomical positions of our brain regions of interest: OFC (purple), vmPFC (purple-pink), pgACC (pink), PCC (gold), and VS (gray). C, Likelihood of choosing the first offer as a function of its value relative to the second (specifically, for signed value difference). Sigmoid fits of raw binary data shown (see Materials and Methods). Gray lines: individual subjects; black line: group average. In this and subsequent panels, a horizontal dashed line indicates the indifference point (the point at which choices are 50/50). D, Likelihood of choosing a safe option as a function of the probability of the risky option for medium (blue) and high (green) stakes offers. All data were analyzed on a subject-by-subject basis, so only data for one example subject (subject B) are shown. Other subjects showed similar patterns. Vertical black lines indicate the probability used as the SV-equivalence point for the subject [the arrow points to the indifference point for medium-stakes (blue) and high-stakes (green) risky offers]. E, Same as D, except data are separated for left and right offers. Side of presentation does not affect choice much. F, Same as D, except data are separated by trials that were in the first (early) or second (late) half of a session.
Subjects consistently performed at a high level, were modestly risk-seeking, and did not differ from each other qualitatively (Fig. 1C). Details of species-typical behavior in this task are given elsewhere (in most detail in Farashahi et al., 2018, 2019). Results of these analyses are not repeated here, except to confirm, as we have previously shown, that subjects' behavior is quite stable and consistent within subjects, both across and within sessions, and across subjects and sessions (Fig. 1D–F). Indeed, all subjects showed the same behavioral patterns we have observed using this task in past studies.
All analyses in this paper make use of subjective values instead of expected values. To identify the relative values of safe offers, we computed the risky-safe indifference point. We calculated, separately for each subject and separately for medium and large stakes offers, the likelihood that the subject would choose the safe offer as a function of the probability associated with the risky offer. We then calculated indifference using a standard approach in which we fit the resulting data with a sigmoid curve and calculated the point at which the best-fitting curve crossed the indifference line (see Materials and Methods).
As in all of our past studies using this task, all subjects were risk-seeking. The cross-subject average indifference point for medium-stakes risky offers corresponded to an offer probability of 0.33 ± 0.05 (SD). A risk-neutral subject would have had an indifference point at 0.76. The average indifference point for high-stakes risky offers corresponded to an offer probability of 0.11 ± 0.04. A risk-neutral subject would have had an indifference point of 0.52. As we have observed many times, preferences were highly consistent across many contexts. For example, indifference points are similar for the first and second offers (offer 1: medium: 0.34; high: 0.11; offer 2: medium: 0.22; high = 0.11), for offers made early and late in the session (early: medium: 0.29; high: 0.09; late: medium: 0.31; high: 0.13), and when risky offers appear on the left or right (left: medium: 0.27, high: 0.11; right: medium: 0.36, high: 0.12). Data for an example subject are shown in Figure 1D–F. Data for individual subjects are shown in Figure 2.
Indifference points for each of our five subjects individually. y-axis shows the probability (from 0% to 100%) associated with a risky offer that is equivalent in subjective value, as assessed by preference indifference. Data are separated by whether the offer is medium (left) or high (right) stakes). Subjects generally prefer risky offers, as indicated by the fact that points tend to be on the lower y-values of the graph. Preferences are lower for high stakes than for medium-stakes, indicating that subjects took account of stakes. Subject indifferent to stakes would show no difference between the medium and high stakes conditions. Error bars are not shown because, because of the large number of trials, they are smaller than the bars.
Lack of pupil size effects
Because our central research goal is to ascertain the influence of offer type on neural activity, we wanted to ensure that our effects were not because of attention or arousal. We therefore examined the relationship between two proxies for attention, looking at time and pupil size in four of our subjects (subjects B, H, P, and S; these are the subjects for which we had pupil size recorded). We found no detectable relationship. Specifically, during the offer 1 epoch, subjects fixated the first offer for 198.5 ms if it was risky and for 199.1 ms if it was safe. These two are not different (p = 0.85 for the group, p-values were the same or higher for all four subjects). During the offer 2 epoch, subjects fixated the second offer for 222.4 ms if it was risky and for 220.9 ms if it was safe (again, these are not different, p = 0.73). During the choice epoch, we calculated the total looking time and, again, found no differences (302.7 ms for chosen risky and 302.5 for chosen safe, p = 0.93). Nor were any of the individual subjects' fixation time differences statistically significant for any of these measures (p > 0.05 in all cases). These results do not appear to be dependent on our choice of epoch; we used longer analysis (1 s) epochs for each of these analyses and found qualitatively matched results.
During the offer 1 epoch, the pupil size did not differ for risky and safe options in any of the four subjects (p = 0.10 for subject S and p > 0.5 for the other three subjects). Specifically, relative to the baseline value (defined as 0), risky offer-evoked pupil size was −0.92 z score units (for all subjects averaged); the corresponding value for safe offers was 0.93 z score units. Likewise, during the offer 2 epoch, relative to the baseline value (again, defined as 0), risky offer-evoked pupil size was −0.81 z score units (for all subjects averaged); the corresponding value for safe offers was 0.80 z score units. These are not different for any subject (p = 0.21 for subject H, p = 0.39 for subject P, p > 0.5 for the other two subjects). Finally, during the choice epoch, relative to the baseline value of 0, risky choice-evoked pupil size was −0.79 z score units (for all subjects averaged); the corresponding value for safe offers was also 0.79 z score units. These are not different for any subject (p > 0.5 in all cases).
No special subpopulations for risky-and safe-preferring neurons
We recorded responses of 843 neurons in five brain regions while our subjects performed the risky choice task: vmPFC (area 14, 156 neurons), OFC (area 13, 157 neurons), pgACC (area 32, 255 neurons), PCC (area 29/31, 151 neurons), and VS (nucleus accumbens, 124 neurons). We recorded in two subjects for all areas, although different subjects were used for the different areas (see Materials and Methods). Detailed analyses of responses to risky offers were reported previously for vmPFC and VS (Strait et al., 2014, 2015). We have never previously examined neural responses to safe offers.
For these and subsequent analyses, we used each individual's subjective indifference point. We then defined a range of probabilities (±2.5%, total range of 5.0%) and treated all offers within that range as being subjectively equivalent to the safe value. We subsequently checked for robustness by repeating the following analyses using a larger range (±5%, total range of 10%) but because we found no qualitative differences, we do not report those results. We also repeated all analyses using within-session estimates of subjective value (rather than within-subject, across-session). Again, because we found no qualitative differences, we do not report those results.
Example neurons vmPFC.70 and pgACC.17 (Fig. 3A,B) showed responses to safe offers whose magnitude could not be predicted from responses to risky offers. Additional sample cells, from each targeted area, including those that showed positive and negative monotonic tuning for risky values and, again, unrelated responses to safe offers (Fig. 3C–E).
Responses of single neurons. This figure shows the average responses of sample neurons to safe and risky offers of differing values, as well as the average response similarity rates. A, Peristimulus time histogram from mean firing rates of sample neuron vmPFC.70. Each line indicates the average response across offers of a given risk profile (gray: all safe offers; blue: all medium-stakes risky offers; green: all large stakes risky offers). The gray shaded box indicates the 1-s period from which the 500-ms epoch 1 analysis window was extracted, where the onset of the first offer is time-locked to 0 s. B, This is a plot of data collected from a sample neuron pgACC.17, which showed a response to safe offers that was statistically different from the response to equivalent risky offers. Depicted are the average responses to medium-stakes (left; blue) and high-stakes (right; green), separated by probability ranges of 0.05. The black point indicates the average response of the given neuron to safe offers (error bars denote the SEM across responses to safe offers). The diagonal black line indicates a fitted regression line, showing positive monotonic tuning. C–E, Same as B but demonstrating sample cell responses to an assortment of medium-stakes and high-stakes offers from across all target areas.
If neural responses to risky and safe offers differ, one reason may be that they make use of different subpopulations of neurons, ones specialized for risky and safe values. To determine whether the brain makes use of separate subpopulations of neurons specialized for encoding the values of safe and risky options, we adapted the approach we developed previously (Azab and Hayden, 2017, 2018). Specifically, we have shown that if there are two categorically distinct populations of neurons, defined by distinct tuned variables (e.g., selectivity for offer 1 and selectivity for offer 2), then correlating the unsigned regression weights (betas) will produce a negative (<0) correlation. Conversely, if the two variables are found in a single population, then correlating their unsigned betas will produce a positive correlation (Fig. 4A). If the variables are distributed at random in the sample of neurons, then correlation will produce a null result. Here, to perform this calculation, we regressed probability for each risky option against firing; for safe options, we computed the response evoked by the presentation of the safe offer by comparing the safe-evoked response to the pretrial baseline firing rate (see Materials and Methods). We found that, in the OFC, the degree to which the neural populations encode safe offers was positively correlated with the extent to which they encode matched risky offers (medium-stakes: r = 0.49, p < 0.001; high-stakes: r = 0.29, p < 0.001; Pearson's correlation; Fig. 4B). We found similar results in all five other areas (p < 0.001, in all cases, Pearson's correlation; Fig. 4C–F).
Overlapping populations encode both safe and risky offers. A, Conceptual schematic indicating the analytical approach for identifying functional subpopulations. The right panels propose the slope of a best fit line describing the encoding formats for each population type. B, For OFC (area 13). Left panel, Scatter plots represent the absolute degree of encoding of safe offers plotted against that of the medium-stakes risky offers for each neuron (each point corresponds to data from one neuron). The black line indicates the line of best fit for the correlation between the absolute degree of encoding of safe and risky offers across neurons. Red bars indicate the 99% confidence interval for the line of best fit. The inlaid numbers indicate the Pearson correlation coefficient (r) and the significance (p). Right panel, Same as left, but comparing safe offer encoding and high-stakes risky offer encoding. C–F, Same as B, but for vmPFC (area 14), pgACC (area 32), PCC (area 29/31), and ventral striatum, respectively.
Note that, because of the non-normality of the data, it is possible that these correlations are unduly driven by the few outlier datapoints. We therefore repeated these correlations using Spearman's correlation. All reported correlations are still significant. Specifically, for the safe versus medium, we find values of OFC: ρ = 0.433; p = 0.007; vmPFC: ρ = 0.501; p < 0.0001; pgACC: ρ = 0.318; p = 0.008; PCC: ρ = 0.498; p < 0.001; VS: ρ = 0.544; p < 0.001. For the safe versus high, we find values of OFC: ρ = 0.288; p = 0.01; vmPFC: ρ = 0.401; p < 0.008; pgACC: ρ = 0.438; p = 0.001; PCC: ρ = 0.543; p < 0.001; VS: ρ = 0.511; p < 0.001. These results are consistent with more detailed studies from our lab using these and similar datasets showing no intrinsic categories in responses (Blanchard et al., 2018).
Offer type (safe vs risky) is decodable in all five regions
Our principal question is how the brain might be able to disambiguate two offers that are behaviorally indistinguishable but constituted by qualitatively distinct risk features. Neurons in these regions may, and likely are, tuned for multiple variables (Rigotti et al., 2013; Raposo et al., 2014; Fusi et al., 2016; Blanchard et al., 2018; Johnston et al., 2020). This fact is important because if we assume a neuron is only tuned to a single variable, we may underweight or ignore its other quite real tunings, which would introduce biases, likely strong ones, into our analysis. To deal with this problem, we use an elastic-net regression, which is a regularization procedure that modifies a generalized linear model (GLM) with two regularization terms: the L1 and L2 norms of both Lasso and Ridge regression, respectively. The Lasso term increases sparsity by penalizing weakly contributing neurons, while the Ridge term increases variance by reducing the size of all predictors. The elastic net GLM can provide parameter estimates with reduced bias and variance when there is collinearity in the predictors (Zou and Hastie, 2005). We used the model as a logistic decoder to predict whether an offer was safe or risky based on the fitted model for population firing rates, using a bootstrap approach (see Materials and Methods).
We found that in the OFC, the elastic-net was able to decode the safe versus medium-risky offer type from population activity with 94.9% accuracy from subject P and 90.4% accuracy in subject S (safe versus high risky: 91.2% accuracy in subject P; 87.9% accuracy in subject S). We found similar results in the other five brain areas (Fig. 5).
Safe and equivalently valued risky offers are readily decoded. Decodability for safe and risky offers is high in all areas for both medium-stakes and high-stakes gambles. Shuffled data refers to decodability of randomly assigned safe/risky labels to neural responses that are completely shuffled across trials and cells. Bars represent the mean decoding accuracy across out of sample cross-validations Error bars indicate the standard error across cross-validations. The horizontal gray line indicates the chance decoding accuracy level.
To determine whether decoding accuracy was significant, we repeated the process after shuffling the pseudo-populations by randomly selecting from each offer type and each offer epoch, and randomly assigning a safe or risky label to the response (see Materials and Methods). In OFC, the decoding accuracy from shuffled data were 49.8% for both subject P and subject S, which constitutes the expected random 50/50 guess for a binary decoder. Decoding safe versus medium-risky offer type was significantly higher than chance (Student's t test, subject P: t = −861.4, p < 0.001; subject S: t = −1058.8, p < 0.001; even after Bonferroni correction). We found similar results in all five other areas, across subjects and risky offer magnitudes (p < 0.001 in all cases).
Orthogonal response subspaces for value-matched risky and safe offers
The underlying connectivity of neuron ensembles can effectively constrain activity to be correlated, rendering a low-dimensional subspace (Gallego et al., 2017; Ebitz and Hayden, 2021). Successfully decoding the safe versus risky identity of equally valued offers could then be accomplished through their organization into distinct subspaces. We adapted previously used approaches to characterize the uniqueness of safe and matched-risky subspaces (Elsayed et al., 2016; Yoo and Hayden, 2020). Specifically, we projected risky offer responses into the safe offer response subspace and computed the explained variance for each (Fig. 6).
Subspace alignment between safe and equivalent risky offers. A, For each structure, we performed a principal components analysis and projected the resulting dimensions for medium (top row) and high (bottom row) stakes offers onto the corresponding ones for safe offers. If subspaces for the risky and safe codes were the same (or collinear), then the projections would match. Instead, the projections for the risky offers (lighter lines) are consistently lower than the control values (the projections for the safe offers, darker lines). In other words, the fact that the lighter (risky) lines are lower than the darker (safe) ones indicates that the two types of offers are encoded in semi-orthogonal subspaces. B, This finding is summarized in panel B, which gives a summary of the difference between the average shuffle alignment index and either the safe-medium (left bar) or the safe-high (right bar) alignment index. Error bars indicate the standard error across computed differences. Note that these data represent the difference between the measured value and the shuffle alignment index; this means that data with higher shuffle alignment indices will appear lower as a result.
When we project data from the risky subspaces (medium and high), they have lower values than when we project the safe values into the same subspace (Fig. 6A), indicating the presence of coding orthogonality. If the brain used collinear codes for risky and safe offers, then the two sets of lines would be the same height. A plot of the difference between the average, for both the medium- and high-stakes conditions (Fig. 6B), shows that in all cases, these are greater than zero. If the risky and safe subspaces were collinear, the differences here would be precisely equal to zero. Note that these data represent the difference between the measured value and the shuffle alignment index; this means that data with higher shuffle alignment indices will appear lower as a result. Indeed, these results should not be taken to imply that the safe versus high alignments are consistently greater than the safe versus medium alignments, although it appears this way. However, these plots are made relative to the shuffled values, which have consistent differences related to the idiosyncratic properties of the statistics of their spike trains. Instead, the only strong conclusion that can be drawn from these data are that both medium and high risky offers are consistently encoded in subspaces semi-orthogonal to those of safe offers. Note also that the projection weights are not necessarily reflective of the amount of orthogonality in a linear sense, meaning two indices that are close to each other but significantly different are not necessarily quantitatively similar.
We used these projections to quantify the extent to which subspaces were aligned (Aidx; see Materials and Methods). Purely orthogonal subspaces would have an alignment of 0; collinear ones would have an alignment of 1.0; semi-orthogonal subspaces would have an intermediate value between 0.0 and 1.0. Note that semi-orthogonal subspaces would be sufficient to produce separate representations and would satisfy our hypotheses. The alignment analysis indicated that in OFC, for example, comparisons of safe and medium-stakes risky response subspaces had an alignment index of Aidx = 0.231. Safe and high-stakes subspaces had an Aidx = 0.266.
These numbers do not account for the measurement limits imposed the by structure of the data. We performed two control procedures, one to determine the practical upper measurable alignment index, and the other to determine the practical lower measurable alignment index. To determine the upper limit, we performed a control procedure to measure a threshold below which indices would be considered at least semi-orthogonal (see Materials and Methods; Elsayed et al., 2016). To do this, we shuffled the data from across all three response matrices (safe, matched-medium, and matched-large) and computed the alignment index between pairs of shuffled sets (see Materials and Methods). We repeated this process over 1000 randomizations. Then, to test for significance, we computed the 99% confidence interval across iterations; a value outside of this range can therefore be said to be significant at p < 0.005 (given that our t test is assumed to be one-tailed). We found that the average shuffled alignment index in OFC was Aidx = 0.276. Both the safe-medium and safe-high alignment indexes were below the 99% confidence interval (0.271–0.281) and thus both significant at p < 0.005 (or p < 0.01 with a two-tailed t test).
To determine the lower limit, we repeated the shuffle procedure, but randomized across all axes. This analysis approach, in effect, identifies the alignment index we would observe whether the data were entirely orthogonal. In OFC, the alignment index across totally shuffled data were Aidx = 0.091 ± 0.009 (99% confidence interval). The safe-medium and safe-high alignment indexes are both quite a bit greater than this noise floor (both significant at p < 0.005). In other words, response subspaces for safe and equally valued risky offers in OFC are less orthogonal than random data, indicating that they are partially, albeit not completely, aligned. We found similar results in all structures (below the 99% confidence interval, in all cases; p < 0.005). We can conclude, then, that these responses have an intermediate level of alignment.
Note that it is worth reading these numbers with a good degree of caution. The space of orthogonality measures is inherently nonlinear, for example, a value of 0.8 is not in any meaningful sense twice as collinear as a value of 0.4. Indeed, a quantitative interpretation of these numbers would require strong assumptions about the decoding process used by downstream structures. Nonetheless, measures of statistical significance here are interpretable and meaningful. Thus, when we say that the measured values are intermediate, we do not mean that they lie roughly halfway between orthogonal and collinear; instead, we mean that they are neither at one extreme nor the other. Moreover, it is worth pausing to emphasize what can and cannot be inferred about orthogonality of subspaces from these numbers. On one hand the results of the significance tests can be interpreted in a conventional way, a significant difference between and upper and lower bound can be taken as evidence of semi-orthogonality. On the other hand, the magnitude of the effect comes with several caveats that make interpreting it, beyond the results of significance tests, difficult. This magnitude depends on, for example, the signal-to-noise ratio in that population of neurons, their baseline firing rate, and the particular nature of their distribution.
Finally, we asked how neural responses to medium-stakes and high-states risky offers related to each other. If the qualitative difference in codes for risky and safe offers reflect, even in part, the qualitative differences between risk and safety, then two different risk offers should differ less than the risky and safe offers. We therefore repeated the above analyses on medium-stakes and high-stakes risky offers. In OFC, we found that the medium-stakes and high-stakes risky responses had an alignment index of Aidx = 0.275. This value is significantly greater than the value of the medium-risky and high-risky indices (0.231 and 0.266, respectively, see above). Moreover, this value is within the confidence interval for shuffled data (0.271–0.281) and is not significantly different from chance (p = 0.29). We found similar effects for the other brain areas. Specifically, in vmPFC, the difference in Aidx between the both medium-stakes and high-stakes and risky-safe is positive (0.051 and 0.018 for medium and high; p < 0.01 for both; for this and the following, we used the bootstrap test described above). In pgACC, these numbers were 0.046 and 0.017 (p < 0.01 for both); in PCC, the numbers were 0.041 and 0.009 (p < 0.01 for both). In VS, the numbers were 0.038 and 0.007 (p < 0.01 for medium and p < 0.05 for high).
Orthogonal risky and safe response subspaces can be transformed to be aligned
Above, we demonstrated that the population subspaces for risky and safe offers are semi-orthogonal (see cartoon in Fig. 7A). A primary question, then, is to what extent can these subspaces be transformed into a common subspace that would aid in their comparison? Such a common subspace could provide a mechanism for comparing offers of equal value (Yoo and Hayden, 2020). We reasoned that if the response subspaces could be transformed such that their hyperplanes were collinear, then the axis along which they become aligned is most likely the axis that describes their relative values (Fig. 7B).
Subspace rotational transformations and canonical correlations. A, A cartoon demonstrating an example of orthogonal (left) and aligned (right) hyperplanes projected onto the first three dimensions (cf. Yoo and Hayden, 2020). B, A procedural schematic demonstrating the process of linear rotational transformation, to align subspaces by maximizing the Pearson's correlation coefficient via canonical correlation.
To investigate whether our data here obey these principles, we performed a canonical correlation analysis on the subspace loadings (i.e., the principal component projection weights, see Materials and Methods; Sussillo et al., 2015; Gallego et al., 2018) for the first three principal components from the safe and risky offer response matrices. We also randomly shuffled the subspace loadings 1000 times and performed the same canonical correlation analysis. In OFC, we found that safe and equally valued medium-stakes offer response subspaces could be significantly aligned to correlation of r = 0.53 (p = 0.023, bootstrap rank test). Safe and matched-high stakes risky offer response subspaces reached a maximal correlation of r = 0.61 (p < 0.01). We found similar results across the remaining five brain areas in our dataset (p < 0.05 in all cases; Fig. 8). Specifically, we found that in all five brain areas, subspaces are linked. As above, we repeated these canonical correlation analyses, but for the two risky offers (medium and high stakes). They are also transformable. Specifically, in OFC, we find a correlation of r = 0.62 (p = 0.011, bootstrap rank test). In vmPFC, we find a correlation of r = 0.69 (p = 0.008, bootstrap rank test); in pgACC, we find a correlation of r = 0.71 (p = 0.007, bootstrap rank test). In PCC, we find a correlation of r = 0.64 (p = 0.013, bootstrap rank test); finally, in VS, we find a correlation of r = 0.72 (p = 0.007, bootstrap rank test).
Scatter plots, for each structure, of projections of medium and safe offer responses (top row) and high and safe offer responses (bottom row) projected into safe offer response subspaces. Plotted are projections onto the first two principal component loadings for the original (darker circles) and transformed (lighter pluses) projections. The inlaid coefficients are the Pearson's correlation coefficients between projections on the first two principal component loading for the original (r1) and transformed (r2) responses. The lines denote the best-fit line for the corresponding correlation coefficients (r1: darker line; r2: lighter line). Asterisks denote significant correlations for p < 0.05 in bootstrap rank tests.
One limitation of this analysis is that it is based on neural responses occurring during the first offer period only. That is, our analysis assumes implicitly that neural responses to the first offer will be identical to those for the second offer, and that cross-trial subspaces will allow comparison. This assumption can be tested. We therefore performed an analysis using neural responses to the second offers. Specifically, we performed a canonical correlation analysis on safe (offer 1) and equally valued middle-risk (offer 2), on safe (offer 1) and equally valued high-stakes (offer 2), as well as the reverse. In all cases, we found that the principle of transformability was preserved. Specifically, in OFC, we find a correlation of r = 0.65 (p = 0.009, bootstrap rank test). In vmPFC, we find a correlation of r = 0.68 (p = 0.01, bootstrap rank test); in pgACC, we find a correlation of r = 0.70 (p = 0.006, bootstrap rank test). In PCC, we find a correlation of r = 0.62 (p = 0.016, bootstrap rank test); finally, in VS, we find a correlation of r = 0.67 (p = 0.010, bootstrap rank test).
Discussion
We find that neural responses to risky and safe offers use distinct encoding subspaces in five core reward areas. Our task uses a single safe value and a dense sampling of 99 different risky values (1–99%), meaning we can use behavior to precisely infer equivalent risky and safe values. Indeed, we find that risky and safe options are encoded in distinct (semi-orthogonal) ensemble subspaces. The risky and safe subspaces, while different, are systematically related so that there is a ready transformation between them; this transformability means that a downstream area can straightforwardly compare the values of the two offers despite the differences in the codes used to represent them. We conjecture that this distinct but transformable code can allow the brain to achieve two conflicting goals, that is, to maintain a separate representation of different offer types, but also to allow for their direct comparison on a single scale.
Typically, neuroeconomic models are concerned with developing theories to explain how we compare disparate option types (Plassmann et al., 2007; Padoa-Schioppa, 2011; D.J. Levy and Glimcher, 2012). While abstraction is important, the more general problem faced by the brain is a bit more complex, it must use a system that simultaneously maintains options' features (so that they can be used to influence behavior if needed) while also allowing for comparison of dissimilar features. For example, circumstances may change rapidly so that surety is more or less valuable; the decision-maker must be able to selectively change the relative value of risky options. The use of linked but semi-orthogonal subspaces for qualitatively different feature types allows this goal to be accomplished quickly. Our results, then, support the notion that these ostensible value regions do contribute to evaluation and comparison processes in choice, but do so in a way that maintains information about the qualities of the options, in addition to their values.
Our results have some bearing on longstanding discussions about the nature of abstract value representation and their role in facilitating comparison (Platt and Glimcher, 1999; McCoy and Platt, 2005; Padoa-Schioppa and Assad, 2006; Kennerley et al., 2009; Peters and Büchel, 2010; So and Stuphorn, 2010; Padoa-Schioppa, 2011; Montague and Berns, 2002; Raghuraman and Padoa-Schioppa, 2014; Kolling et al., 2016; Hayden and Niv, 2021). Traditional neuroeconomics proceeds from the “neuron doctrine,” which, in neuroeconomics, implies that comparison across offer types requires the existence of neurons whose responses are the same for equally valued offers of different types. By contrast, the “population doctrine” allows for other forms of equivalence, including translatable but distinct subspaces (Elsayed et al., 2016; for review, see Saxena and Cunningham, 2019; Ebitz and Hayden, 2021). Equally valued risky and safe offers are a well-known example of offer types with qualitatively different features that can be readily compared, and for this reason, have long been the focus of studies about value representation (I. Levy et al., 2010; Tobler and Weber, 2014). Thus, our results both raise the possibility of and add empirical support for the idea that qualitatively different values can be compared in a way that occurs at the population level and does not require value neurons. To speculate a bit, subspace orthogonalization may offer more encoding flexibility than single neuron encodings because they can be rapidly adjusted to context without requiring rewiring or retraining; they may also be more robust to certain forms of error or degradation.
The concept of neural subspaces originates in motor cortex and can be used to explain how motor preparation is kept separate from action, so as to allow for fast responding while preventing precocious movement (Kaufman et al., 2014; Elsayed et al., 2016). We have argued that the same principles apply to core value regions, and that subspace orthogonalization allows for the separation of evaluation and comparison processes (Yoo and Hayden, 2020). The present results suggest a new use for subspace partitioning, keeping track of two qualitatively different types of rewards in a format so that the details of their properties (here, risky vs safe) are maintained, while also allowing for ready comparison in a downstream structure.
Orthogonalized subspaces are an emergent property of neurons with mixed selectivity. Mixed selectivity, or the simultaneous tuning to multiple features, is an important property of neurons in prefrontal and associated regions (Barak et al., 2013; Rigotti et al., 2013; Fusi et al., 2016). Mixed selectivity is the foundation of many useful properties, including feature binding, learning, abstraction, and generalization, and code morphing (Parthasarathy et al., 2017; Bernardi et al., 2020). Notably, a good deal of the analysis of physiological data assumes, either explicitly or tacitly, that neurons have singular tuning, not mixed selectivity. For example, approaches that divide neurons into specific categorical types tend to classify those neurons according to which feature drives them most strongly. By doing so, these approaches zero out those neurons' tuning for other parameters, and make the population appear more categorical than it really is. That work, however, risks misinterpretation of neural data, precisely because of the remarkable power of mixed selectivity (Fusi et al., 2016).
One highlight of our study is that we were able to directly compare responses in five brain regions in the same task. This fact means that we can ask questions about the unique functional properties of each region, such as whether different regions contribute differentially to evaluation, comparison, and action selection elements of choice. Here, we replicate our past findings showing that functional properties are largely qualitatively the same (Strait et al., 2015, 2016; Maisson et al., 2021; Fine and Hayden, 2022). This does not necessarily prove these areas are strictly overlapping in their functions, nor does it prove that economic functions are purely distributed. Indeed, there is a quite a good deal of evidence of functional specialization in the brain (Wilson et al., 2010; Rushworth et al., 2011; Passingham and Wise, 2012). Instead, we propose that, to some extent, economic functions are a general feature of prefrontal cortex (and related structures like PCC and VS), and that, for core economic functions, these regions function as a hierarchy, rather than as a series of modules (Hunt and Hayden, 2017; Yoo and Hayden, 2018; Fine and Hayden, 2022; Maisson et al., 2021). Moreover, our results here extend these previous ideas and suggest that these regions not only have similar coding repertoires but use similar computational algorithms (here, judicious control of subspace) to implement them.
Warren Weaver (1982) and Lola Lopes (1987) have both argued, in their work on decision-making and risk, that it is a mistake to assume that two options with the same expected value (including subjective expected value) are or should be treated the same way by decision-makers. There are many natural situations in which a risky prospect is quite different from a safe one, even if they are matched for subjective value. To give some examples, risky options elicit emotions, and anxieties, promote learning, reward curiosity, generate error signals, require maintenance of an eligibility trace, may be associated with exploratory rather than exploitative states, require additional brain computations, and may in some cases differentially elicit executive control (Loewenstein et al., 2001; McCoy and Platt, 2005; Slovic et al., 2007; Platt and Huettel, 2008; Barseghyan et al., 2013). For these reasons, risky and safe options ought to elicit at least somewhat distinct brain responses, even when they are matched for subjective value. Our results show that in five brain areas, they elicit strikingly different response patterns. This does not mean that an abstract single-neuron value code does not exist in the brain; it may be found, for example, in a hierarchically later area, such as dorsal anterior cingulate cortex (dACC; Cai and Padoa-Schioppa, 2012), or supplementary motor areas (So and Stuphorn, 2010). Another possibility, however, is that the brain makes do without an abstract value subspace, and instead achieves comparison through alternative means (Vlaev et al., 2011; Yoo and Hayden, 2018; Hayden and Niv, 2021; Walasek and Brown, 2021).
Footnotes
This work was supported by the by National Institute on Drug Abuse Grant P30 DA048742-01A1 (to B.Y.H. and J.Z.), the National Institute for Biomedical Imaging Grant P41 EB027061 (to B.Y.H. and J.Z.), and the UMN AIRP Award (B.Y.H. and J.Z.). We thank Geoffrey Schoenbaum for helpful discussions. We also thank Marc Mancarella, Caleb Strait, and Tommy Blanchard for assistance with data collection; Sarah Heilbronner for help with anatomy; and the rest of the Hayden and Zimmermann labs for valuable discussions.
The authors declare no competing financial interests.
- Correspondence should be addressed to Benjamin Y. Hayden at benhayden{at}gmail.com
