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Inferences on a multidimensional social hierarchy use a grid-like code

Nature Neuroscience volume 24, pages 1292–1301 (2021)Cite this article

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Abstract

Generalizing experiences to guide decision-making in novel situations is a hallmark of flexible behavior. Cognitive maps of an environment or task can theoretically afford such flexibility, but direct evidence has proven elusive. In this study, we found that discretely sampled abstract relationships between entities in an unseen two-dimensional social hierarchy are reconstructed into a unitary two-dimensional cognitive map in the hippocampus and entorhinal cortex. We further show that humans use a grid-like code in entorhinal cortex and medial prefrontal cortex for inferred direct trajectories between entities in the reconstructed abstract space during discrete decisions. These grid-like representations in the entorhinal cortex are associated with decision value computations in the medial prefrontal cortex and temporoparietal junction. Collectively, these findings show that grid-like representations are used by the human brain to infer novel solutions, even in abstract and discrete problems, and suggest a general mechanism underpinning flexible decision-making and generalization.

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Fig. 1: Behavioral training procedure and hypothesized neural representations.
Fig. 2: Partner selection task.
Fig. 3: Building a 2D representation of a social hierarchy.
Fig. 4: Hexagonal modulation for inferred trajectories.
Fig. 5: GP and value comparison.

Data availability

The data that support the findings of this study are available on the Open Science Framework (https://doi.org/10.17605/osf.io/w96yk)75. Unthresholded group-level statistical maps are available on NeuroVault (identifiers.org/neurovault.collection:9352)76.

Code availability

The code that supports the findings of this study is available on the Open Science Framework (https://doi.org/10.17605/osf.io/w96yk). The associated behavioral training protocols51 and code are available on the Open Science Framework (https://doi.org/10.17605/osf.io/bnc3w)77. The behavioral data during the fMRI experiment were collected in Presentation v21.0 (Neurobehavioral Systems). The task for behavioral training was programmed in PsychoPy v3.0 (ref. 78). Data analysis was performed in MATLAB v.2018a (MathWorks). We used SPM (v12) (ref. 79) (Wellcome Centre for Human Neuroimaging), MarsBaR toolbox v0.44 (ref. 80), Circular Statistics Toolbox v31i10 (ref. 73) and RSA toolbox (v3)81 for analyzing neuroimaging data.

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Acknowledgements

We thank K. Yang, J. Barajas and X. He for behavioral training assistance. We thank D. Fox, R. Chaudhuri, T. Muller and M. Garvert for helpful comments on earlier drafts and discussions of the paper. This work was supported by a National Science Foundation CAREER Award (1846578), NIMH (1R01MH123713-01A1) and the University of California, Davis.

Author information

Authors and Affiliations

  1. Center for Mind and Brain, University of California, Davis, Davis CA, USA

    Seongmin A. Park, Douglas S. Miller & Erie D. Boorman

  2. Center for Neuroscience, University of California, Davis, Davis CA, USA

    Douglas S. Miller

  3. Department of Psychology, University of California, Davis, Davis CA, USA

    Erie D. Boorman

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  1. Seongmin A. Park
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  2. Douglas S. Miller
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Contributions

S.A.P. and E.D.B. conceived the project and designed the experiments. S.A.P. and D.S.M. trained participants and collected data. With supervision from E.D.B., S.A.P. and D.S.M. analyzed data. S.A.P. and E.D.B. wrote the paper.

Corresponding authors

Correspondence to Seongmin A. Park or Erie D. Boorman.

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Peer review information Nature Neuroscience thanks Nicolas Schuck and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Multidimensional scaling (MDS).

Visualization of the group representation of the social hierarchy in a 2-D space using MDS on the neural activity extracted from the HC and EC ROIs. There were considerably fewer presentations of individuals at the rank positions 1 and 16, making their estimates less reliable, and so these less frequently sampled individuals were excluded in computing the MDS. The 2-D representations (top) can be factorized into two 1-D hierarchies: competence (middle) and popularity (bottom). The lines indicate the individuals at the same rank in the social hierarchy. The thicker the line, the higher the rank in the given dimension. a. The MDS computed from the mean pattern dissimilarity across participants after matching the number of samples per face. Numbers indicate face position as shown in the true hierarchy in the Model on the left. Blue colors correspond to competence the dimension and red to the popularity dimension. The distances and angles between the estimated individual locations in the HC and EC MDS are significantly correlated with the pairwise Euclidean distances (Spearman’s ρ = 0.84 for HC and ρ = 0.63 for EC) and cosine angles (ρ = 0.93 for HC and ρ = 0.71 for EC) in the true 4×4 social hierarchy structure, compared to random configurations (both p<0.01 compared to 1000 random permutations). b. The MDS estimated from the mean neural activity patterns including every presentation of the 14 face stimuli. Associated with Fig. 3g and Extended Data Fig. 2.

Extended Data Fig. 2 Representational similarity analysis (RSA) including all events of face stimuli presentation.

a. RSA including neural responses to all the events associated with 14 individuals in the social hierarchy. Consistent with the results of the RSA based on down-sampling shown in Fig. 3c, we found effects of Euclidean distance on the pattern dissimilarity in the HC and EC but not in M1. The HC-EC system utilizes a 2-D relational cognitive map to represent the social hierarchy rather than representing 1-D map (τA of Euclidean distance (gray) > τA of one-dimensional rank distance in competence dimension (blue) and in popularity dimension (red)). **, pFWE<0.001 after correction for the number of bilateral ROIs (n=4) with the Bonferroni-Holm method; n.s., p>0.05, uncorrected. b. The dissimilarity between activity patterns estimated in bilateral HC and EC increases in proportion to the true pairwise Euclidean distance between individuals in the 2-D abstract social space (left, gray). The dissimilarity between activity patterns increases not only with the 1-D rank distance in the competence dimension (middle, blue) but also the 1-D rank distance in the popularity dimension (right, red). Methods and notation are identical to Fig. 3. Box, lower and upper quartiles; line, median; whiskers, range of the data excluding outliers; +, the whiskers’ range of outliers.

Extended Data Fig. 3 The analysis procedure to examine the effects of grid-like codes.

a. Identifying brain regions sensitive to hexagonal symmetry across the whole brain without aligning to the entorhinal grid orientation, ϕ. To identify hexagonally symmetric signals, we adopted previously developed methods from a previous study14. We used a Z-transformed F-statistic to examine the BOLD activity modulated by any linear combination of sin(6θ) and cos(6θ). Hexagonal modulation was found in brain regions including in medial prefrontal cortex (mPFC; peak MNI coordinate, [x,y,z]=[2,66,-4], z=5.58), posterior cingulate cortex/precuneus (PCC; [2,-50, 36], z=3.19), bilateral posterior parietal cortex (PPC; [36,-46, 62], z=4.27 for right; [-38,-50, 50], z=3.81 for left), left lateral orbitofrontal cortex (OFC; [-42,44,-8], z=3.79), and retrosplenial cortex (RSC; [x,y,z] = [2,–54,28], z = 3.45) at a threshold pTFCE<0.05 (whole brain TFCE correction), as well as the right entorhinal cortex (EC; [26, -10, -40], z=2.80) at a threshold, pTFCE<0.05 (corrected within a priori anatomically defined EC region of interest (ROI)62,63). For visualization purposes, the maps are thresholded at z>2.6 (p<0.005 uncorrected). b. We did not use the results of F-test for statistical inference but to functionally define ROIs in EC and mPFC for future tests. The ROIs were defined within the anatomically defined masks in the EC62,63 and mPFC72 by including effects at a threshold of z>2.3, which corresponded to p<0.01. Using these independently defined ROIs, we then tested if the grid orientation estimated in the ROI was consistent across separate fMRI sessions in an unbiased way. It is important to note that the ROIs were defined from results of a statistically independent analysis, which was not dependent on the grid orientation. c. Illustrations of the cross-validation (CV) procedure. By splitting a dataset for estimating the grid orientation, ϕ, from another dataset to test for hexagonal modulation for inferred trajectories, θ, we could test for brain regions where activity was modulated by cos(6[θ-ϕ]) in alignment with the grid orientation estimated from the independent dataset for each participant. The CV was possible because the grid orientation, ϕ, is thought to be relatively stable but different across participants, whereas the direction of inferred trajectories θ varies only according to the position of F0, F1, and F2 (left panel). We performed a CV procedure both from fMRI sessions acquired within the same day (middle panel), and also from fMRI sessions acquired more than a week apart (right panel). d. We estimated the angle of the F1F2 vector (χ) and inputted the cos(6[χ-ϕ]) at the time of F2 presentation as an additional parametric regressor into GLM2. We did not find any brain areas encoding the angles of F1F2 vectors, except at a reduced threshold, in the bilateral somatosensory cortex ([x,y,z] = [-52,-14, 56], t=3.33 and [58,-8,50], t=3.17, p<0.005 uncorrected). e. Consistency of grid orientation in EC across sessions acquired more than a week apart. Concretely, in alignment with the EC grid orientation estimated from sessions acquired on a different day, we found hexadirectional modulation in a network of brain regions, including the mPFC ([-2, 36, -8], t=5.04), PCC ([6,- 58, 30], t=3.68), and TPJ ([-36, -64, 22], t=4.06) at our whole brain corrected threshold pTFCE<0.05, as well as in EC ([36, -10, -38], t=4,21) at pTFCE<0.05, small-volume-corrected in our a priori EC ROI (Supplementary Table 5b).

Extended Data Fig. 4 Hexagonal modulation for inferred trajectories only for the novel pairs when presented for the first-time.

a. Among all the 88 (83) pairs (F0-F1 and F0-F2) presented during the partner selection task, those pairs that were not presented during behavioral training (always in the absence of feedback) but presented during fMRI for the first time are shown: 83 pairs in white were presented for the first-time for 4 participants; 88 pairs in white and gray were shown for the first-time for 17 participants. The grid effects were tested only for those pairs presented for the first time during the day1 scan. We extracted the mean activity and GP effects for each bin, restricted to when each pair was presented for the first time to participants. b and c. Associated with Fig. 4b and c. The mean EC (left panel) and mPFC (middle panel) activity in 30° bins aligned to the EC grid orientation estimated from different blocks acquired in the same day’s scan (b) and the EC grid orientation acquired from a different day’s (day 2) scan (c) with six-fold symmetry. Right panel shows formal comparison of trajectories aligned and misaligned with both methods of computing the EC grid orientation. We found greater activity for the aligned pairs compared to the misaligned pairs to the EC grid orientation in EC and mPFC ROIs (one-sample t-test). d. Associated with Fig. 5b. The GP effects in mPFC and bilateral TPJ are modulated by the grid alignment of the inferred trajectories aligned with the EC grid orientation. The GP effects are greater for the aligned pairs compared to misaligned pairs, even when they were presented for the first time (one-sample t-test). Box, lower and upper quartiles; line, median; whiskers, range of the data excluding outliers; +, the whisker’s range of outliers. **, p<0.01; *, p<0.05.

Extended Data Fig. 5 Individual differences in the relationship between the gridness and the effects of growth potential.

a. In addition to the relationship between EC gridness (β \(\cos (6[\theta - {\phi}])\)) and GP effects (βGP) in bilateral TPJ that we present in Fig. 5c (upper left), we found a marginal positive correlation between the mPFC gridness and GP effects in mPFC and right TPJ (p<0.1) (upper middle). The gridness estimated in TPJ, however, does not correlate with their GP effects nor with the mPFC GP effect (p>0.1) (bottom left and middle). **, p<0.01; +, p<0.01. To further examine the relationship between the EC and mPFC gridness, we formally test which one better explains the GP effects in TPJ and mPFC. To address this question, we inputted the z-scored gridness of EC and mPFC into the same GLM to predict the GP effects in TPJ and mPFC. We found that the GP effect in bilateral TPJ was better explained by the EC gridness than the mPFC gridness (regression coefficient βEC=0.24** > βmPFC=0.17* for right TPJ; βEC=0.16* > βmPFC=0.13 for left TPJ; **, p<0.01 and *, p<0.05), and the GP effect in mPFC was better explained by the mPFC gridness than the EC gridness (βmPFC=0.09 (p=0.066) > βEC=0.01). Right: Colormap in matrix depicts regression coefficients for each regions’ gridness effect used to explain each regions’ GP effect. b. Left: Positive correlation between effects of differences in GP (|GP1-GP2|) in vmPFC during partner selection decisions and the EC gridness (r=0.43, p=0.05) but not mPFC gridness (r=-0.22, p=0.33). Right: Colormap shows regression coefficients for rEC and vmPFC gridness effects used to predict the vmPFC value difference effect. **, p<0.01; *, p<0.05; +, p<0.1. Box, lower and upper quartiles; line, median; whiskers, range of the data excluding outliers; +, the whiskers’ range of outliers.

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Supplementary Figs. 1–11 and Supplementary Tables 1–9.

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Park, S.A., Miller, D.S. & Boorman, E.D. Inferences on a multidimensional social hierarchy use a grid-like code. Nat Neurosci 24, 1292–1301 (2021). https://doi.org/10.1038/s41593-021-00916-3

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