Countless daily social encounters pose people with the need to organize information about social encounters efficiently. Though people may ascribe a variety of traits to others, these inferences have been identified to rely on a few universal dimensions (Fiske et al., 2007; Stolier et al., 2020). The most widely recognized dimensions are warmth, which concerns others’ intentions, and competence, which concerns others’ capability and possession of resources (Cuddy, 2008). These universal dimensions can be used to construct a structured representation organizing impressions of other people or other social information alike, just like how one would specify a location in a plane using orthogonal dimensions for spatial navigation. Analogous to Tolman’s original concept (Tolman, 1948), here we termed this structured representation of social information about other people as ‘social cognitive map’, which may form the basis for social cognition. Having such a cognitive map for social perception is crucial. It helps us organize various experiences, track updates, and guide novel inferences efficiently (Son et al., 2021). Despite its importance in navigating the social world, its neural underpinning remains underinvestigated.

The resemblance between social and spatial cognitive maps has led to the proposition that social cognitive map is also supported by similar mechanisms that map physical space (Schafer and Schiller, 2018). In the domain of spatial navigation, it has been demonstrated that entorhinal grid cell activity supports representational coding of cognitive map. Direct recordings in rodents (Hafting et al., 2005) and humans Jacobs et al., 2013 have found that the firing locations of grid cells form periodic triangular that covers the entire available arena during spatial navigation task. In this sense, grid cells form the basic units of a neural map of the spatial environment. One of the prominent properties of grid cells is their consistent grid orientation (i.e., the orientation of the grid relative to the environment) shared by neighboring grid cells (Hafting et al., 2005; Sargolini et al., 2006). Moreover, the overlapping population formed by grid cells and head direction cells as well as conjunctive grid × head-direction cells in deeper layers of the entorhinal cortex (EC) enables directional as well as positional tuning of the firing rate (Sargolini et al., 2006). It has been proposed that this conjunctive representation at a population level can yield a directionally modulated firing pattern with hexagonal periodicity in which population activity is enhanced when an agent’s moving direction is aligned to the grid axes (Kriegeskorte and Storrs, 2016; Kunz et al., 2019). Human studies using noninvasive neuroimaging techniques rely on this directional preference of populational conjunctive grid × head-direction cell activity to detect evidence of grid-like code in functional MRI (fMRI) BOLD signals during spatial navigation (Doeller et al., 2010). Follow-up studies have reported entorhinal grid code during virtual as well as imagined navigation (Horner et al., 2016), and even mental simulation (Bellmund et al., 2016). More importantly, pioneering studies showed that the function of grid-like code goes beyond the scope of spatial navigation. Grid-like codes in EC and prefrontal cortex (PFC) have been observed during nonspatial navigation such as perceptual (Aronov et al., 2017; Bao et al., 2019; Killian et al., 2012; Nau et al., 2018), conceptual (Constantinescu et al., 2016), semantic space (Viganò and Piazza, 2020; Viganò et al., 2021), and, more recently, discrete social hierarchy (Park et al., 2021). Evidence from the above studies converges into a domain-general role of grid-like codes in organizing cognitive maps of various types, including spatial and nonspatial domains (Bellmund et al., 2018).

In this study, we tested the above hypothesis that the social cognitive map is supported by a grid cell-like coding mechanism observed in spatial navigation. First, leveraging the theoretical framework of the stereotype content model, we set up an abstract two-dimensional social value map composed of competence and trustworthiness dimensions of social perception. Next, we adapted paradigms used in human fMRI grid-code study to test the hypothesis that grid-like codes and distance codes resembling those underpinning spatial navigation are involved in navigation in this abstract social space. Finally, to complete the argument that neural codes for social navigation subserve social cognition, we explored the link between neural codes during social navigation and social skills measured by navigational performance and social trait scores.

To look for neural underpinnings of navigation in an abstract social space, we adapted a set of tasks from previous studies illustrating the relevance of grid-like code in navigating abstract concept space (Constantinescu et al., 2016). Participants received intensive training on navigating in this abstract social space with precision. They completed a learning session, a review session during behavioral training on the first day, and a scanning session on the second day (Figure 1—figure supplement 1F).

We designed the social value map, an abstract social space structuring one’s social perception of other people’s social values. It was defined by two ecologically important dimensions: competence and trustworthiness. A visualization with two adjacent bars enclosed by a square box was designed to represent the location on this social value map, with the height of each bar representing the value of each dimension. We operationally defined these two dimensions under the framework of an investment game, in which the trustee’s social value is determined by the ability to earn a profit (i.e., profit rate as competence) and the proportion of earnings returned to the investor (i.e., return rate as trustworthiness). The range of competence and trustworthiness was limited to between 0 and 1 to make sure that they are realistic (i.e., it is unlikely that trustees will return you more than they have gained), and more importantly, orthogonal and share the same metric system. Participants played the role of an investor in this investment task (Figure 1—figure supplement 1A) at the very beginning of the experiment to develop a concrete understanding of the visual analog and the quantitative meaning of these two dimensions.

Six avatars with different levels of competence and trustworthiness (Figure 1A), analogous to landmarks in the physical environment, were placed on the social value map of size 1 unit × 1 unit in accordance with the range of competence and trustworthiness. The current spatial arrangement aimed to make avatars distinguishable on both dimensions while spreading widely across the whole space. Specifically, each participant’s set of avatars' coordinates was sampled within circles of 1/30-unit radius around center coordinates (Figure 1B). In the experiment, avatars were represented by passport-style photos of the faces of volunteers taken against a plain blue background. Photographs were matched on competence and trustworthiness ratings based on data from an independent online sample. Additionally, scanned participants completed ratings on the selected faces before and after the experiment to reassure that there was no pre-existing bias in social perception of the avatars and to test whether they updated social perception according to learned characteristics of the avatars.

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In the training, participants explored the social space by morphing the bars with different competence:trustworthiness ratio using the nonspatial controller to look for the six avatars (Figure 1—figure supplement 1C). Morphing the bars resembles making a transition in the social space in that it was done in two steps: (1) deciding a trajectory to follow by changing the competence:trustworthiness ratio using the nonspatial controller, and (2) how further along to follow that trajectory. No prior information about the characteristics of the avatars was provided to the participants. Thus, participants could only explore social space as if they were looking for landmarks in a newly introduced physical environment. An avatar would pop out when the visualization matched his/her characteristics. Specifically, the avatar would pop out when participants’ current location fell within a 0.01-unit radius of the correct location on the social value map. In this way, participants not only learned the characteristics of each avatar but also became familiar with the whole space even though this map-like structure was never revealed to them.

After participants were fully acquainted with the avatars and the social space, a set of memory tasks were used to test whether participants learned the avatars, and, more importantly, if they formed an internal representation of the social value map, even though the map-like structure was never directly revealed to them. Participants never received feedback on these memory test tasks, so they had to rely on knowledge learned in the explore task. The first one was the collect task (Figure 1—figure supplement 1D), which required participants to navigate to the location of the avatars from random starting locations in the abstract space. In each trial, they were instructed to morph the box on the left to match the characteristic of the avatar shown on the right. Specifically, we asked participants to make as few transitions as possible. Two performance indices were calculated: (1) the deviation of participants’ first transition from the ideal trajectory, and (2) the Euclidean distance between the location corresponding to participants’ morphed bars and the avatar’s actual location in the abstract space. The second one was the recall task, which required participants to mentally traverse the abstract social space according to a half-seen trajectory and identify the destination that follows (Figure 1D, Figure 1—animation 1). In each trial, participants were first shown the two bars morphing according to a predefined competence:trustworthiness ratio for 1 s. The bars then stopped morphing, and participants were instructed to imagine the bars keep morphing according to the same ratio, at the same speed, and for the same amount of time. After this, participants had to choose which of the three given options matched the bars after imagination. Essentially, each trial is a trajectory vector defined by moving direction (i.e., morphing ratio) and traveled distance on the social value map. We specifically sample the trajectories from a uniform distribution (Figure 1—figure supplement 2). We investigated the neural representation of the trajectories while participants performed this task. The third one was the compare task (Figure 1—figure supplement 1E), which required participants to compare different pairs of avatars on one given dimension (competence and trustworthiness) or by a fair combination of both dimensions (willingness to cooperate). Assuming distance is a measure of similarity between two avatars, the closer two avatars are, the more similar they are, hence distinguishing them will be harder, which results in less accurate response and longer reaction time (similar to the inferential distance effect in ordered relationships; Potts, 1974). If participants had map-like representations, then their response in this task would show such a correlation pattern with distance in the 2D social space. The final one was a map task at the end of the experiment in which participants were informed about the map-like structure and were asked to indicate the location of each avatar on an empty social value map using a mouse click.

Participants construct a social value map after associative learning of avatars and corresponding characteristics

Participants were successful in reconstructing the designed layout of avatars in a map task at the end of the experiment (Figure 1C). Linear mixed effect models revealed that participants’ performance in tasks significantly improved over sessions. In the explore task, it took them significantly less time to find all avatars in the review session compared to the learning session (β_session = –67.589, t = –37.604, p<0.001). They also spent much less time at the edge (β = –0.104, t = –9.070, p<0.001) and more time at avatars (β_session = 0.023, t = 7.367, p<0.001) during exploration in the review session compared to the learning session (Figure 1E). Likewise, there was evident improvement in collect and recall task as training progressed (Figure 1F, percentage of first transition deviation < 15° in collect task: β_session = 0.050411, t = 3.2187, p=0.002; percentage of distance < 0.01 in collect task: β_session = 0.047, t = 3.002, p=0.003; accuracy in the recall task: β_session = 0.020, t = 4.213, p<0.001). Furthermore, participants were able to form an implicit map-like structure and integrate both dimensions when making decisions between avatars. In the compare task, linear mixed effect models revealed a significant effect of distance between avatars in the compared dimension on response time and accuracy as predicted (Figure 2G, all p<0.001). Lastly, learning-induced changes in participants’ ratings of avatars on all rating items (competence, trustworthiness, and attractiveness) (Figure 2H, Table 1A). There was no preference over the six presented faces when participants were naïve to the social value of different avatars (Table 1B, all p>0.890), but their ratings became significantly dissociable according to the learned social value at the end of the experiment (Table 1B, all p<0.001). These results indicated the successful formation of a 2D social map by associating each avatar with its respective social value.

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Table 1

A. Linear mixed effect model for different rating items
	Competence	Trustworthiness	Attractiveness
(Intercept)	5.157 *** [4.775, 5.539]	5.614 *** [5.276, 5.951]	4.590 *** [4.168, 5.011]
Post vs pre	–2.173 *** [–2.707, –1.639]	–1.998 *** [-2.469,–1.527]	–0.828 ** [–1.364, –0.292]
Avatar	–0.395 [–1.024, 0.234]	–0.637 * [–1.240, –0.034]	–0.281 [–0.710, 0.149]
avatar * (post vs pre)	4.812 *** [3.923, 5.702]	5.185 *** [4.333, 6.038]	1.964 *** [1.357, 2.572]
N (observation)	456	456	456
N (id)	38	38	38
AIC	1600.834	1589.456	1808.221
BIC	1625.569	1614.191	1832.956
R2 (fixed)	0.302	0.337	0.129
R2 (total)	0.313	0.347	0.223
B. Follow-up analysis of interaction term in mixed effect models: simple slope of avatars in different sessions
Rating item	Moderator levels session	Estimate [lower CI, upper CI]	SE	t (415)	p
Competence	Pre-experiment	–0.395 [-1.026, 0.236]	0.321	–1.231	0.89
	Post-experiment	4.417 [3.786, 5.048]	0.321	13.766	<0.001
Trustworthiness	Pre-experiment	–0.637 [-1.241, 0.032]	0.308	–2.069	0.98
	Post-experiment	4.549 [3.944, 5.154]	0.308	14.787	<0.001
Attractiveness	Pre-experiment	–0.281 [-0.711, 0.150]	0.219	–1.281	0.9
	Post-experiment	1.684 [1.253, 2.114]	0.219	7.684	<0.001

1. Statistic results for right-sided t-test against zero (noninferiority).

2. AIC=Akaike Information Criterion；MNI=Montreal Neurological Institute；ACC=Anterior Cingulate Cortex；FWE=Family Wise Error；DMN=Default Mode Network，SAD=Social Anxiety Disorder；BIC=Bayesian Information Criterion.

3. *p<0.05; **p<0.01; ***p<0.001.

Grid-like activity aligned to prefrontal and entorhinal grid orientation

To look for grid-like activity, we implemented the orientation-estimation approach (Bellmund et al., 2018; Doeller et al., 2010) based on univariate analysis. First, a whole-brain quadrature filter analysis was conducted, which served as a functional localizer to identify the regions sensitive to hexagonal modulation, independent of grid orientation (‘Materials and methods’). This GLM had two regressors modeling the morph stage and choice stage. For the morph stage regressor, we included two parametric modulators corresponding to the sixfold sinusoidal sixfold modulation of trajectory direction (i.e., sin6θ and cos6θ, θ is the direction). Next, we defined spherical region of interest (ROI) with a 5 mm radius centered at the peak coordinate of each significant cluster (Table 3) to estimate the grid orientation of each ROI. As no region in the EC survived this analysis, we additionally defined four entorhinal ROIs based on subdivisions of EC (left/right and posterior–medial/anterior–lateral, i.e., pmEC/alEC) from an anatomical mask (Maass et al., 2015). Finally, we conducted the leave-one-out cross-validation analysis to test for hexagonal modulation aligned to grid orientation of the ROIs for each participant, that is, the grid orientation consistency effect (‘Materials and methods’). In this cross-validation approach, we estimated grid orientation using data from three runs and tested the grid orientation consistency effect in the held-out run. Grid consistency effect was tested using a GLM that classified trials into 12 bins according to its trajectory direction offset from the estimated grid orientation and built a contrast to test whether activity is stronger in aligned trials than in misaligned trials (Figure 3A).

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Table 3

Anatomical description	Hemisphere	Peak coordinates (MNI)			Peakt-value	Cluster
		x	y	z		Size	pFWE
Superior parietal gyrus	R	28	–66	56	5.021	522	<0.001
Precuneus	L	-6	–46	38	5.707	426	<0.001
Middle frontal gyrus	R	42	24	34	5.221	271	<0.001
Paracentral Lobule	R	10	–36	68	4.835	120	<0.001
Middle frontal gyrus	R	38	42	30	4.849	103	0.001
Frontal pole	L	–26	50	0	4.269	71	0.014
Frontal pole	R	26	52	-2	4.494	69	0.017
Angular	L	–52	–60	26	4.718	58	0.041

1. L, left; R, right.

Of all the grid orientations derived from the above ROIs, we only found grid consistency effect aligned to the grid orientation of the ROI in the right frontal pole (right FP) cluster (Figure 3B, peak coordinate [x, y, z] = [26, 52, –2], t(37) = 4.494, cluster-level p=0.017 FWE-corrected, cluster-defining threshold p<0.001) and the grid orientation of the anatomically defined right posterior–medial EC (right pmEC, Figure 3C). For the right FP grid orientation, whole-brain analysis revealed consistency effect in bilateral ventral medial PFC (vmPFC, Figure 3D, left and middle panels, peak coordinate [x, y, z] = [–14, 56, –12], t(37) = 4.245, cluster-level p=0.033 FWE-corrected, cluster-defining threshold p<0.005) and the left EC (left EC) extending to the parahippocampus (Figure 3E, left and middle panels, peak coordinate [x, y, z] = [–16, –22, –26], t(37) = 4.563, cluster-level p=0.024 FWE-corrected, cluster-defining threshold p<0.005). For the right pmEC grid orientation, significant consistency effect was found in two clusters in bilateral vmPFC (Figure 3F, left and middle panels, right rectus: peak coordinate [x, y, z] = [10, 34, –18], t(37) = 4.908, cluster-level p=0.033 FWE-corrected; left ACC: peak coordinate [x, y, z] = [–8, 32, 6], t(37) = 4.810, cluster-level p=0.009 FWE-corrected; cluster-defining threshold p<0.005) and one cluster in right superior temporal pole (right STP, Figure 3G, left and middle panels, peak coordinate [x, y, z] = [36, 20, –30], t(37) = 4.962, cluster-level p=0.018 FWE-corrected, cluster-defining threshold p<0.005). The above analysis did not identify grid-like pattern in EC that is aligned to the grid orientation of itself. It could be that the signal-to-noise ratio is too low in EC to pass the stringent whole-brain test. Another possibility is that a distributed coding scheme is employed by the EC. However, in the more statistically lenient ROI-based analysis, we failed to find evidence of grid-like code in the EC aligned to its own putative grid orientation either with this orientation estimation approach or with the representation similarity analysis (RSA) approach (‘Materials and methods’, Figure 3—figure supplements 1 and 2).

One important assumption underlying the univariate analysis for grid-like code in human fMRI data is that neighboring grid cells share similar grid orientation. Consistent with previous studies, we examined this assumption in our dataset by testing the distribution of putative voxel-wise grid orientations in the right FP ROI and in the right pmEC ROI for each participant (‘Materials and methods’). This revealed a clustered distribution of voxel-wise grid orientations in FP ROI (V-test, all p<0.011, except in one participant’s estimating set p=0.176; see Figure 3—figure supplement 3A for representative participants). Previous studies using a similar approach in fMRI have also shown that grid orientations across participants tend to distribute uniformly (Bao et al., 2019). This has been replicated in the right FP ROI in our dataset (Figure 3—figure supplement 4, top, Rayleigh’s tests for nonuniformity, all p>0.782). However, in the pmEC ROI, these results are less consistent. With regard to voxel-wise orientations, 31 participants show the above clustered distribution (V-test, all p<0.040; see Figure 3—figure supplement 3B for representative participants), but there are seven participants each of whom has at least one estimating set that did not pass the statistical test (V-test, all p>0.068). Across participants, only grid orientations from two estimating sets conformed to the uniform distribution (Figure 3—figure supplement 4, bottom panel, Rayleigh’s tests for nonuniformity, run 1,2,3: p=0.010, run 1,2,4: p=0.019).

For completeness, we tested the specificity of hexagonal modulation. That is, the identified alignment effect only exists with sixfold periodicity. The above orientation estimation and cross-validation procedure was repeated for each of the four controlled periodicity (i.e., fourfold, fivefold, sevenfold, and eightfold). Signals were extracted from the clusters that showed significant hexagonal consistency. One-sample t-tests showed that signals within these clusters were not modulated by any of the controlled periodicities, and paired t-test showed that sixfold periodicity in general showed greater alignment effect (Figure 3D–G, right panels). In sum, our univariate analysis revealed that the vmPFC and left EC showed sixfold-specific grid-like code aligned to the right FP’s grid orientation and that the vmPFC and right STP showed sixfold-specific grid-like code aligned to the right pmEC’s grid orientation.

Behavioral relevance of spatial codes for the social value map

Next, we want to address whether the identified distance or grid-like code could have any behavioral relevance. Previous studies have found that hexagonal modulation effect and hexagonal consistency effect positively correlate with accuracy in the recall task in the scanner (Constantinescu et al., 2016). However, we did not find such a correlation in our data (Figure 4—figure supplement 1). Then, we explored if there is any correlation between neural indices of map-like representation and behavior performance outside the scanner as well as individual differences. The covariates we explored can be classified into two categories. The first category reflects participants’ ability to make decisions based on the social value map, that is, the distance effect in the compare task. Specifically, we focused on the distance effect during the cooperation block when participants choose the avatar they are more willing to cooperate with by taking into account both dimensions. This is essentially the beta weight of the distance regressor in predicting participants’ accuracy and log-transformed response time. The second category reflects participants’ social trait, including social anxiety and social avoidance scores. The covariates were entered into the second-level analysis of the consistency effect GLM separately.

Whole-brain analysis revealed significant clusters in the temporal lobe whose consistency effect scaled with distance effect in response time. For grid orientation of right FP ROI (Figure 4A), hexagonal consistency effect in the left middle temporal gyrus and right lingual gyrus correlated with the distance effect (left middle temporal gyrus: peak coordinate [x, y, z] = [–36, –70, 8], t(37) = 4.528, cluster-level p<0.001 FWE-corrected; right lingual gyrus: peak coordinate [x, y, z] = [–38, –66, 4], t(37) = 4.369, cluster-level p<0.001 FWE-corrected; cluster-defining threshold p<0.005). For grid orientation of right pmEC ROI (Figure 4B), hexagonal consistency effect in bilateral lingual correlated with the distance effect (left lingual gyrus: peak coordinate [x, y, z] = [–12, –68, –2], t(37) = 4.355, cluster-level p=0.077 FWE-corrected; right lingual gyrus: peak coordinate [x, y, z] = [16, –62, –2], t(37) = 3.934, cluster-level p=0.032 FWE-corrected; cluster-defining threshold p<0.005). In general, greater distance effect in the comparison task correlated with greater hexagonal consistency in temporal lobe aligned to both prefrontal and entorhinal grid orientations. In addition, this analysis also revealed a cluster in the left precuneus/posterior cingulate cortex (left PCC, Figure 4C, peak coordinate [x, y, z] = [0, –64, 28], t(37) = 4.965, cluster-level p<0.001 FWE-corrected, cluster-defining threshold p<0.001). Its consistency effect aligned to the right FP grid orientation was negatively correlated with social avoidance score.

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In this study, we investigated whether cognitive map in social cognition domain recruits the neural processing mechanism similar to its spatial counterpart. We identified distance representation in the precuneus, fusiform gyrus, and middle occipital gyrus. In addition, we demonstrated some evidence of grid-like activity in PFC and EC. Furthermore, we explored the behavioral relevance of grid-like activity in temporal pole and precuneus.

When participants were mentally traversing a predefined social value map, we found that activities in the bilateral precuneus were positively correlated with traveled distance, while activities in bilateral FFG and right MOG were negatively correlated with traveled distance. In spatial navigation literature, though intracranial electroencephalography studies have shown the relevance of hippocampal theta oscillation in encoding traveled distance, neural correlates of traveled distance at the macroscopic level using fMRI are relatively sparsely investigated (Kunz et al., 2019). Patai et al., 2019 showed that retrosplenial cortex positively correlated with path distance in that greater distance is associated with increased precuneus activity and that this effect remained robust after controlling for Euclidean distance. Likewise, we showed that precuneus activity was positively correlated with traveled Euclidean distance during implicit navigation in the abstract social space. Moreover, the present peak coordinates coincide with those reported in a previous study by Park et al., 2020. In their study, participants learned 2D social hierarchy (competence and popularity) of two groups of agents and were asked to perform a transitive inference task in which they compared a pair of agents on their competence or popularity. The authors found that bilateral precuneus represented pairwise difference in the task-relevant dimension instead of pairwise Euclidean distance in the 2D space. Another study reported that posterior cingulate cortex/precuneus tracks the length of the vector of social relationship change, that is, an egocentric distance (Tavares et al., 2015). Taken together, we speculate that precuneus may encode the distance of the route, either on a concrete or an abstract map, that participants trespass under task demand. Less clear is the negative correlation we observed between traveled distance and activity in fusiform as well as middle occipital gyrus. Both FFG and MOG are involved in human spatial navigation (Boccia et al., 2014). In particular, fusiform gyrus extending into the parahippocampal place area has been shown to be involved in processing spatial information such as landmark and orientation cues (Qiu et al., 2019). However, to our knowledge, there is no study that reports such negative distance coding in these occipitotemporal regions during navigation.

Apart from the distance code, another focus of the current study was to test whether grid-like codes support the organization of social knowledge. Previous studies on reporting grid-like codes mostly report hexagonal modulated pattern in the EC and medial prefrontal regions aligned to putative grid orientation from both regions (Constantinescu et al., 2016). The current study partly replicated these findings, most of which are in the prefrontal region. In terms of prefrontal orientation, whole-brain analysis revealed alignment effects in the bilateral vmPFC and left EC. In terms of entorhinal orientation, however, alignment effect was found in the bilateral vmPFC and right superior temporal pole, but not in the EC. Though we found evidence of prefrontal grid-like codes subserving social navigation, its origin remains elusive. To date, there has been no significant evidence of grid-like neuronal tuning in this area (Wikenheiser et al., 2021). Jacobs et al., 2013 examined grid-like cells in a variety of brain regions, including the frontal cortex in neurosurgical patients during a virtual navigation task, but the proportion of significant grid-like cells in the frontal cortex did not exceed type I error rate (they did identify grid-like cells in cingulate cortex, which is posterior to the prefrontal regions). Therefore, it is less likely that the prefrontal grid-like codes reported in our study and previous literature come from grid cells in the PFC. A more plausible explanation is that the anatomically and functionally connected medial- and orbitofrontal cortex and EC (Navarro Schröder et al., 2015; Peng et al., 2018; Squire and Zola, 1996) coordinated together to support flexible decision-making. However, adopting both univariate and multivariate approaches, the current study did not find the reliable effect of hexagonal grid-like code in the entorhinal region aligned to its own grid orientation, which should be evident if such hypothesis stands. Previous studies postulated that the lack of univariate evidence of grid-like code may have to do with a low signal-to-noise ratio (tSNR) in data from the EC (Bao et al., 2019). Indeed, analysis (‘Materials and methods’) revealed lower tSNR in all four entorhinal subregions compared to the frontal pole cluster from the quadrature filter analysis (Figure 3—figure supplement 5A). But we did not identify a significant relationship between tSNR and the Z-transformed F statistics of hexagonal modulation either across participants or within participants (Figure 3—figure supplement 5B and C, Table 4). Thus, we cannot conclude that a low signal-to-noise ratio in EC led to this null finding in our study.

Nonetheless, our study did provide some incomplete evidence of grid-like activity in the EC and prefrontal region while participants were mentally trespassing an abstract social space. Grid codes are proposed to provide a metric of space (Moser and Moser, 2008) and underlie the process of path integration (McNaughton et al., 2006). Previous studies have suggested that entorhinal grid codes are capable of representing space even at a higher level of abstraction that goes beyond spatial navigation to support cognitive flexibility in general (Bellmund et al., 2018). Existing literature revealed correlation between entorhinal and prefrontal grid-like code and performance in spatial, perceptual, and conceptual space. Indeed, our exploratory analysis showed that the univariate hexagonal consistency effect in temporal lobe scaled with the distance effect in a comparison task block when participants chose their preferred partner for future cooperation. The distance effect reflected the extent to which participants relied on their preference judgment on the pairwise distance between the given pair of avatars. As we explicitly required participants to take both dimensions into consideration, it reflected participants’ ability to plan a route between landmarks (which represents the retained impression of social encounters) in the abstract social space. This is very similar to what Park et al., 2021 reported in their recent study. In this study, participants were trained on the rankings of 16 individuals on two dimensions (competence and popularity) separately, then they were asked to make comparisons between novel pairings unseen during training. Replicating their previous findings (Park et al., 2020), the authors found that the entorhinal and hippocampus system successfully reconstruct the unseen whole spectrum of social hierarchies as a 2D cognitive map. Moreover, they found that grid-like representations support trajectories of novel inferences on this 2D cognitive map that underpins decision-making. Park’s study and ours differed in that they focused on discrete relational structures whilst we constructed a continuous social space. Collectively, this evidence supports the notion that grid-like codes underpin navigation in an abstract social cognitive map, be it discrete or continuous.

Intriguingly, our study found that the intensity of hexagonal modulation in the precuneus aligned to estimated grid orientation of the prefrontal region is negatively correlated with participants’ social avoidance tendency. While previous studies mainly reported grid-like codes in the EC and PFC and its relevance to spatial navigation deficit in a clinically risky population (Kunz et al., 2015), to the best of our knowledge, no report has shown the psychological relevance of grid-like code outside these classical regions to potential social deficit. One study of direct neuronal recording revealed grid-like neuronal activity in patients’ cingulate cortex during virtual spatial navigation task (Jacobs et al., 2013), implying that the human grid-cell network previously focused around the entorhinal and prefrontal regions also extends to the cingulate cortex. However, our study did not find evidence of grid-like pattern in the precuneus. Thus, we cannot conclude that our result points to a direct relationship between precuneus grid-like code and social functionality. Meanwhile, precuneus, as a core node of the DMN, has abundant neuroanatomical connections with prefrontal regions (Greicius et al., 2009; Khalsa et al., 2014; Oane et al., 2020). Precuneus has also been reported to show a decrease in resting-state connectivity to parahippocampal gyrus and medial PFC in patients with SAD (Yuan et al., 2018). Therefore, it is likely that downstream projections from the OFC/vmPFC motivated the observed correlation pattern in our study.

In conclusion, the present study demonstrates that navigating in a continuous social space recruited distance codes and grid-like codes in brain regions reported by spatial navigation studies and their behavioral and psychological relevance. Our findings further strengthen the notion that neural mechanisms involved in spatial cognitive map may play a domain-general role in maintaining an abstract, structured representation of knowledge that supports flexible cognitive behavior.

Our study has a few limitations. First, as we used a visual analog to guide participants to imagine moving in this abstract social space, grid-like coding could reflect the processing of both the sensory information and the abstract social concept. It would be better to control for this as in Bao et al., 2019. Second, to make our study comparable to those investigating the representation of abstract nonsocial knowledge, our scanner task investigates social navigation in a static environment and no social interaction or social decision is involved. Further studies should be conducted to investigate how such a structured representation of social knowledge is reused and updated during social decisions and social interactions. Third, we specifically designed the abstract social value map to be formed by two orthogonal dimensions that have the same scale. This allows us to examine grid-like activity pattern with sixfold periodicity unambiguously. But this set-up may lack generality. For one thing, it is unlikely that all parts of the whole social value space span by the warmth and competence dimension are equally important. Social ties are more likely to be formed among humans alike (McPherson et al., 2001) and humans show the tendency to represent ingroup members more differentially than outgroup members (Hugenberg et al., 2010; Ostrom et al., 1993), so it is likely that some area of the social value space is represented in finer granularity than the other. In spatial navigation, entorhinal grid cells showed sensitivity to geometric and environmental features, and the resulting distorted grid fields no longer form a regular hexagonal lattice and fail to show sixfold periodicity (Derdikman et al., 2009; He and Brown, 2019; Krupic et al., 2015). For instance, grid fields have been found to sometimes warp toward reward (Boccara et al., 2019). In this sense, spontaneous social value space may bear more resemblance to such kind of reward map covered by distorted grid fields rather than a regular, uniform square/circular open arena where sixfold symmetric grid-like coding was originally identified. For another, the geometric properties of social and nonsocial cognitive space in real life can be very different from that of the physical space in navigation. Our knowledge of other people in real life is often high-dimensional integrating multimodal information from sensory features (face, voice, etc.) to social cognitive information (hobbies, social status, etc.). Moreover, while dimensions of physical space (the cartesian axes) are orthogonal and their metrics are on the same scale, the dimensions of social perception in real life may not be orthogonal and may be incomparable. The stereotype content model predicted that there is a weak but low correlation between warmth and competence (Cuddy et al., 2009) and other studies have found there exists compensation between these dimensions (Kervyn et al., 2010). To the best of our knowledge, it remains elusive whether and how grid cells can represent such high-dimensional space with a non-orthonormal basis and how the univariate and multivariate analyses pipeline used to identify grid-like coding in fMRI signal could be revised to address these concerns. Taken together, the intrinsic social cognitive map in which humans structure their knowledge of others may be nonuniform, high-dimensional, and have non-orthonormal dimensions. Future studies would need to take this into account and explore beyond the sixfold grid-like activity pattern in regular 2D space.

We have published preprocessed smoothed and unsmoothed functional MRI data, the code to run the experiment and the code to run the univariate analysis reported in the main text. Dataset and code are publicly available at https://doi.org/10.57760/sciencedb.08637.

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Author details

1. Zilu Liang

   State Key Laboratory of Cognitive Neuroscience and Learning & IDG/McGovern Institute for Brain Research, Beijing Normal University, Beijing, China

   Contribution

   Conceptualization, Formal analysis, Investigation, Visualization, Writing - original draft, Writing - review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0009-0009-3446-5117

2. Simeng Wu

   State Key Laboratory of Cognitive Neuroscience and Learning & IDG/McGovern Institute for Brain Research, Beijing Normal University, Beijing, China

   Contribution

   Investigation

   Competing interests

   No competing interests declared

3. Jie Wu

   State Key Laboratory of Cognitive Neuroscience and Learning & IDG/McGovern Institute for Brain Research, Beijing Normal University, Beijing, China

   Contribution

   Investigation

   Competing interests

   No competing interests declared

4. Wen-Xu Wang

   School of Systems Science, Beijing Normal University, Beijing, China

   Contribution

   Conceptualization

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-4170-8676

5. Shaozheng Qin

   State Key Laboratory of Cognitive Neuroscience and Learning & IDG/McGovern Institute for Brain Research, Beijing Normal University, Beijing, China

   Contribution

   Conceptualization, Supervision, Funding acquisition, Writing - review and editing

   For correspondence

   szqin@bnu.edu.cn

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-1859-2150

6. Chao Liu

   State Key Laboratory of Cognitive Neuroscience and Learning & IDG/McGovern Institute for Brain Research, Beijing Normal University, Beijing, China

   Contribution

   Conceptualization, Supervision, Funding acquisition, Writing - review and editing

   For correspondence

   liuchao@bnu.edu.cn

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0003-1149-2314

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