Map Making: Constructing, Combining, and Inferring on Abstract Cognitive Maps

Abstract

Cognitive maps enable efficient inferences from limited experience that can guide novel decisions. We tested whether the hippocampus (HC), entorhinal cortex (EC), and ventromedial prefrontal cortex (vmPFC)/medial orbitofrontal cortex (mOFC) organize abstract and discrete relational information into a cognitive map to guide novel inferences. Subjects learned the status of people in two unseen 2D social hierarchies, with each dimension learned on a separate day. Although one dimension was behaviorally relevant, multivariate activity patterns in HC, EC, and vmPFC/mOFC were linearly related to the Euclidean distance between people in the mentally reconstructed 2D space. Hubs created unique comparisons between the hierarchies, enabling inferences between novel pairs. We found that both behavior and neural activity in EC and vmPFC/mOFC reflected the Euclidean distance to the retrieved hub, which was reinstated in HC. These findings reveal how abstract and discrete relational structures are represented, are combined, and enable novel inferences in the human brain.

Keywords: 2D space; Cognitive map; Entorhinal cortex; Euclidean; Generalization; Hippocampus; Inference; Model based; Orbitofrontal cortex; Social network.

Figure 1.

A. Examples of “zero-shot inferences” in physical space, transitions between objects, and family trees. Representing abstract relationships as a cognitive map allows making novel direct inferences that do not only rely on previously experienced associations. Black: experienced relationships; Red: inferred relationships. B. Bilateral ROIs generated independently from probabilistic maps. C and D. Two hypotheses concerning how the brain could represent and flexibly switch between different dimensions that characterize the same entities to guide inferences. C. The brain could construct two separate maps for representing each 1-D hierarchy learned on a separate day and distinct regions could encode the one-dimensional (1-D) rank difference in the task-relevant dimension (D) and the task-irrelevant dimension (I). D. Alternatively, the brain could construct a unified map consisting of two dimensions and encode the inferred Euclidean distance (E) over the 2-D representation.

Figure 2.

A. Participants learned the rank of members of each of two groups (brown and gray) separately in two dimensions: competence and popularity. Subjects were never shown the 1- or 2-D structures. B. Illustration of a trial of the fMRI experiment. Participants made inferences about the relative status of a novel pair (F1 and F2) in a given dimension (signaled by the Cue color). A cover task (to indicate the gender of the face stimulus, F3) followed at the end of every trial. C. On day 1 and day 2, participants learned within-group ranks of the two groups in each of two dimensions through binary decisions about the status of members who differed by only one rank level in a given dimension. On day3, subjects learned from between-group comparisons limited to ‘hub’ individuals, which created a unique path between groups per person in each dimension. Subsequently, on day3, participants were asked to infer the unlearned between-group status while undergoing fMRI. D. Participants could use hubs to infer the relationship between novel pairs. Possible trajectories for example inferences can be shown for each trajectory: the behaviorally-relevant 1-D distance (D, Fig.1C) and the 2-D Euclidean distance (E, Fig.1D). Subjects could use either of two trajectories: a forward inference from F1 to its hub (H1) that has a unique connection to F2 (D_H1F2, E_H1F2; yellow); or a backward inference from F2 to its hub (H2) that has a unique connection to F1 (D_H2F1, E_H2F1; red). E. As alternative paths, subjects may not use the hubs, but instead compute the distance in the relevant dimension between F1 and F2 directly (D_F1F2), or their Euclidean distance (E_F1F2) in the combined cognitive map of two groups (blue). F. Multiple linear regression results show that both the rank distance (D_H2F1) and the Euclidean distance from H2 (E_H2F1), but not from H1, significantly explain variance in RTs, in addition to the direct distance between F1 and F2 (D_F1F2), while competing with other distance terms.

Figure 3.

A. The bilateral entorhinal cortex (EC) and ventromedial prefrontal cortex (vmPFC/mOFC), p_TFCE<0.05 corrected within a small volume ROI encode the Euclidean distance from the hub (H2) to F1 in the 2-D social space (E_H2F1). Whole-brain parametric analyses showing neural correlates of each of the distance metrics that could theoretically drive inferences between pairs at the time of decisions (F2 presentation). D: 1-D rank distance in the task-relevant dimension (D_H2F1 and D_F1F2); L: the shortest link distance between F1 and F2 (L equals to D_H2F1+1); I: the 1-D rank distance in the task-irrelevant dimension (I_H2F1 and I_F1F2); A: the cosine vector angle (A_H2F1 and A_F1F2). For visualization purposes, the whole-brain maps are thresholded at p<0.005 uncorrected. B. The results of Bayesian model selection (BMS). The exceedance probabilities revealed that the Euclidean distance from the hub (E_H2F1) best accounted for variance in both EC and vmPFC/mOFC activity compared to the other distance measures, providing evidence that these regions compute or reflect a Euclidean distance metric to a retrieved hub (H2) in abstract space in order to infer the relationship between F1 and F2. C. Conjunction analysis shown in purple revealed that both D_H2F1 and I_H2F1 are reflected in the vmPFC/mOFC and the EC bilaterally. D. The effect of D_H2F1 does not differ from I_H2F1 in the EC or vmPFC/mOFC, even at a lenient threshold (p>0.1), suggesting that these areas assign equal or similar weights to D_H2F1 and I_H2F1, consistent with activity reflecting E_H2F1, during decision-making.

Figure 4.

Repetition suppression analyses. Left: When one of the eight hubs was presented randomly following F2 presentation, as subjects performed a cover task (F3 presentation), BOLD contrast of task-irrelevant hub (Non-relevant hub) > H2, displayed at p<0.005 uncorrected (no masking is applied to the image). The HC effect is significant at p_TFCE<0.05 corrected in an independent anatomically defined bilateral HC ROI. Right: beta estimates from an independently defined right HC ROI (see Fig. 1B). The activity in the right HC differed significantly according to which type of hub was shown at F3 presentation (Wilks’ =.553, F_2,25=10.11, p=0.001, repeated-measures ANOVA). Activity in the right HC was suppressed when the relevant hub (H2) was presented, compared to matched Non-relevant hubs (p<0.001). No suppression was found when the hub inferred from F1 (H1) was presented (p>0.05; See Fig. S4 for additional confirmatory analyses).

Figure 5.

Representational similarity analysis (RSA). A. The representational dissimilarity matrix (RDM) was computed in a priori ROIs from the pairwise Mahalanobis distance in the multi-voxel activity patterns evoked when face stimuli were presented at the time of F1 and F2. People were modeled separately when they were shown in the competence (left panel) and popularity contexts (right panel). B. The neural RDM was tested against model predictions of four separate dissimilarity matrices, including pairwise differences in the rank in the task-relevant dimension (D), pairwise Euclidean distances on the 2-D social space (E), the behavioral context indicating for which social hierarchy dimension the face was presented (C), and in which group (group 1 or 2) the face belonged during training (G). C. Kendall’s τ indicates to what extent a predictor RDM explains the pattern dissimilarity between voxels in each of the ROIs. The model RDMs of D and E, but not C or G, show robust effects on the pattern dissimilarity estimated in the HC, EC, and vmPFC/mOFC but not in amygdala and primary motor cortex (M1) (***, p_FWE<0.001 corrected for the number of ROIs as well as the number of comparisons with the Bonferroni-Holm method). D. The patterns dissimilarity in bilateral HC, EC, and vmPFC/mOFC increases in proportion to the true pairwise Euclidean distance between individuals in the 2-D abstract space. E and F. The pattern dissimilarity increases not only with the task-relevant distance (D) but also the task-irrelevant distance (I), suggesting that the HC-EC system utilizes 2-D space (E). G. The effects of pairwise Euclidean distance (E) between faces and the pattern dissimilarity in the HC, EC, and vmPFC/mOFC were separately analyzed for within-group (E Wth) and between-group relationships (G). Moreover, the interaction effect between E and G were separately analyzed also based on whether the faces had been directly compared during training (E Btw Hub) or not (E Btw Non). Effects are strongest for those individuals who had been previously compared during training. That is, activity patterns are better explained by E Wth and E Btw Hub than E Btw Non (two-sided Wilcoxon signed-rank test). The between-group E for novel pairs is only significant in HC. Multiple comparisons are corrected with the Holm-Bonferroni method (***, p_FWE<0.001). H. Whole-brain searchlight RSA indicates effects of E in the HC, EC, mOFC (a part of vmPFC), central OFC, and lateral OFC, among other regions (p_TFCE<0.05). I. The activity patterns in the HC, EC, and central and medial OFC are still explained by the model RDM for pairwise Euclidean distance (E) after partialling out its correlation with the model RDM for D (p_TFCE<0.05; Fig. S5B). For visualization purposes, the whole-brain searchlight maps are thresholded at p<0.005 uncorrected.