The successor representation subserves hierarchical abstraction for goal-directed behavior
Fig 2
(A) Horizontal stacked bar charts for every participant, illustrating the posterior model probability derived from random effects Bayesian model comparison between four cognitive models, “Null” (orange), explicit hierarchical “Exp” (pink), model-based “MB” (yellow), and successor representation “SR” (blue). Participants were sorted by posterior model probability for the “Exp” model for interpretability. (B) Regression coefficient of the “rotation” variable in the explicit hierarchical logistic regression. Density plot shows the full posterior distribution of the population mean, with orange lines indicating the 95% highest density interval. Dots represent posterior means of individual participant (random) effects. (C) Proportion of <m> choices over the course of the testing phase, grouped for every participant by trials where <m> was the optimal rotation vs where <z> was the optimal rotation. Empirical data are shown in blue. Posterior predictions from the explicit hierarchical logistic regression are shown in orange. (D) Regression coefficients for the response switch analysis, describing the probability of switching response key upon “entry” of the goal wing, “leave” of the goal wing, and the number of “repetitions” of pressing the current key. Colors similar to B. (E) Proportion of trials on which the participant switched their response key, grouped by trials where the participant just entered the goal wing or just left the goal wing. Switch proportion of all other (“baseline”) trials is subtracted, so values below 0 reflect a decreased tendency to switch, and values above 0 an increased tendency. Color coding as in C. (F) Given a particular goal outside the current wing, one action corresponds to the correct “rotation” to follow for most of the rooms in the current wing. However, one room in each community actually leads to better outcomes when the participants would follow the opposite action (antirotation, here colored in orange). In this figure, possible outcomes of the rotational action are colored blue, and possible outcomes of the antirotational action are colored orange. As can be observed, the orange room has a preferred transition in the direction of the goal wing (colored with an orange to blue gradient, indicating both choices can lead to this outcome). Interestingly, when following the rotation action (blue transitions), one possible transition leads in the correct direction whereas the other possible transition leads to a room for which the transition in the direction of the goal wing was removed (X in the figure). By contrast, when following the antirotation (orange transitions), the other possible outcome leads to a state that still has a transition in the direction of the goal wing (blue circle). For this reason, model-based and (converged) successor representation models predict participants would pick the antirotational action in this orange room, and the rotational action in the blue room. (G) Proportion of rotational actions chosen in the orange (antirotation) and blue (rotation) rooms (“Node type”, x-axis, colored as in F), considered separately when the correct rotation would be <z> (left panel) or <m> (right panel). Black dots with error bars correspond to mean with 95% confidence interval. (H) Regression coefficients for the (anti)rotation selection analysis, describing the probability of selecting the correct rotation when it is <m> (over <z>, left) and when occupying the blue room (as opposed to the orange room, see F; middle). The interaction term is displayed on the right. Colors similar to B.