Figures and data
Feature-based model simulations.
Simulation environments varied in (A) dimensionality and (B) causal depth. (A) Environments had either one or two features per state. Since A1→A2 and B1→B2 unfold together in the two-dimensional environment, spurious transitions A1⇢B2 and B1⇢A2 are also observed. We additionally consider a causal learner model that fully suppresses spurious information during updating. (B) Environments consisted of either (light) 1-, 2-, 3-, or 4-step (dark) causal chains, beginning with fSTARTand ending with fTERMINAL. (C) Mean learning curves in the one-dimensional environments by causal depth. (D) Mean learning curve in the two-dimensional environments by causal depth for causal learners (grey lines) and “regular” learners (red lines). For C and D, P(Reward) is the proportion of the maximum reward (C = 1, D = 2) agents could earn on each trial. (E) Proportion of spurious information in successor matrix M by environment depth and the number of steps a feature is from fTERMINAL. (F) Schematic demonstrating how spurious information may compound in deeper feature representations (as shown in E). Causal observations (solid lines) are constrained by the deterministic causal processes that generate them, producing simple chains of observations over multiple steps. Conversely, since spurious observations (dashed lines) are not constrained by a mechanism in the environment, they can occur between a more diffuse set of features. This diffusivity expands over multiple steps, producing increasingly less constrained chains of spurious observations. Due to this, features that are deeper in causal chains (more steps away from fTERMINAL) will compound much more spurious information through these diffuse webs (see E). In turn, predictive inferences (red arrows) about deeper features will be noisier and more diffusive, leading to poorer behavioral performance (see D). (G) The representational similarity of start feature pairs (Pearson’s correlation of 
Robot task design.
(A) Trial procedure (1-step, 2-dimensional environment). Participants are presented with a blueprint for the robot they are to ultimately build. They then compose a builder robot they think will produce the target robot. During training, they then first see the builder (start) robot they composed followed by the final built (terminal) robot. Finally, they receive reward commensurate to the number of features that overlap between the terminal and target. The example here is from the semantic congruent condition, where start and terminal features are drawn from the same semantic categories. The top-bottom placement of a robot’s features was randomized within and across trials. For example, here, the start robot was displayed with the antenna on top, while the terminal robot was displayed with the antenna on the bottom. (B) Example transition structures in the semantic incongruent and congruent conditions. Causal transitions (solid arrows) are defined between start and terminal features, and the co-occurrence of start features generates spurious observations (dashed arrows). However, whereas all transitions are defined out-of-category in the semantic incongruent condition, the causal transitions are defined within category in the semantic congruent condition (e.g., head→head). Thus, a semantic bias would be expressed as upweighted learning of the causal transitions in the congruent relative to incongruent condition. (C) Feature co-occurrences at training and test, by target and options definition and semantic congruency condition. During training, a subset of feature combinations (AB or CD – old) were presented in each training block. However, at test, both these old combinations and new feature combinations comprising features from across the two training blocks were observed. Moreover, at test, all possible combinations of old and novel targets and options sets were presented (bidirectional arrows), producing 144 unique trials.
Training Performance.
(A) Spurious and causal transition influence coefficients by semantic congruency condition. (B). Training reward earnings by training target frequency and semantic congruency condition. (C) Training reward earnings by spurious transition influence coefficient fit. All error bars are 95% HDIs. Density plots show posteriors from the Bayesian regression models, with red lines indicating 0.
Test Performance.
(A) Test reward earnings by semantic congruency condition and options novelty. (B). Test reward earnings by semantic congruency condition and target novelty. For A and B, analyses were restricted to test trials where only one possible causal and spurious inference was possible based on the options and target. (C) Composition spurious predictiveness by semantic congruency condition on test trials where only spurious inferences were possible based on the options and target. All error bars are 95% HDIs. Density plots show posteriors from the Bayesian regression models, with red lines indicating 0.
Model-based analyses.
(A) Relative likelihoods of computational model fits by participant. (B). Spurious and causal transition influence coefficient fit by bfit. (C) Training reward earnings on trials with frequent versus infrequent targets by bfit. (D) Test reward earnings on trials with old versus novel options by bfit. (E) Composition spurious predictiveness by bfit. All error bars are 95% HDIs. Density plots show posteriors from the Bayesian regression models, with red lines indicating 0.
Simulated test performance of best-fitting feature-based models.
Feature-based models that provided a best fit to participants’ data were simulated in environments varying in dimensionality and causal depth for either (A) 72 training trials or (B) 1080 training trials. P(Reward) is the proportion of the maximum reward (1) agents could earn on each trial. Here we compare P(Reward) on trials with old versus novel options for agents with a low bias (b< 0.5) versus high bias (b> 0.5). The cell outlined in black is the robot task environment.
