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People construct simplified mental representations to plan

Mark K. Ho, David Abel, Carlos G. Correa, Michael L. Littman, Jonathan D. Cohen, Thomas L. Griffiths

arXiv:2105.06948v2cs.AI

TL;DR

The paper asks whether planning relies on fixed task representations or whether people can control how they represent tasks. It formalizes this control as value-guided construal and evaluates representations by complexity and utility for planning and acting. Findings support controlled value-guided construal, while how people learn optimal construals remains outside the paper’s scope.

Abstract

from arXiv · show

One of the most striking features of human cognition is the capacity to plan. Two aspects of human planning stand out: its efficiency and flexibility. Efficiency is especially impressive because plans must often be made in complex environments, and yet people successfully plan solutions to myriad everyday problems despite having limited cognitive resources. Standard accounts in psychology, economics, and artificial intelligence have suggested human planning succeeds because people have a complete representation of a task and then use heuristics to plan future actions in that representation. However, this approach generally assumes that task representations are fixed. Here, we propose that task representations can be controlled and that such control provides opportunities to quickly simplify problems and more easily reason about them. We propose a computational account of this simplification process and, in a series of pre-registered behavioral experiments, show that it is subject to online cognitive control and that people optimally balance the complexity of a task representation and its utility for planning and acting. These results demonstrate how strategically perceiving and conceiving problems facilitates the effective use of limited cognitive resources.

Task construals from first principles

The paper replaces fixed task representations with controllable construals that select among cause–effect relations. It evaluates each construal by balancing its complexity against its utility for planning and acting.

Task construals from first principles

A paradigm for examining construals

The maze paradigm provides fully visible, compositionally structured problems in which participants must choose which elements to integrate into a useful planning representation. The experiments use obstacle awareness and recall probes to assess attention to those elements.

A paradigm for examining construals

  • Each trial presents a new maze with a changing start, goal, and obstacle arrangement, requiring participants to inspect the layout and plan an efficient route.Source: A paradigm for examining construals · p. 7
  • Each obstacle represents a cause–effect relation: attempting to move into its occupied space results in being blocked.Source: A paradigm for examining construals · p. 7
  • The mazes are fully observable and compositionally structured, so participants must choose which visible components to integrate into a representation for planning.Source: A paradigm for examining construals · p. 7
  • Obstacle attention is assessed with post-navigation awareness ratings or, when obstacles are visible only before movement, paired-obstacle recall and confidence probes.Source: Figure 2 · p. 8

Traces of construals in people’s memory

Memory and awareness measures supported the prediction that people’s maze representations reflect value-guided construal. The evidence extended across obstacle recall accuracy, confidence, and awareness judgments.

Traces of construals in people’s memory

  • χ2(1) = 2297.21, p < 1.0 × 10−16; normalized value-guided construal probabilities predicted awareness judgments (β = 0.133, S.E. = 0.003).Source: Traces of construals in people’s memory · p. 9
  • Awareness predictions persisted when obstacles were hidden during movement (β = 0.115, S.E. = 0.004) and when awareness was probed before execution (β = 0.106, S.E. = 0.004).Source: Traces of construals in people’s memory · p. 9
  • χ2(1) = 249.34, p < 1.0×10−16; value-guided construal predicted recall accuracy (β = 0.648, S.E. = 0.042) and confidence (χ2(1) = 432.76, p < 1.0 × 10−16; β = 0.104, S.E. = 0.005).Source: Traces of construals in people’s memory · p. 11
  • χ2(1) = 837.47, p < 1.0 × 10−16; in critical mazes, value-guided construal predicted awareness judgments (β = 0.175, S.E. = 0.006), alongside recall accuracy and confidence.The authors report evidence across three memory measures: recall accuracy, recall confidence, and awareness judgments.Source: Traces of construals in people’s memory · p. 11

Controlling for perception and execution

The authors tested whether memory responses attributed to planning could instead reflect perception or execution. Value-guided construal continued to explain responses after accounting for non-planning controls.

Controlling for perception and execution

  • The controls used maze-viewing without planning and yoked path execution, addressing whether perception or execution could shape memory-probe responses.Source: Controlling for perception and execution · p. 13
  • After accounting for perceptual and execution-control responses, value-guided construal improved fits for accuracy (χ2(1) = 106.36, p = 6.2 × 10−25), confidence (χ2(1) = 18.56, p = 1.6 × 10−5), and awareness (χ2(1) = 55.34, p = 1.0 × 10−13).Source: Controlling for perception and execution · p. 14
  • Planning responses were not reducible to perception and execution alone; value-guided construal predictions were positively associated with accuracy, confidence, and awareness responses.Source: Controlling for perception and execution · p. 14

Externalizing the planning process

A process-tracing task let participants reveal individual obstacles while planning, providing behavioral measures of obstacle attention as planning unfolded. Value-guided construal predicted both whether obstacles were inspected and inspection duration.

Externalizing the planning process

  • Participants revealed individual obstacles by hovering after seeing the start and goal, externalizing the planning process without seeing all obstacles at once.Source: Externalizing the planning process · p. 14
  • χ2(1) = 1221.76, p < 1.0 × 10−16; on initial mazes, value-guided construal predicted hovering (β = 0.704, S.E. = 0.021) and hover duration (χ2(1) = 169.90, p < 1.0 × 10−16; β = 0.161, S.E. = 0.012).Source: Externalizing the planning process · p. 14
  • χ2(1) = 1361.92, p < 1.0 × 10−16; on critical mazes, value-guided construal predicted hovering (β = 0.802, S.E. = 0.023) and hover duration (χ2(1) = 540.63, p < 1.0 × 10−16; β = 0.369, S.E. = 0.016).Source: Externalizing the planning process · pp. 14–15

Value-guided construal modification

The authors extend value-guided construal from choosing whether to include an obstacle to representing how much it influences a plan. Their analyses explore this graded, potentially changing construal during planning.

Value-guided construal modification

Accounting for alternative mechanisms

The authors tested whether value-guided construal explains planning measures beyond alternative mechanisms. It predicted all nine measures and ranked among the strongest predictors in model comparisons.

Accounting for alternative mechanisms

  • The authors considered whether differential awareness could instead reflect passive planning effects or alternative representational and perceptual processes.Examples included heuristic search, successor representations, subgoaling, and spatial factors such as distance to the goal or path.Source: Accounting for alternative mechanisms · p. 16
  • The authors compared value-guided construal with ten alternative predictors in global models fit to each planning measure.The alternatives were included alongside fixed value-guided construal modification predictions.Source: Accounting for alternative mechanisms · p. 17
  • Value-guided construal was a significant predictor in global models for all nine planning-experiment measures.Removing it produced the first- or second-largest reduction in fit across measures.Source: Accounting for alternative mechanisms · p. 17
  • Across all nine measures, value-guided construal was among the top two single-predictor models and among the factors in the best two-predictor model.The authors interpret these analyses as evidence of explanatory necessity and sufficiency.Source: Accounting for alternative mechanisms · p. 17

Discussion

The discussion frames value-guided construal as forming a simplified task representation sufficient to solve a problem, balancing representational complexity and utility. The reported findings support controlled construal as an explanation for planning efficiency, while pointing to open questions about how construal strategies are acquired and selected.

Discussion

  • People can plan by constructing a simplified task representation sufficient to solve the problem, a process termed value-guided construal.The account formalizes how an ideal cognitively limited decision-maker balances complexity and utility.Source: Discussion · p. 17
  • Pre-registered model predictions explained awareness, recall accuracy and confidence, and behavior in process-tracing, controlling for perception, execution, and ten alternative mechanisms.The findings support controlled value-guided construal as an account that can help explain the efficiency of human planning.Source: Discussion · pp. 17–18
  • The account provides a framework for investigating how construal strategies are acquired and how their selection is shaped by computation costs, time, or constraints.The discussion also connects construal control with acquiring structured representations such as objects and their parts.Source: Discussion · p. 18
  • The authors identify understanding mechanisms that interface with representation control as important for a comprehensive theory of flexible and efficient planning.Source: Discussion · p. 18

Methods

The methods specify how construal and heuristic search are modeled and compared, deriving predictions for static and revisable construal and defining value-guided, successor-representation, bottleneck, and perceptual-landmark predictors. They operationalize these predictors using maze structure and participants’ navigation behavior.

Value-guided Construal

  • The model assumes primitive cause-effect relationships for movement, walls, and obstacles; because every maze shares the same movements and walls, it selects only which obstacle effects to include.Movement in the arrow-key direction occurs with probability 1−ε, where ε = 10−5.Source: Value-guided Construal · p. 22
  • Value-guided construal uses a bilevel optimization over obstacle-effect subsets, exactly solves the planning inner loop for each construal, and evaluates plans under actual task dynamics.The procedure aims to derive theoretically optimal predictions for the inner loop and is not a process model of human construal.Source: Value-guided Construal · p. 22
  • A softmax choice rule over construal value estimates obstacle awareness from the probability each obstacle is included, using preregistered α = 0.1.The model also extends static construal to sequential modification, representing task state and construal jointly and penalizing added cause-effect relationships to encourage consistency.Source: Value-guided Construal · pp. 23–24
  • For fitted dynamic-construal models, construals were limited to size three and 1,000 policy rollouts estimated obstacle-inclusion probabilities; results were comparable to the fixed-parameter model.The fixed-parameter model used the full construal set; these procedures were intended to derive optimal predictions of fine-grained construal dynamics, not an algorithmic account.Source: Value-guided Construal · p. 25

Heuristic Search Over Action Sequences

  • The heuristic-search alternative tests whether differential attention could emerge passively from simulating promising action sequences, without actively simplifying task representations.One considered algorithm, RTDP [44,45], simulates physically realizable trajectories that greedily maximize a heuristic while performing Bellman updates at simulated states.Source: Heuristic Search Over Action Sequences · pp. 25–26
  • RTDP uses heuristic-guided realizable trajectories, initialized with an obstacle-free maze value function, and estimates obstacle awareness from log-transformed hit counts across 200 simulations per maze.A hit is a visit to a state adjacent to an obstacle lying between that state and the goal.Source: Heuristic Search Over Action Sequences · p. 26
  • LAO*, a graph-based A* variant for Markov decision processes, expands the simulated task graph at its frontier and replans until it finds an optimal plan within the graph.Obstacle hits during graph expansion, using the same initial heuristic and hit definition, were counted across 200 simulations per maze.Source: Heuristic Search Over Action Sequences · p. 27
  • RTDP and LAO* predict greater awareness for obstacles near the start and consistent with the initial heuristic, unlike value-guided construal’s emphasis on relevant obstacles, even when distant.The search models also predict attention to obstacles in initially promising dead ends, regardless of whether they affect the optimal path.Source: Heuristic Search Over Action Sequences · p. 27

Successor Representation-based Predictors

  • Successor-representation predictors test whether obstacle overlap with an obstacle-free maze’s optimal-policy occupancy map, or distance to bottlenecks, relates to awareness.Bottlenecks are states around partitions with high within-region and low between-region connectivity, considered as possible subgoals.Source: Successor Representation-based… · pp. 29–30
  • The successor-representation predictors used a Laplacian eigenvector to identify bottlenecks, retained those reachable under the optimal stochastic policy, and scored obstacles by minimum Manhattan distance.States nearest zero on the eigenvector were bottlenecks; the eigenvector projects the state space along a dimension that best preserves connectivity.Source: Successor Representation-based… · p. 30
  • Value-guided construal predicts attention to bottleneck-forming obstacles and to relevant obstacles affecting the optimal plan, even when distant from bottlenecks.Bottleneck obstacles may require careful navigation to reach the goal.Source: Successor Representation-based… · p. 30

Perceptual Landmarks

  • Perceptual-landmark predictors measured obstacle distance to maze landmarks and participant-visited locations, object recency, and distance to sampled optimal-policy trajectories when navigation distance was unsuitable.The trajectory measure averaged minimum Manhattan distances over 100 optimal-policy samples.Source: Perceptual Landmarks · p. 31

Experimental Design

Across maze-navigation experiments, designs increasingly separated planning from execution, added yoked perception and execution controls, and externalized planning through process tracing. Process-tracing analyses measured hovering over obstacles and its duration in initial- and critical-maze-set samples after exclusions.

Experimental Design

  • All experiments were preregistered and approved by the Prince-ton Institutional Review Board; participants were recruited on Prolific and gave informed consent.Experiments used psiTurk and jsPsych.Source: Experimental Design · p. 31

Initial experiment

  • In the initial experiment, participants navigated a circle through 11 × 11 mazes with obstacles and center walls, then rated awareness of each obstacle on post-trial probes.The green goal square shrank and reset with arrow-key presses, encouraging continued movement.Source: Initial experiment · pp. 31–32

Up-front planning experiment

  • The up-front planning experiment removed visible obstacles after the first move while they continued to block movement, encouraging participants to plan before execution.On half of trials, awareness probes followed two steps to measure awareness after planning but before execution; the rest continued as full trials.Source: Up-front planning experiment · p. 32

Critical mazes experiment

  • Participants in the critical mazes experiment planned with obstacles hidden during execution and completed four mazes featuring decision-relevant obstacles distant from the optimal path.Half also received location-recall probes asking which of two possible locations contained an obstacle, followed by confidence judgments.Source: Critical mazes experiment · p. 33

Control Experiments

  • Yoked perceptual controls matched maze displays, timing, and probes to memory-study participants, while execution controls used breadcrumbs reproducing their paths so participants did not need to plan.Perceptual controls replaced obstacle references with tile references; execution-control probe and maze order matched the yoked counterpart.Source: Control Experiments · pp. 33–34

Process-Tracing Experiments

  • Process-tracing experiments externalized planning by revealing individual obstacles only when participants hovered over them, rather than showing the whole maze at once.After participants began moving with arrow keys, the cursor became temporarily invisible to prevent it from guiding execution.Source: Process-Tracing Experiments · p. 35
  • The experiments measured whether participants hovered over each obstacle and, if so, hovering duration in log units.Source: Process-Tracing Experiments · p. 35
  • For the initial maze set, 200 participants were requested on Prolific; 174 completed submissions were received, and after excluding participants who did not hover over any obstacles on more than half the trials, n=167 were analyzed.Source: Process-Tracing Experiments · p. 35
  • For the critical maze set, 188 people submitted data and 179 participants remained after exclusions (median age 32; 89 male, 86 female, 4 neither).Source: Process-Tracing Experiments · p. 35

Experiment Analyses

The analyses used hierarchical generalized linear models to assess value-guided construal alongside alternative predictors, testing its explanatory contribution, the necessity of individual mechanisms, and the sufficiency of single predictors or pairs.

Experiment Analyses

  • In memory analyses, normalized value-guided construal probabilities were tested as a fixed effect, while control-experiment responses were included as fixed effects in planning models.Likelihood-ratio tests assessed whether value-guided construal predicted memory responses.Source: Experiment Analyses · p. 36
  • The analyses considered 11 obstacle-scoring predictors, including value-guided construal, heuristic-search scores, and distance-based measures.Predictors were included where appropriate to each experiment; for up-front planning, optimal-policy distance replaced navigation distance, and predictors were z-score normalized.Source: Experiment Analyses · p. 36
  • Likelihood-ratio tests compared models with all predictors against models excluding value-guided construal to test its added explanatory contribution.These models included the alternative predictors; the comparison tested whether removing value-guided construal significantly changed fit.Source: Experiment Analyses · p. 36
  • Removing each predictor in turn and measuring the resulting AIC change evaluated its relative necessity for explaining attention to obstacles.The global models were compared with versions omitting each predictor.Source: Experiment Analyses · p. 37
  • Models containing individual predictors or pairs were compared with the best-fitting model using ΔAIC to assess predictor sufficiency.AIC values were summed over participants.Source: Experiment Analyses · p. 37

Methods References

The methods references include Nassar and Frank’s discussion of extracting generalizable knowledge from computational models of cognition [35].

Methods References

  • Nassar and Frank discuss extracting generalizable knowledge from computational models of cognition [35].Their article appeared in Current Opinion in Behavioral Sciences 11, pages 49–54 (2016).Source: Methods References · p. 37
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