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-People construct simplified mental representations to plan
-Mark K. Ho1,2,*, David Abel3,+, Carlos G. Correa4, Michael L. Littman3, Jonathan D. Cohen1,4,
-and Thomas L. Griffiths1,2
-1Princeton University, Department of Psychology, Princeton, NJ, USA;2Princeton University, Department
-of Computer Science, Princeton, NJ, USA;3Brown University, Department of Computer Science,
-Providence, RI, USA;+Now at DeepMind, London, United Kingdom;4Princeton University, Princeton
-Neuroscience Institute, Princeton, NJ, USA;*Corresponding author: Mark K Ho,
-mho@princeton.edu
-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 impres-
-sive because plans must often be made in complex environments, and yet people successfully
-plan solutions to myriad everyday problems despite having limited cognitive resources1–3.
-Standard accounts in psychology, economics, and artificial intelligence have suggested hu-
-man planning succeeds because people have a complete representation of a task and then use
-heuristics to plan future actions in that representation4–11. However, this approach gener-
-ally 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 simplifica-
-tion process and, in a series of pre-registered behavioral experiments, show that it is subject
-to online cognitive control12–14and that people optimally balance the complexity of a task
-representation and its utility for planning and acting. These results demonstrate how strate-
-gically perceiving and conceiving problems facilitates the effective use of limited cognitive
-resources.
-1arXiv:2105.06948v2  [cs.AI]  26 Nov 2022In the short story “On Exactitude in Science,” Jorge Luis Borges describes cartographers who
-seek to create the perfect map, one that includes every possible detail of the country it represents.
-However, this innocent premise leads to an absurd conclusion: The fully detailed map of the
-country must be the size of the country itself, which makes it impractical for anyone to use. Borges’
-allegory illustrates an important computational principle. Namely, useful representations do not
-simply mirror every aspect of the world, but rather pick out a manageable subset of details that
-are relevant to some purpose (Figure 1a). Here, we examine the consequences of this principle for
-how humans flexibly construct simplified task representations to plan.
-Classic theories of problem solving distinguish between representing a task andcomputing a
-plan4,15,16. For instance, Newell and Simon17introduced heuristic search , in which a decision-
-maker has a full representation of a task (e.g., a chess board, chess pieces, and the rules of chess),
-and then computes a plan by simulating and evaluating possible action sequences (e.g., sequences
-of chess moves) to find one that is likely to achieve a goal (e.g., checkmate the king). In artificial
-intelligence, the main approach to making heuristic search tractable involves limiting the com-
-putation of action sequences (e.g., only thinking a few moves into the future, or only examining
-moves that seem promising)5. Similarly, psychological research on planning largely focuses on
-how limiting, prioritizing, pruning, or chunking action sequences can reduce computation6–11,18–20.
-However, people are not necessarily restricted to a single, full, or fixed representation for a
-task. This matters since simpler representations can make better use of limited cognitive resources
-when they are tailored to specific parts or versions of a task. For example, in chess, considering the
-interaction of a few pieces, or focusing on part of the board, is easier than reasoning about every
-piece and part of the board. Furthermore, it affords the opportunity to adapt the representation,
-tailoring it to the specific needs of the circumstance—a process that we refer to as controlling a
-task construal . Although studies show that people can flexibly form representations to guide action
-(e.g., forming the ad hoc category of “things to buy for a party” when organizing a social gath-
-ering21), a long-standing challenge for cognitive science and artificial intelligence is explaining,
-predicting, and deriving such representations from general computational principles22,23.
-2a
-Task Action PlanDecision-Maker
-Decision-Maker
-Plan ConstrualTask
-Task Actionb
-cFigure 1. Construal and planning. a, A satellite photo of Princeton, NJ (top) and maps of
-Princeton for bicycling versus automotive use cases (bottom). Like maps and unlike photographs,
-a decision-maker’s construal picks out a manageable subset of details from the world relevant to
-their current goals. Imagery ©2022 Google, Map data ©2022. b,Standard models assume that a
-decision-maker computes a plan, , with respect to a fixed task representation, T, and then uses
-it to guide their actions, a.c,According to our model of value-guided construal , the decision-
-maker forms a simplified task construal, Tc, that is used to compute a plan, c. This process can
-be understood as two nested optimizations: an “outer loop” of construal and an “inner loop” of
-planning.
-Our approach to studying how people control task construals starts with the premise that ef-
-fective decision-making depends on making rational use of limited cognitive resources1–3. Specif-
-ically, we derive how an ideal, cognitively-limited decision-maker should form value-guided con-
-3struals that balance the complexity of a representation and its utility for planning and acting. We
-then show that pre-registered predictions of this account explain how people attend to task elements
-in several planning experiments (see Data Availability Statement). Our analysis and findings sug-
-gest that controlled, moment-to-moment task construals play a key role in efficient and flexible
-planning.
-Task construals from first principles
-We build on models of sequential decision-making expressed as Markov Decision Processes24.
-Formally, a taskTconsists of a state space, S; an initial state, s02S; an action space, A; a
-transition function P:SAS ! [0;1]; and a utility function U:S ! R. In standard
-formulations of planning, the value of a plan:SA! [0;1]from a state sis determined
-by the expected, cumulative utility of using that plan25:V(s) =U(s) +P
-a(ajs)P
-s0P(s0j
-s;a)V(s0). Standard planning algorithms5(e.g., heuristic search methods) attempt to efficiently
-compute plans that optimize value by directly planning over a fixed task representation, T, that
-is not subject to the decision-maker’s control (Figure 1b). Our aim is to relax this constraint and
-consider the process of adaptively selecting simplified task representations for planning, which we
-call the construal process (Figure 1c).
-Intuitively, a construal “picks out” details in a task to consider. Here, we examine construals
-that pick out cause-effect relationships in a task. This focus is motivated by the intuition that a key
-source of task complexity is the interaction of different causes and their effects with one another.
-For instance, consider interacting with various objects in someone’s living room. Walking towards
-the couch and hitting it is a cause-effect relationship, while pulling on the coffee table and moving
-itmight be another such relationship. These individual effects can interact and may or may not be
-integrated into a single representation of moving around the living room. For example, imagine
-pulling on the coffee table and causing it to move, but in doing so, backing into the couch and
-hitting it. Whether or not a decision-maker anticipates and represents the interaction of multiple
-4effects depends on what causes and effects are incorporated into their construal; this, in turn, can
-impact the outcome of behavior.
-Related work has studied how attention guides learning about how different state features pre-
-dict rewards26. By contrast, to model construals, we require a way to express how attention flexibly
-combines different causes and their effects into an integrated model to use for planning. For this,
-we use a product of experts27, a technique from the machine learning literature for combining dis-
-tributions that is similar to factored approximations used in models of perception28. Specifically,
-we assume that the agent has Nprimitive cause-effect relationships that each assign probabili-
-ties to state, action, and next-state transitions, i:SAS ! [0;1],i= 1;:::;N . Each
-i(s0js;a)is a potential function representing, say, the local effect of colliding with the couch or
-pulling on the coffee table. Then a construal is a subset of these primitive cause-effect relation-
-ships,cf1;:::;Ng, that produces a task construal, Tc, with the following construed transition
-function:
-Pc(s0js;a)/Y
-i2ci(s0js;a): (1)
-Here, we assume that task construals ( Tc) and the original task ( T) share the same state space,
-action space, and utility function. But, crucially, the construed transition function can be simpler
-than that of the actual task.
-What task construal should a decision-maker select? Ideally, it would be one that only includes
-those elements (cause-effect relationships) that lead to successful planning, excluding any others
-so as to make the planning problem as simple as possible. To make this intuition precise, it is
-essential to first distinguish between computing a plan with a construal and using the plan induced
-by a construal. In our example, suppose the decision-maker forms a construal of their living
-room that includes the effect of pulling on the coffee table but ignores the effect of colliding with
-the couch. They might then compute a plan in which they pull on the coffee table without any
-complications, but when they usethat plan in the actual living room, they inadvertently stumble
-over their couch. This particular construal is less than optimal.
-Thus, we formalize the distinction between the computed plan associated with a construal and
-5its resulting behavioral utility : If the decision-maker has a task construal Tc, denote the plan that
-optimizes it as c. Then, the utility of the computed plan when starting at state s0is given by its
-performance when interacting with the actual transition dynamics, P:
-U(c) =U(s0) +X
-ac(ajs0)X
-s0P(s0js0;a)Vc(s0): (2)
-Put simply, the behavioral utility of a construal is determined by the consequences of using it to
-plan and act in the actual task.
-Having established the relationship between a construal and its utility, we can define the value
-of representation (VOR) associated with a construal. Our formulation resembles previous models
-of resource-rationality2and the expected value of control13by discounting utilities with a cognitive
-cost,C. This cost could be further enriched by specifying algorithm-specific costs29or hard con-
-straints30. However, our aim is to understand value-guided construal with respect to the complexity
-of the construal itself and with minimal algorithmic assumptions. To this end, we use a cost that
-penalizes the number of effects considered: C(c) =jcj, wherejcjis the cardinality of c. Intuitively,
-this cost reflects the description length of a program that expresses the construed transition func-
-tion in terms of primitive effects31. It also generalizes recent economic models of sparsity-based
-behavioral inattention32. The value of representation for construal cis then its behavioral utility
-minus its cognitive cost:
-VOR (c) =U(c)C(c): (3)
-In short, we introduce the notion of a task construal (Equation 1) that relaxes the assumption
-of planning over a fixed task representation. We then define an optimality criterion for a construal
-based on its complexity and its utility for planning and acting (Equations 2-3). This optimality
-criterion provides a normative standard we can use to ask whether people form optimal value-
-guided construals33,34. We note that the question of precisely how people identify or learn optimal
-construals is beyond the scope of our current aims. Rather, here our goal is to simply determine
-whether their planning is consistent with optimal construal. If so, then understanding how people
-6achieve (or approximate) this ability will be a key direction for future research (see Supplementary
-Discussion of Construal Optimization Algorithms).
-A paradigm for examining construals
-Do people form construals that optimally balance complexity and utility? To answer this question,
-we designed a paradigm analogous to the example in Figure 1a, in which participants were shown
-a two-dimensional map of a maze and had to move a blue dot to reach a goal location. On each
-trial, participants were shown a new maze composed of a starting location, a goal location, center
-black walls in the shape of a +, and an arrangement of blue obstacles. The goal, starting state,
-and the blue obstacles (but not the center black walls) changed on every trial, which required
-participants to examine the layout of the maze and plan an efficient route to the goal (Figure 2a).
-In our framework, each obstacle corresponds to a cause-effect relationship, i—i.e., attempting to
-move into the space occupied by the obstacle and then being blocked. This is analogous to the
-effect of being blocked by a piece of furniture in our earlier example.
-Two key features make our maze-navigation paradigm useful for isolating and studying the
-construal process. First, the mazes are fully observable : Complete information about the task
-is immediately accessible from the visual stimulus. Second, each instance of a maze emerges
-from a particular composition of individual elements (e.g., the obstacles). This means that while
-all the components of a particular maze are immediately accessible, participants need to choose
-which ones to integrate into an effective representation for planning (i.e., select a construal). Fully
-observable but compositionally-structured problems occur routinely in everyday life—e.g., using
-a map to navigate through exhibits in a museum—as well as in popular games—e.g., in chess,
-figuring out how to move one’s knight across a board occupied by an opponent’s pieces. By
-providing people with immediate access to all the components of a task while planning, we can
-examine which ones they attend to versus ignore and whether these patterns of awareness reflect
-a process of value-guided construal (Methods, Model Implementations, Value-guided Construal
-7Implementation; Code Availability Statement). Furthermore, this general paradigm can be used in
-concert with several different experimental measures to assess attention (Extended Data Figures
-1-3; Supplementary Experimental Materials; Data Availability Statement).
-b
-An obstacle was either in the yellow or 
-green location (not both), which one was it?
-How confident are you?Goal, agent, and
-obstacles appearObstacles are invisible
-during navigationRecall probe
-Confidence probea
-Trial BeginsGoal, agent, and
-obstacles appearParticipant navigatesAwareness probe
-How aware of the highlighted 
-obstacle were you at any point?
-Figure 2. Maze-navigation paradigm and design of memory probes, Value-guided con-
-strual predicts how people will form representations that are simple but useful for planning
-and acting. These predictions were tested in a new paradigm in which participants controlled
-a blue circle and navigated mazes composed of center black walls in the shape of a cross, blue
-tetronimo-shaped obstacles, and a yellow goal state with a shrinking green square. We assume
-that attention to obstacles as a result of construal is reflected in memory of obstacles and used
-two types of probes to assess memory. a,In our initial experiment, participants were shown the
-maze and navigated to the goal (dashed line indicates an example path). After navigating, partic-
-ipants were given awareness probes in which they were asked to report their awareness of each
-obstacle on an 8-point scale (for analyses, responses were scaled to range from 0 to 1). b,In a
-subsequent experiment, obstacles were only visible prior to moving in order to encourage plan-
-ning up-front, and participants were given recall probes in which they were shown a pair of ob-
-stacles in green and yellow, only one of which had been present in the maze they had just com-
-pleted. They were then asked which one had been in the maze as well as their confidence.
-8Traces of construals in people’s memory
-We assume that the obstacles included in a construal will be associated with greater awareness
-and thereby memory; accordingly, we began by probing memory for obstacles after participants
-completed each maze to test whether they formed value-guided construals of the mazes. In our ini-
-tial experiment, participants received awareness probes in which, following navigation, they were
-shown a picture of the maze they had just completed with one of the obstacles highlighted. Then,
-they were asked, “How aware of the highlighted obstacle were you at any point?” and responded
-on an 8-point scale that was later scaled to range from 0 to 1 for analyses (Figure 2a). If participants
-formed representations of the mazes that balance utility and complexity, their responses should be
-positively predicted by value-guided construal. This is precisely what we found: Value-guided con-
-strual predicted awareness judgments (likelihood ratio test comparing hierarchical linear models
-with and without z-score normalized value-guided construal probabilities: 2(1) = 2297:21;p <
-1:01016;= 0:133, S.E. = 0:003; Methods, Experiment Analyses; Figure 3). Furthermore,
-we also observed the same results when participants could not see the obstacles while moving and
-so needed to plan their route entirely up front ( 2(1) = 726:95;p < 1:01016;= 0:115,
-S.E.= 0:004). This was also the case when we probed awareness judgments immediately after
-planning but before execution (2(1) = 679:20;p< 1:01016;= 0:106, S.E. = 0:004; Meth-
-ods, Experimental Design, Up-front Planning Experiment; Supplementary Memory Experiment
-Analyses).
-9Value-Guided Construal
-Expected Obstacle Probability
-≤ 0.5 > 0.5ab
-c
-0.00.51.0
-Participant mean awareness response (experiment)
-Value-guided construal probability (predicted)
-0.00 0.25 0.50 0.75 1.00
-Initial Experiment Mean Awareness051015Count
-Figure 3. Initial experiment results, In our initial planning experiment (out of four), each
-person (n= 161 independent participants) navigated twelve 2D mazes, each of which had seven
-blue tetronimo-shaped obstacles. To assess whether attention to obstacles reflects a process of
-value-guided construal, participants were given an awareness probe (see Figure 2a) for each ob-
-stacle in each maze. a,For our first analysis, we split the set of 84 obstacles across mazes based
-on whether value-guided construal assigned a probability less than or equal to 0:5or greater than
-0:5. Here, we plot two histograms of participants’ mean awareness responses corresponding to
-the two sets of obstacles ( 0:5in grey,>0:5in blue; individual by-obstacle mean awareness un-
-derlying the histograms are represented underneath). We then similarly split the obstacles based
-on whether mean awareness responses were less than or equal to 0:5or greater than 0:5and, us-
-ing a chi-squared test for independence, found that this split was predicted by value-guided con-
-strual (2(1;N= 84) = 23:03,p= 1:6106, effect size w= 0:52).b,Value-guided construal
-predictions for three of the twelve mazes used in the experiment (blue circle indicates the starting
-location, green and yellow square indicates the goal; obstacle colors represent model probabilities
-according to the colorbar). c,Participant mean awareness judgments for the same three mazes
-(obstacle colors represent mean judgments according to the colorbar). Responses in this initial
-experiment generally reflect value-guided construal of mazes. Participants were recruited through
-the Prolific online experiment platform.
-While the awareness probes provide useful insight into people’s task construals, it is a step
-removed from their memory (which is already a step removed from the construal process itself)
-since it requires participants to reflect on their earlier awareness during planning. To address this
-limitation, we developed a second set of critical mazes with two properties. First, the mazes were
-10designed to test the distinctive predictions of value-guided construal (e.g., Figure 4a). Second,
-these new mazes allowed us to use a more stringent measure of memory for task elements. Specif-
-ically, we used obstacle recall probes , in which, following navigation, participants were shown a
-grid with the black center walls, a green obstacle, a yellow obstacle, and no other obstacles. Either
-the green or yellow obstacle had actually been present in the maze, whereas the other obstacle did
-not overlap with any of those that had been present. Participants were then asked, “An obstacle
-was either in the yellow or green location (not both), which one was it?” and could select either op-
-tion, followed by a confidence judgment on an 8-point scale (Figure 2b; Extended Data Figure 4a).
-The recall probes thus provided two measures, accuracy and confidence, and using hierarchical
-generalized linear models (HGLMs) we found that value-guided construal predicted both types of
-responses (likelihood ratio tests comparing models on accuracy: 2(1) = 249:34;p< 1:01016;
-= 0:648, S.E. = 0:042; and confidence: 2(1) = 432:76;p < 1:01016;= 0:104,
-S.E.= 0:005. Methods, Experiment Analyses). Additionally, when we gave a separate group
-of participants the awareness probes on these mazes, value-guided construal was again predictive
-(Awareness: 2(1) = 837:47;p < 1:01016;= 0:175, S.E. = 0:006). Thus, using three
-different measures of memory (recall accuracy, recall confidence, and awareness judgments), we
-found further evidence that when planning, people form task representations that optimally balance
-complexity and utility.
-11a b
-c
-0.0 0.4 0.5 0.6 0.7 0.8 0.9 1.0
-Accuracy0.00.30.40.50.60.70.80.9ConfidencePlanning
-0.0 0.4 0.5 0.6 0.7 0.8 0.9 1.0
-Accuracy0.00.30.40.50.60.70.80.9Perception Control
-Obstacle Type
-Relevant/Near
-Relevant/Far (Critical)
-Irrelevant
-0.0 0.4 0.5 0.6 0.7 0.8 0.9 1.0
-Accuracy0.00.30.40.50.60.70.80.9Execution Control
-Optimal PathIrrelevantIrrelevant
-Relevant/Far
-(Critical)Relevant/Near
-0 20 40 60 80 100 120
-Change in AICVGC
-Traj HS
-Graph HS
-Bottleneck
-SR Overlap
-Nav Dist
-Nav Dist Step
-Goal Dist
-Start Dist
-Wall Dist
-Center DistLesioned
-Predictor
-Figure 4. Critical mazes recall experiment, model comparisons, and control studies. a,
-The critical mazes recall experiment ( n= 78 independent participants; one version of one of the
-four planning experiments) used critical mazes that included critical obstacles that were highly
-relevant to planning but far from an optimal path (dashed line). Value-guided construal predicts
-critical obstacles will be included in a construal while irrelevant obstacles will not, indepen-
-dent of distance to the optimal path. b,We fit a global model to recall responses that included
-the fixed parameter value-guided construal modification model (VGC) along with ten alternative
-predictors based on heuristic search models, successor representation-based predictors, and low-
-level perceptual cues (see Methods, Experiment Analyses). Then, each predictor was removed
-from this global model, and we calculated the resulting change in fit (in AIC). Removing value-
-guided construal led to the largest degradation of fit (greatest increase in AIC), underscoring its
-unique explanatory value. c,In a pair of non-planning control experiments, new participants ei-
-ther viewed patterns that looked exactly like the mazes (perceptual control; n= 88 independent
-participants) or followed “breadcrumbs” through the maze along a path taken by a participant
-from the original experiment (execution control; n= 80 independent participants). They then an-
-swered the exact same recall questions. Value-guided construal remains a significant factor when
-explaining recall in the original critical mazes experiment (planning) while including mean re-
-call from the perceptual and execution controls as covariates (likelihood ratio test for accuracy:
-2(1) = 106:36;p= 6:21025; confidence: 2(1) = 18:56;p= 1:6105;p-values
-are unmodified). This confirms that responses consistent with value-guided construal are not a
-simple function of perception and execution. Participants were recruited through the Prolific on-
-line experiment platform. Plotted are the mean values for each obstacle, with relevant/near, rele-
-vant/far (critical), and irrelevant obstacle types distinguished. Error bars are standard errors about
-the mean.
-12Controlling for perception and execution
-The memory studies provide preliminary confirmation of our hypothesis, but they have several
-limitations. One is that, although participants were engaged in planning , they were also necessarily
-engaged in other forms of cognitive processing, and these unrelated processes may have influenced
-memory of the obstacles. In particular, participants’ perception of a maze or their execution of a
-particular plan through a maze may have influenced their responses to the memory probes. This
-potentially confounds the interpretation of our results, since a key part of our hypothesis is that
-task construals arise from planning , rather than simply perceiving or executing.
-Thus, to test that responses to the memory probes cannot be fully explained by perception
-and/or execution, we administered two sets of yoked controls that did not require planning (Meth-
-ods, Experimental Design, Control Experiments). In the perceptual controls , new participants were
-shown patterns that looked exactly like the mazes, but they performed an unrelated, non-planning
-task. Each pattern was presented to a new participant for the same amount of time that a partic-
-ipant in the original experiments had examined the corresponding maze before moving—i.e., the
-amount of time the original participant spent examining the maze to plan. The new participant then
-responded to the same probes, in the same order, as the original participant. For the execution con-
-trols, we recruited another group of participants and gave them instructions similar to those in the
-planning experiments. However, unlike the original experiments, the task did not require planning.
-Rather, these mazes included “breadcrumbs” that needed to be collected and that appeared every
-two steps. Breadcrumbs appeared along the exact path taken by one of the original participants,
-meaning that the new participant executed the same actions but without having planned . After
-completing each maze, the participant then received the same probes, in the same order, as the
-original participant.
-We assessed whether responses in the planning experiments can be explained by a simple
-combination of perception and/or execution by testing whether value-guided construal remained
-a significant factor after accounting for control responses. Specifically, we used the mean by-
-obstacle responses from the perceptual and execution controls as predictors in HGLMs fit to
-13the corresponding planning responses. We then tested whether adding value-guided construal
-as a predictor improved fits. For the awareness, accuracy, and confidence responses in the re-
-call experiment, we found that including value-guided construal significantly improved fits (like-
-lihood ratio tests comparing models on accuracy: 2(1) = 106:36;p= 6:21025; confi-
-dence:2(1) = 18:56;p= 1:6105; and awareness: 2(1) = 55:34;p= 1:01013)
-and that value-guided construal predictions were positively associated with responses (coefficients
-for accuracy: = 0:58;S.E. = 0:058; confidence: = 0:039;S.E. = 0:009; and awareness:
-= 0:054;S.E. = 0:007). Thus, responses following planning are not reducible to a simple
-combination of perception andexecution , and they can be further explained by the formation of
-value-guided construals (Figure 4c; Supplementary Control Experiment Analyses).
-Externalizing the planning process
-Another limitation of the previous planning experiments is that they assess construal after planning
-is complete (i.e., by probing memory). To obtain a measure of the planning process as it unfolds ,
-we developed a novel process-tracing paradigm . In this version of the task, participants never
-saw all of the obstacles at once. Instead, at the beginning of the trial, after being shown the start
-and goal locations, they could use their mouse to reveal individual obstacles by hovering over them
-(Methods, Experimental Design, Process-tracing Experiments; Extended Data Figure 4b). This led
-participants to externalize the planning process, and so their behavior on this task provides insight
-into how planning computations unfolded internally. We tested whether value-guided construal
-accounted for behavior by analyzing two measures: whether an obstacle was hovered over and, if
-it was hovered over, the duration of hovering. Value-guided construal was a significant predictor
-for both these measures on both the initial mazes (likelihood ratio tests comparing HGLMs for
-hovering:2(1) = 1221:76;p < 1:01016;= 0:704, S.E. = 0:021; and hover duration [log
-milliseconds]: 2(1) = 169:90;p < 1:01016;= 0:161, S.E. = 0:012) and on the critical
-mazes (hovering: 2(1) = 1361:92;p < 1:01016;= 0:802, S.E. = 0:023; hover duration
-14[log milliseconds]: 2(1) = 540:63;p < 1:01016;= 0:369, S.E. = 0:016). These results
-thus complement our original memory-based measurements of people’s task representations and
-strengthen the interpretation of them in terms of value-guided construal during planning.
-Value-guided construal modification
-Thus far, our account of value-guided construal has assumed that an obstacle is either always
-or never included in a construal. This simplification is useful since it enables us to derive clear
-qualitative predictions based on whether a plan is influenced by an obstacle, but it overlooks graded
-factors such as how much of a plan is influenced by an obstacle. For example, an obstacle may only
-be relevant for planning a few movements around a participant’s initial location in a maze and, as
-a result, could receive less total attention than one that is relevant for deciding how to act across
-a larger area of the maze. To characterize these more fine-grained attentional processes, we first
-generalized the original construal selection problem to a one in which the decision-maker revisits
-and potentially modifies their construal during planning. Then, we derived obstacle awareness
-predictions based on a theoretically optimal construal modification policy that balances complexity
-and utility (Methods, Model Implementation, Value-Guided Construal).
-To assess value-guided construal modification, we re-analyzed our data using three versions of
-the model with increasing ability to capture variability in responses. First, we used an idealized
-fixed parameter model to derive a single set of obstacle attention predictions and confirmed that
-they also predict participant responses on the planning tasks (Supplementary Construal Modifica-
-tion Analyses). Second, for each planning measure and experiment, we calculated fitted parameter
-models in which noise parameters for the computed plan and construal modification policy were
-fit (Methods, Model Implementation, Value-Guided Construal). Scatter plots comparing mean by-
-obstacle responses and model outputs for parameters with the highest R2are shown in Figure 5.
-Finally, we fit a set of models that allowed for biases in computed plans (e.g., a bias to stay along
-the edge of a maze or an explicit penalty for bumping into walls) and found that this additional ex-
-15pressiveness led to obstacle attention predictions with an improved correspondence to participant
-responses (Supplementary Construal Modification Analyses). Together, these analyses provide
-additional insight into the fine-grained dynamic structure of value-guided construal modification.
-0.00 0.25 0.50 0.75 1.00
-Fitted Value-Guided
-Construal Modification Prob0.20.40.60.8Initial Exp
-Awareness Judgment
-R2=0.53 
-0.00 0.25 0.50 0.75 1.00
-Fitted Value-Guided
-Construal Modification Prob0.20.40.60.8Up-Front Planning Exp
-Awareness Judgment
-R2=0.44 
-0.00 0.25 0.50 0.75 1.00
-Fitted Value-Guided
-Construal Modification Prob0.40.50.60.70.80.91.0Critical Maze Exp
-Recall Accuracy
-R2=0.87 
-0.00 0.25 0.50 0.75 1.00
-Fitted Value-Guided
-Construal Modification Prob0.40.50.60.70.80.9Critical Maze Exp
-Recall Confidence
-R2=0.81 
-0.00 0.25 0.50 0.75 1.00
-Fitted Value-Guided
-Construal Modification Prob0.20.40.60.8Critical Maze Exp
-Awareness Judgment
-R2=0.74 
-0.00 0.25 0.50 0.75 1.00
-Fitted Value-Guided
-Construal Modification Prob0.00.20.40.60.81.0Process-Tracing
-(Initial Mazes)
-Hovering
-R2=0.42 
-0.0 0.5 1.0
-Fitted Value-Guided
-Construal Modification Prob5.05.56.06.57.07.5Process-Tracing
-(Initial Mazes)
-Log-Hover Duration
-R2=0.30 
-0.00 0.25 0.50 0.75 1.00
-Fitted Value-Guided
-Construal Modification Prob0.00.20.40.60.81.0Process-Tracing
-(Critical Mazes)
-Hovering
-R2=0.61 
-0.00 0.25 0.50 0.75 1.00
-Fitted Value-Guided
-Construal Modification Prob5.56.06.57.0Process-Tracing
-(Critical Mazes)
-Log-Hover Duration
-R2=0.48 
-Figure 5. Fitted value-guided construal modification. Our initial model of value-guided
-construal focuses on whether an obstacle should or should not be included in a construal. We de-
-veloped a generalization that additionally accounts for how much an obstacle influences a plan if
-a decision-maker is optimally modifying their construal during planning (Methods, Model Im-
-plementations, Value-Guided Construal). We used an "-softmax noise model [35] for computed
-action plans and construal modification policies and, for each experiment and measure, searched
-for parameters that maximize the R2between model predictions and mean by-obstacle responses.
-Shown here are plots comparing scores that the fitted construal modification model assigns to
-each obstacle with participants’ mean by-obstacle responses for the nine measures.
-Accounting for alternative mechanisms
-While the analyses so far confirm the predictive power of value-guided construal, it is also im-
-portant to consider alternative planning processes. For instance, differential awareness could have
-been a passive side-effect of planning computations , rather than an active facilitator of planning
-computations as posited by value-guided construal. In particular, participants could have been
-planning by performing heuristic search over action sequences without actively construing the task,
-which would have led to differential awareness of obstacles as a byproduct of planning. Differ-
-ential awareness could also have arisen from alternative representational processes, such as those
-16based on the successor representation36or related subgoaling mechanisms37. Similarly, perceptual
-factors, such as the distance to the start, goal, walls, center, optimal path, or path taken, could have
-influenced responses.
-Based on these considerations, we identified ten alternative predictors (Methods, Model Imple-
-mentations; Extended Data Figures 5, 6, and 7; Code Availability Statement). All ten predictors
-plus the fixed value-guided construal modification predictions were included in global models that
-were fit to each of the nine planning experiment measures, and, in all cases, value-guided construal
-was a significant predictor (Extended Data Table 1; see Supplementary Alternative Mechanisms
-Analyses for the same analyses with the single-construal model).
-Furthermore, to assess the relative importance of each predictor, we calculated the change in
-fit (in terms of AIC) that resulted from removing each predictor from a global model (Methods,
-Experiment Analyses). Across all planning experiment measures, removing value-guided con-
-strual led to the first or second largest reduction in fit (Figure 4b; Extended Data Table 1). These
-“knock-out” analyses demonstrate the explanatory necessity of value-guided construal. To assess
-explanatory sufficiency , we fit a new set of single-predictor and two-predictor models using all pre-
-dictors and then calculated their 
AICs (Methods, Experiment Analyses; Extended Data Figure 8).
-For all nine experimental measures, value-guided construal was one of the top two single-predictor
-models and was one of the two factors included in the best two-predictor model. Together, these
-analyses confirm the explanatory necessity and sufficiency of value-guided construal.
-Discussion
-We tested the idea that when people plan, they do so by constructing a simplified mental representa-
-tion of a problem that is sufficient to solve it—a process that we refer to as value-guided construal.
-We began by formally articulating how an ideal, cognitively-limited decision-maker should con-
-strue a task so as to balance complexity and utility. Then, we showed that pre-registered predictions
-of this model explain people’s awareness, ability to recall problem elements (obstacles in a maze),
-17confidence in recall ability, and behavior in a process-tracing paradigm, even after controlling for
-the baseline influence of perception and execution as well as ten alternative mechanisms. These
-findings support the hypothesis that people make use of a controlled process of value-guided con-
-strual, and that it can help explain the efficiency of human planning. More generally, our account
-provides a framework for further investigating the cognitive mechanisms involved in construal. For
-instance, how are construal strategies acquired? How is construal selection shaped by computation
-costs, time, or constraints? From a broader perspective, our analysis suggests a deep connection
-between the control of construals and the acquisition of structured representations like objects and
-their parts that can be cognitively manipulated38,39, which can inform the development of intelli-
-gent machines. Future investigation into these and other mechanisms that interface with the control
-of representations will be crucial for developing a comprehensive theory of flexible and efficient
-intelligence.
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-21Methods
-Model Implementations
-Value-guided Construal
-Our model assumes the decision-maker has a set of cause-effect relationships that can be combined
-into a task construal that is then used for planning. To derive empirical predictions for the maze
-tasks, we assume a set of primitive cause-effect relationships, each of which is analogous to the
-example of interacting with furniture in a living room (see main text). For each maze, we modeled
-the following: The default effect of movement (i.e., pressing an arrow key causes the circle to
-move in that direction with probability 1"and stay in place with probability ","= 105),Move;
-the effect of being blocked by the center, plus-shaped ( +) walls (i.e., the wall causes the circle to
-notmove when the arrow key is pressed), Walls; and effects of being blocked by each of the N
-obstacles,Obstacle i;i= 1;:::;N . Since every maze includes the same movements and walls, the
-model only selected which obstacle effects to include. The utility function for all mazes was given
-by a step cost of1until the goal state was reached.
-Value-guided construal posits a bilevel optimization procedure involving an “outer loop” of
-construal and an “inner loop” of planning. Here, we exhaustively calculate potential solutions to
-this nested optimization problem by enumerating and planning with all possible construals (i.e.,
-subsets of obstacle effects). We exactly solved the inner loop of planning for each construal us-
-ing dynamic programming40and then evaluated the optimal stochastic computed plan under the
-actual task dynamics (i.e., Equation 2). For planning and evaluation, transition probabilities were
-multiplied by a discount rate of :99was used to ensure values were finite. The general procedure
-for calculating the value of construals is outlined in the algorithm in Extended Data Table 2. To
-be clear, our current research strategy is to derive theoretically optimal predictions for the inner
-loop of planning and outer loop of construal in the spirit of resource-rational analysis2. Thus,
-this specific procedure should not be interpreted as a process model of human construal. In the
-Supplemental Discussion of Algorithms for Construal Optimization, we discuss the feasibility of
-22optimizing construals and how an important direction for future research will involve investigating
-tractable algorithms for finding good construals.
-Given a value of representation function, VOR, that assigns a value to each construal, we model
-participants as selecting a construal according to a softmax decision-rule:
-P(c)/exp
-1VOR (c)	
-; (4)
-where > 0is a temperature parameter (for our pre-registered predictions = 0:1). We then
-calculated a marginalized probability for each obstacle being included in the construal, from the
-initial state, s0, corresponding to the expected awareness of that obstacle:
-P(Obstacle i) =X
-c1[Obstacle i2c]P(c); (5)
-where, for a statement X, 1[X]evaluates to 1ifXis true and 0ifXis false. We implemented this
-model in Python 3.7 using the msdm library (see Code Availability Statement).
-The basic value-guided construal model makes the simplifying assumption that the decision-
-maker plans with a single static construal. We can extend this idea to consider a decision-maker
-who revisits and potentially modifies their construal at each stage of planning. In particular, we
-can conceptualize this process in terms of a sequential decision-making problem induced by the
-interaction between task dynamics (e.g., a maze) and the internal state of an agent (e.g., a con-
-strual) [41]. The solution to this problem is then a sequence of modified construals associated with
-planning over different parts of the task (e.g., planning movements for different areas of the maze).
-Formally, we denote the set of possible construals as C=P(f1;:::;Ng), the powerset of
-cause-effect relationships, and define a construal modification Markov Decision Process , which
-has a state space corresponding to the Cartesian product of task states and construals, (s;c)2SC ,
-and an action space corresponding to possible next construals, c02 C. Having chosen a new
-construalc0, the probability of transitioning from task state stos0comes from first calculating
-a joint distribution using the actual transition function P(s0js;a)and planc0(ajs)and then
-23marginalizing over task actions a:
-P(s0js;c0) =X
-ac0(ajs)P(s0js;a): (6)
-In this construal modification setting, the analogue to the value of representation (VOR; Equa-
-tion 3) is the optimal construal modification value function , defined over all s;c:
-V(s;c) =U(s) + max
-c0"X
-s0P(s0js;c0)V(s0;c0)C(c0;c)#
-; (7)
-whereC(c0;c) =jc0cjis the number of additional1cause-effect relationships in the new construal
-c0compared to c. Importantly, this cost on modifying the construal encourages consistency—i.e.,
-withoutC(c0;c), a decision-maker would have no disincentive to completely change their construal
-for each state. Note that in the special case where c=?, we recover the original static construal
-cost for a single step. Finally, using the construal modification value function, we define a softmax
-policy over the task/construal state space, (c0js;c)/expf1
-c[P
-s0P(s0js;c0)V(s0;c0)C(c0;c)]g.
-For the fixed parameter model we set c= 0:1(as with the single-construal model).
-The construal modification formulation allows us to consider not just whether an obstacle ap-
-pears in a construal, but also how long it appears in a construal. In particular, we would like to
-compute a quantity that is analogous to Equation 5 that assigns model values for each obstacle.
-To do this, we use the normalized task/construal state occupancy induced by a construal policy 
-from the initial task/construal state, (s;cjs0;c0)/M(s0;c0;s;c), wherec0=?andMis
-the successor representation under (for a self-contained review of M, see the section on Succes-
-sor Representation-based Predictors below). Given a policy and starting task state s0, for each
-obstacle, we calculate the probability of having a construal that includes that obstacle:
-P(Obstacle i) =X
-s;c1[Obstacle i2c](s;cjs0;c0): (8)
-1For sets AandB, the set difference AB=fa:a2Aanda =2Bg.
-24To calculate the optimal construal modification value function, V(s;c), for each maze, we con-
-structed construal modification Markov Decision Processes in Python (3.7) using scipy (1.5.2)
-sparse matrices [42]. We then exactly solved for V(s;c)using a custom implementation of policy
-iteration [43] designed to take advantage of the sparse matrix data structure (see Code Availability
-Statement). For the fitted parameter models, we used separate "-softmax noise models [35] for the
-computed plans, c(ajs), and construal modification policy, (c0js;c), and performed a grid
-search over the four parameters for each of the nine planning measures ( 1
-a2f1;3;5;7g;"a2
-f0:0;0:1;0:2g;1
-c2f1;3;5;7;9g;"c2f0;0:05;0:1;0:2;0:3g). Additionally, for parameter fit-
-ting, we limited the construals c02C to be of size three. This improves the speed of parameter
-evaluation and yields results comparable to the fixed parameter model, which uses the full con-
-strual set. Finally, to obtain obstacle value-guided construal probabilities we simulate 1000 rollouts
-of the construal modification policy to estimate (
js0;c0). As with the initial model, we empha-
-size that these procedures are not intended as an algorithmic account of construal modification, but
-rather allow us to derive theoretically optimal predictions of the fine-grained dynamics of value-
-guided construals during planning.
-Heuristic Search Over Action Sequences
-Value-guided construal posits that people control their task representations to actively facilitate
-planning , which, in the maze navigation paradigm, leads to differential attention to obstacles. How-
-ever, differential attention could also occur as a passive side-effect of planning , even in the absence
-of active construal. In particular, heuristic search over action sequences is another mechanism for
-reducing the cost of planning, but it accomplishes this in a different way: by examining possible
-action sequences in order of how promising they seem, not by simplifying the task representation.
-If people are simulating candidate action sequences via heuristic search (and not engaged in an ac-
-tive construal process), differential attention to task elements could have simply been a side-effect
-of how those simulations unfolded.
-Thus, we wanted to derive predictions of differential awareness as a byproduct of search over
-25action sequences. To do so, we considered two general classes of heuristic search algorithms.
-The first, a variant of Real-Time Dynamic Programming (RTDP)44,45, is a trajectory-based search
-algorithm that simulates physically realizable trajectories (i.e., sequences of states and actions that
-could be generated by repeatedly calling a fixed transition function). The algorithm works by
-first initializing a heuristic value function (e.g., based on domain knowledge). Then, it simulates
-trajectories that greedily maximize the heuristic value function while also performing Bellman
-updates at simulated states44. This scheme then leads RTDP to simulate states in order of how
-promising they are (according to the continuously updated heuristic value function) until the value
-function converges. Importantly, RTDP can end up visiting a fraction of the total state space,
-depending on the heuristic. Our implementation was based on the Labeled RTDP algorithm of
-Bonet & Geffner45, which additionally includes a labeling scheme that marks states where the
-estimate of the value function has converged, leading to faster overall convergence.
-To derive obstacle awareness predictions, we ran RTDP (implemented in msdm ; see Code
-Availability Statement) on each maze and initialized it with a heuristic corresponding to the optimal
-value function assuming there are plus-shaped walls but no obstacles . This models the background
-knowledge participants have about distances, while also providing a fair comparison to the initial
-information provided to the value-guided construal implementation. Additionally, if at any point
-the algorithm had to choose actions based on estimated value, ties were resolved randomly, making
-the algorithm stochastic. For each maze, we ran 200 simulations of the algorithm to convergence
-and examined which states were visited by the algorithm over all simulations. We calculated the
-mean number of times each obstacle was hitby the algorithm, where a hit was defined as a visit
-to a state adjacent to an obstacle such that the obstacle was in between the state and the goal.
-Because the distribution of hit counts has a long tail, we used the natural log of hit counts +1as
-the obstacle hit scores. The reason why the raw hit counts have a long tail is due to the particular
-way in which RTDP calculates the value of regions where the heuristic value is much higher than
-the actual value (e.g., dead ends in a maze). Specifically, RTDP explores such regions until it has
-confirmed that it is no better than an alternative path, which can take many steps. More generally,
-26trajectory-based algorithms are limited in that they can only update states by simulating physically
-realizable trajectories starting from the initial state.
-The limitations of trajectory-based planning algorithms motivated our use of a second class
-ofgraph-based planning algorithms. We used LAO46, a version of the classic Aalgorithm47
-generalized to be used on Markov Decision Processes (implemented in msdm ; see Code Availabil-
-ity Statement). Unlike trajectory-based algorithms, graph-based algorithms like LAOmaintain a
-graph of previously simulated states. LAOin particular builds a graph of the task rooted at the
-initial state and then continuously plans over the graph. If it computes a plan that leads it to a state
-at the edge of the graph, the graph is expanded according to the transition model to include that
-state and then the planning cycle is restarted. Otherwise, if it computes an optimal plan that only
-visits states in the simulated graph, the algorithm terminates. By continuously expanding the task
-graph and performing planning updates, the algorithm can intelligently explore the most promising
-(according to the heuristic) regions of the state space being constrained to physically realizable se-
-quences. In particular, graph-based algorithms can quickly “backtrack” when they encounter dead
-ends.
-Obstacle awareness predictions based on LAOwere derived by using the same initial heuristic
-as was used for RTDP and a similar scheme for handling ties. We then calculated the total number
-of times an obstacle was hit during graph expansion phases only, using the same definition of a hit
-as above. For each maze, we generated 200 planning simulations and used the raw hit counts as
-the hit score.
-Algorithms like RTDP and LAOplan by simulating realizable action sequences that begin at
-the start state. As a result, these models tend to predict greater awareness to obstacles that are near
-the start state and are consistent with the initial heuristic, regardless of whether those obstacles
-strongly affect or lie along the final optimal path. For instance, obstacles down initially promising
-dead ends have a high hit score. This contrasts with value-guided construal, which predicts greater
-attention to relevant obstacles, even if they are distant, and lower attention to irrelevant ones, even
-if they are nearby. For an example of these distinct model predictions, see maze #14 in Extended
-27Data Figure 6.
-To be clear, our goal was to obtain predictions for search over action sequences in the absence
-of an active construal process for comparison with value-guided construal. However, in general,
-heuristic search and value-guided construal are complementary mechanisms, since the former is a
-way to plan given a representation and the latter is a way to choose a representation for planning.
-For instance, one could perform heuristic search over a construed planning model, or a construal
-could help with selecting a heuristic to guide search over actions. These kinds of interactions
-between action-sequence search and construal are important directions for future research that can
-be built on the ideas developed here.
-Successor Representation-based Predictors
-We also considered two measures based on the successor representation , which has been proposed
-as a component in several computational theories of efficient sequential decision-making36,48. Im-
-portantly, the successor representation is not a specific model; rather it is a predictive coding of a
-task in which states are represented in terms of the future states likely to be visited from that state,
-given the decision-maker follows a certain policy. Formally, the value function of a policy (ajs)
-can be expressed in the following two equivalent ways:
-V(s) =U(s) +X
-a(ajs)X
-s0P(s0js;a)V(s0) (9)
-=X
-s+M(s;s+)U(s+); (10)
-whereM(s;s+)is expected occupancy of s+starting from s, when acting according to . The
-successor representation of a state sunderis then the vector M(s;
). Algorithmically, Mcan
-be calculated by solving a set of recursive equations (implemented in Python with numpy49; see
-Code Availability Statement):
-M(s;s+) = 1[s=s+] +X
-a;s0(ajs)P(s0js;a)M(s0;s+): (11)
-28Again, the successor representation is not itself an algorithm, but rather a policy-conditioned re-
-coding of states that can be a component of a larger computational process (e.g, different kinds
-of learning or planning). Here, we focus on its use in the context of transfer learning48,50and
-bottleneck states37,51.
-Research on transfer learning posits that the successor representation supports transfer that is
-more flexible than pure model-free mechanisms but less flexible than model-based planning. For
-example, Russek et al.50model agents that learned a successor representation for the optimal pol-
-icy in an initial maze and then examined transfer when the maze was changed (e.g., adding in a
-new barrier). While their work focuses on learning, rather than planning, we can borrow the ba-
-sic insight that the successor representation induced by the optimal policy for a source task can
-influence the encoding of a target task, which constitutes a form of construal. In our experiments,
-participants were not trained on any particular source task, but we can use the maze with all obsta-
-cles removed as a proxy (i.e., representing what all mazes had in common). Thus, we calculated
-the optimal policy for the maze without any obstacles (but with the start and goal), computed the
-successor representation M, and then calculated, for each obstacle iin the actual maze with the
-obstacles, a successor representation overlap (SR-Overlap) score:
-SR-Overlap (i) =X
-s2ObsiM(s0;s); (12)
-wheres0is the starting state and Obs iis the set of states occupied by the obstacle i. This quantity
-can be interpreted as the amount of overlap between an obstacle and the successor representation of
-the starting state. If the successor representation shapes how people represent tasks, this quantity
-would be associated with greater awareness of certain obstacles.
-The second predictor is related to the idea of bottleneck states . These emerge from how the
-successor representation encodes multi-scale task structure37, and they have been proposed as a
-basis for subgoal selection51. If bottlenecks guide subgoal selection, then distance to bottleneck
-states could give rise to differential awareness of obstacles via subgoaling processes. Thus, we
-29wanted to test that responses consistent with value-guided construal were not entirely attributable to
-the effect of bottleneck states calculated in the absence of an active construal process. Importantly,
-we note that as with alternative planning mechanisms like heuristic search, the identification of
-bottleneck states for subgoaling is compatible with value-guided construal (e.g., one could identify
-subgoals for a construed version of a task).
-When viewing the transition function of a task (e.g., a maze) as a graph over states, bottleneck
-states lie on either side of a partitioning of the state space into two regions such that there is high
-intra-region connectivity and low inter-region connectivity. This can be computed for any transition
-function using the normalized min-cuts algorithm52or derived from the second eigenvector of the
-successor representation under a random policy37. Here, we use a variant of the second approach
-as described in the appendix of37. Formally, given a transition function, P(s0js;a), we define an
-adjacency matrix, A(s;s0) = 1[9as.t.P(s0js;a)>0], and a diagonal degree matrix, D(s;s) =
-P
-s0A(s;s0). Then, the graph Laplacian, a representation often used to derive low-dimensional
-embeddings of graphs in spectral graph theory, is L=DA. We take the eigenvector with
-the second largest eigenvalue, which assigns a positive or negative value to each state in the task.
-This vector can be interpreted as projecting the state space onto a single dimension in a way that
-best preserves connectivity information, with a zero point that represents the mid-point of the
-projected graph. Bottleneck states correspond to those states nearest to 0. For each maze, we
-used this method to identify bottleneck states and further reduced these to the optimal bottleneck
-states , defined as bottleneck states with a non-zero probability of being visited under the optimal
-stochastic policy for the maze. Finally, for each obstacle, we calculated a bottleneck distance score,
-the minimum Manhattan distance from an obstacle to any of these bottleneck states.
-Notably, value-guided construal also predicts greater attention to obstacles that form bottle-
-necks because one often needs to carefully navigate through them to reach the goal. However,
-the predictions of our model differ for obstacles that are distant from the bottleneck. Specifically,
-value-guided construal predicts greater attention to relevant obstacles that affect the optimal plan,
-even if they are far from the bottleneck (e.g., see model predictions for maze #2 in Extended Data
-30Figure 5).
-Perceptual Landmarks
-Finally, we considered several predictors based on low-level perceptual landmarks and partici-
-pants’ behavior. These included the minimum Manhattan distance from an obstacle to the start
-location, the goal location, the center black walls, the center of the grid, and any of the locations
-visited by the participant in a trial (navigation distance). We also considered the timestep at which
-participants were closest to an object as a measure of how recently they were near an object. In
-cases where navigation distance was not an appropriate measure (e.g., if participants never nav-
-igated to the goal), we used the minimum Manhattan distance to trajectories sampled from the
-optimal policy averaged over 100 samples.
-Experimental Design
-All experiments were pre-registered (see Data Availability Statement) and approved by the Prince-
-ton Institutional Review Board (IRB). All participants were recruited from the Prolific online plat-
-form and provided informed consent. At the end of each experiment, participants provided free-
-response demographic information (age and gender, coded as male/female/neither). Experiments
-were implemented with psiTurk53and jsPsych54frameworks (see Code Availability Statement).
-Instructions and example trials are shown in the Supplementary Experimental Materials.
-Initial experiment
-Our initial experiment used a maze-navigation task in which participants moved a circle from
-a starting location on a grid to a goal location using the arrow keys. The set of initial mazes
-consisted of twelve 11 11 mazes with seven blue tetronimo-shaped obstacles and center walls
-arranged in a cross that blocked movement. On each trial, participants were first shown a screen
-displaying only the center walls. When they pressed the spacebar, the circle they controlled, the
-goal, and the obstacles appeared, and they could begin moving immediately. In addition, to ensure
-31that participants remained focused on moving, we placed a green square on the goal that shrank
-and would disappear after 1000ms but reset whenever an arrow key was pressed, except at the
-beginning of the trial when the green square took longer to shrink (5000ms). Participants received
-$0.10 for reaching the goal without the green square disappearing (in addition to the base pay
-of $0.98). The mazes were pseudo-randomly rotated or flipped, so the start and end state was
-constantly changing, and the order of mazes were pseudo-randomized. After completing each
-trial, participants received awareness probes, which showed a static image of the maze they had
-just navigated, with one of the obstacles shown in light blue. They were asked “How aware of the
-highlighted obstacle were you at any point?” and could respond using an 8-point scale (rescaled
-from 0 to 1 for analyses). Probes were presented for the seven obstacles in a maze. None of the
-probes were associated with a bonus.
-We requested 200 participants on Prolific and received 194 complete submissions. Following
-pre-registered exclusion criteria, a trial was excluded if, during navigation, >5000ms was spent at
-the initial state, >2000ms was spent at any non-initial state, >20000ms was spent on the entire
-trial, or>1500ms was spent in the last three steps in total. Participants with <80% of trials after
-exclusions or who failed 2 of 3 comprehension questions were excluded, which resulted in n= 161
-participants’ data being analyzed (median age of 28;81male, 75female, 5neither).
-Up-front planning experiment
-The up-front planning version of the memory experiment was designed to dissociate planning
-and execution. The main change was that after participants took their first step, all of the blue
-obstacles (but not the walls or goal) were removed from the display (though they still blocked
-movement). This strongly encouraged planning prior to execution. To provide sufficient time to
-plan, the green square took 60000ms to shrink on the first step. Additionally, on a random half
-of the trials, after taking two steps, participants were immediately presented with the awareness
-probes ( early termination trials). The other half were fulltrials. We reasoned that responses
-following early termination trials would better reflect awareness after planning but before execution
-32(see Supplementary Memory Experiment Analyses for analyses comparing early versus full trials).
-We requested 200 participants on Prolific and received 188 complete submissions. The exclu-
-sion criteria were the same as in the initial experiment, except that the initial state and total trial
-time criteria were raised to 30000ms and 60000ms, respectively. After exclusions, we analyzed
-data fromn= 162 participants (median age of 28; 85 male, 72 female, 5 neither).
-Critical mazes experiment
-In the critical mazes experiment , participants again could not see the obstacles while executing
-and so needed to plan up front, but no trials ended early. There were two main differences with
-the previous experiments. First, we used a set of four critical mazes that included critical obsta-
-cles chosen to test predictions specific to value-guided construal. These were obstacles relevant
-to decision-making, but distant from the optimal path (see Supplementary Memory Experiment
-Analyses for analyses focusing on these critical obstacles). Second, half of the participants re-
-ceived recall probes in which they were shown a static image of the grid with only the walls, a
-green obstacle, and a yellow obstacle. They were then asked “An obstacle was either in the yellow
-or green location (not both), which one was it?” and could select either option, followed by a
-confidence judgment on an 8-point scale (rescaled from 0 to 1 for analyses). Pairs of obstacles
-and their contrasts in the critical mazes are shown in Extended Data Figure 4a. Participants each
-received two blocks of the four critical mazes, pseudo-randomly oriented and/or flipped.
-We requested 200 participants on Prolific and received 199 complete submissions. The trial
-and participant exclusion criteria were the same as in the up-front planning experiment. After
-exclusions, we analyzed data from n= 156 participants (median age of 26; 78 male, 75 female, 3
-neither).
-Control Experiments
-The aim of the control experiments was to obtain yoked baselines for perception and execution for
-comparison with probe responses in the memory studies. The perceptual control used a variant of
-33the task in which participants were shown patterns that were perceptually identical to the mazes.
-Instead of solving a maze, they were told to “catch the red dot”: On each trial, a small red dot could
-appear anywhere on the grid, and participants were rewarded based on whether they pressed the
-spacebar after it appeared. Each participant was yoked to the responses of a participant from either
-theup-front planning orcritical mazes experiments. On yoked trials , participants were shown
-the exact same maze/pattern as their counterpart. Additionally, they were shown the pattern for
-the amount of time that their counterpart took before making their first move—since the obstacles
-were not visible during execution for the counterpart, this is roughly the time the counterpart spent
-looking at the maze to plan. A red dot never appeared on these trials, and they were followed by
-the exact same probes that the counterpart received. References to “obstacles” were changed to
-“tiles” (e.g., “highlighted tiles” as opposed to “highlighted obstacle” for the awareness probes).
-We also included dummy trials , which showed mazes in orientations not appearing in the yoked
-trials, for durations sampled from the yoked durations. Half of the dummy trials had red dots. We
-recruited enough participants such that at least one participant was matched to each participant
-from the original experiments and excluded people who said that they had participated in a similar
-experiment. This resulted in data from n= 164 participants being analyzed for the initial mazes
-perceptual control (median age of 30:5; 84 male, 79 female, 1 neither) and n= 172 for the critical
-mazes perceptual control (median age of 36.5; 86 male, 85 female, 1 neither).
-The execution control used a variant of the task in which participants followed a series of
-“breadcrumbs” through the maze to the goal and so did not need to plan a path to the goal. Each
-participant was yoked to a counterpart in either the initial experiment or the critical mazes experi-
-ment so that the breadcrumbs were generated based on the exact path taken by the counterpart. The
-ordering of the mazes and obstacle probes (i.e., awareness or location recall) were also the same.
-We recruited participants until at least one participant was matched to each participant from the
-original experiments. Additionally, we used the same exclusion criteria as in the initial experiment
-with the additional requirement that all black dots be collected on a trial. This resulted in data from
-n= 163 participants being analyzed for the initial mazes execution control (median age of 29; 86
-34male, 77 female) and n= 161 for the critical mazes execution control (median age of 30; 94 male,
-63 female; 4 neither).
-Process-Tracing Experiments
-We ran process-tracing experiments using the initial mazes and the critical mazes. These experi-
-ments were similar to the memory experiments, except they used a novel process-tracing paradigm
-designed to externalize the planning process. Specifically, participants never saw all the obstacles
-in the maze at once. Rather, at the beginning of a trial, after clicking on a red X in the center
-of the maze, the goal and agent appeared, and participants could use their mouse to hover over
-the maze and reveal individual obstacles. An obstacle would become completely visible if the
-mouse hovered over any tile that was part of it for at least 25ms, until the mouse was moved to a
-tile that was not part of that obstacle. Once the participant started to move using the arrow keys,
-the cursor became temporarily invisible (to prevent using the cursor as a cue to guide execution),
-and the obstacles could no longer be revealed. We examined two dependent measures for each
-obstacle: whether participants hovered over an obstacle, and if so, the duration of hovering in log
-milliseconds.
-For each experiment with each set of mazes, we requested 200 participants on Prolific. Partic-
-ipants who completed the task had their data excluded if they did not hover over any obstacles on
-more than half of the trials. For the experiment with the initial set, we received completed submis-
-sions from 174 people and, after exclusions, analyzed data from n= 167 participants (median age
-of 30; 82 male, 82 female, 3 neither). For the experiment with the critical set, we received com-
-pleted submissions from 188 people and, after exclusions, analyzed data from n= 179 participants
-(median age of 32; 89 male, 86 female, 4 neither).
-Experiment Analyses
-Hierarchical generalized linear models (HGLMs) were implemented in Python and R using the
-lme455andrpy256packages (see Code Availability Statement). For all models, we included by-
-35participant and by-maze random intercepts, unless the resulting model was singular, in which case
-we removed by-maze random intercepts. For the memory experiment analyses testing whether
-value-guided construal predicted responses, we fit models with and without z-score normalized
-value-guided construal probabilities as a fixed effect and performed likelihood ratio tests to assess
-significance. For the control experiment analyses reported in the main text, we calculated mean
-by-obstacle responses from the perceptual and execution controls, and then included these values
-as fixed effects in models fit to the responses in the planning experiments. We then contrasted
-models with and without value-guided construal and performed likelihood ratio tests (additional
-analyses are reported in the Supplementary Memory Experiment Analyses and Supplementary
-Control Experiment Analyses).
-For our comparison with alternative models, we considered 11 different predictors that assign
-scores to obstacles in each maze: fixed-parameter value-guided construal modification probabil-
-ity (VGC), trajectory-based heuristic search score (Traj HS), graph-based heuristic search score
-(Graph HS), bottleneck state distance (Bottleneck), successor representation overlap (SR Over-
-lap), minimum navigation distance (Nav Dist), timestep of minimum navigation distance (Nav
-Dist Step), minimum optimal policy distance (Opt Dist), distance to goal (Goal Dist), distance to
-start (Start Dist), distance to center walls (Wall Dist), and distance to the center of the maze (Cen-
-ter Dist). We included predictors in the analysis of each experiment’s data where appropriate. For
-example, in the up-front planning experiment, participants did not navigate on early termination
-trials, and so we used the optimal policy distance rather than navigation distance. All predictors
-were z-score normalized before being included as fixed effects in HGLMs in order to facilitate
-comparison of estimated coefficients.
-We performed three types of analyses using the 11 predictors. First, we wanted determine
-whether value-guided construal captured variability in responses from the planning experiments
-even when accounting for the other predictors. For these analyses, we compared HGLMs that
-included all predictors to HGLMs with all predictors except value-guided construal and tested
-whether there was a significant difference in fit using likelihood ratio tests (Extended Data Table 1).
-36Second, we wanted to evaluate the relative necessity of each mechanism for explaining attention to
-obstacles when planning. For these analyses, we compared global HGLMs to HGLMs with each
-of the predictors removed and calculated the resulting change in AIC (see Extended Data Table
-1 for estimated coefficients and resulting AIC values). Finally, we wanted to assess the relative
-sufficiency of predictors in accounting for responses on the planning tasks. For these analyses, we
-fit HGLMs to each set of responses that included only individual predictors or pairs of predictors,
-and for each model we calculated the 
AIC relative to the best-fitting model (Extended Data
-Figure 8). Note that for all of these models, AIC values are summed over participants.
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-38Acknowledgements : The authors would like to thank Jessica Hamrick, Louis Gularte, Ceyda
-Sayalı, Qiong Zhang, Rachit Dubey, and William Thompson for valuable feedback on this work.
-This work was funded by NSF grant #1545126, John Templeton Foundation grant #61454, and
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-Author Contributions : All authors contributed to conceptualizing the project and editing the
-manuscript. MKH, DA, MLL, and TLG developed the value-guided construal model. MKH im-
-plemented it. MKH and CGC implemented the heuristic search models and msdm library. MKH,
-JDC, and TLG designed the experiments. MKH implemented the experiments, analyzed the re-
-sults, and drafted the manuscript.
-Competing Interest Declaration : The authors declare no competing interests.
-Supplementary Information is available for this paper.
-Data Availability Statement : Data for the current study are available through the Open Science
-Foundation repository http://doi.org/10.17605/OSF.IO/ZPQ69.
-Code Availability Statement : Code for the current study are available through the Open Science
-Foundation repository http://doi.org/10.17605/OSF.IO/ZPQ69, which links to a GitHub repository
-and contains an archived version of the repository. The value-guided construal model and alterna-
-tive models were implemented in Python (3.7) using the msdm (0.6) library, numpy (1.19.2), and
-scipy (1.5.2). Experiments were implemented using psiTurk (3.2.0) and jsPsych (6.0.1).
-Hierarchical generalized linear regressions were implemented using rpy2 (3.3.6), lme4 (1.1.21),
-and R (3.6.1).
-39Maze 0.68
-.42 .74.26
-.83
-.60.19Initial Exp
-Awareness
-.53
-.38 .69.25
-.73
-.57.20Up-front planning
-Awareness
-.72
-.69 .75.31
-.93
-.90.35Process-tracing
-Hovering
-6.6
-6.1 6.85.8
-7.2
-7.05.9Process-tracing
-DurationMaze 1
-.66 .63.29.76.28
-.26.22
-.57 .69.28.70.23
-.27.21
-.81 .85.26.75.31
-.56.24
-6.6 7.05.76.76.1
-6.06.0Maze 2.70
-.50
-.59.50.79
-.31
-.44.56
-.41
-.65.50.71
-.35
-.47.94
-.67
-.75.64.88
-.27
-.796.6
-5.7
-6.56.36.6
-6.0
-6.6Maze 3.36.28
-.33
-.75.81
-.66.51.36.25
-.29
-.71.75
-.64.44.63.57
-.45
-.93.77
-.87.686.66.5
-6.4
-7.06.5
-6.86.0Maze 4.47
-.72.76
-.56.73
-.72.33
-.36
-.71.69
-.52.59
-.59.32
-.93
-.86.83
-.79.60
-.81.56
-6.5
-6.96.8
-5.96.0
-6.66.5Maze 5.71
-.37
-.41
-.76.54.83.24
-.61
-.29
-.31
-.71.53.73.23
-.77
-.52
-.71
-.84.85.89.52
-6.7
-6.1
-6.4
-7.47.17.36.4Extended Data Fig. 1 jExperimental measures on mazes 0 to 5, Average responses as-
-sociated with each obstacle in mazes 0 to 5 in the initial experiment (awareness judgment), the
-40up-front planning experiment (awareness judgment), and the process-tracing experiment (whether
-an obstacle was hovered over and, if so, the duration of hovering in log milliseconds). Obstacle
-colors are normalized by the minimum and maximum values for each measure/maze, except for
-awareness judgments, which are scaled from 0 to 1.
-41Maze 6.39
-.48.40
-.44.71.51
-.38Initial Exp
-Awareness
-.33
-.46.33
-.61.74.49
-.41Up-front planning
-Awareness
-.90
-.68.39
-.72.50.55
-.60Process-tracing
-Hovering
-6.5
-5.66.4
-6.76.46.4
-5.8Process-tracing
-DurationMaze 7.36.19
-.74
-.20.43 .18
-.69
-.31.27
-.76
-.25.47 .26
-.69
-.71.16
-.67
-.25.27 .13
-.67
-6.25.4
-6.3
-6.15.8 5.8
-6.6Maze 8.18
-.61.29
-.41.25.35
-.70.20
-.72.28
-.35.24.40
-.79.09
-.51.49
-.70.18.14
-.885.0
-6.36.0
-6.25.75.5
-6.5Maze 9
-.30
-.20.79.81.39
-.34
-.78.27
-.23.73.80.42
-.30
-.78.50
-.66.82.88.79
-.82
-.915.8
-6.86.97.56.9
-6.6
-6.9Maze 10.66
-.77 .27
-.23
-.39.56 .43.74
-.73 .24
-.30
-.36.51 .39.92
-.65 .41
-.29
-.50.72 .416.8
-6.2 6.4
-5.9
-6.26.3 6.0Maze 11.71
-.47.23.80.83
-.19.41
-.65
-.32.22.77.79
-.23.38
-.59
-.57.21.77.93
-.15.63
-6.3
-6.45.97.17.5
-6.06.5Extended Data Fig. 2 jExperimental measures on mazes 6 to 11, Average responses as-
-sociated with each obstacle in mazes 6 to 11 in the initial experiment (awareness judgment), the
-42up-front planning experiment (awareness judgment), and the process-tracing experiment (whether
-an obstacle was hovered over and, if so, the duration of hovering in log milliseconds). Obstacle
-colors are normalized by the minimum and maximum values for each measure/maze, except for
-awareness judgments, which are scaled from 0 to 1.
-43Maze 12
-.67.51.57.92
-.78Critical Mazes Exp
-Accuracy
-.59.43.44.84
-.61Critical Mazes Exp
-Confidence
-.35.23.32.81
-.71Critical Mazes Exp
-Awareness
-.62.18.39.90
-.62Process-tracing
-Hovering
-6.45.35.36.8
-6.5Process-tracing
-DurationMaze 13
-.70.60.51.76.92
-.58.46.47.66.78
-.34.35.26.69.84
-.65.44.18.52.89
-6.25.45.46.26.9Maze 14.65.49
-.54.79.94
-.54.53
-.40.68.81
-.41.35
-.23.81.79
-.78.69
-.28.88.85
-6.36.5
-5.37.26.8Maze 15.66
-.58.45
-.85.87
-.56
-.42.62
-.74.79
-.39
-.23.32
-.81.76
-.75
-.56.67
-.85.88
-6.5
-6.56.6
-6.96.8Extended Data Fig. 3 jExperimental measures on mazes 12 to 15, Average responses as-
-sociated with each obstacle in mazes 12 to 15 in the critical mazes experiment (recall accuracy,
-recall confidence, and awareness judgment) and the process-tracing experiment (whether an ob-
-stacle was hovered over and, if so, the duration of hovering in log milliseconds). Obstacle colors
-are scaled to range from 0.5 to 1.0 for accuracy, 0 to 1 for hovering, confidence, and awareness
-judgments, and the minimum to maximum values across obstacles in a maze for hovering duration
-in log milliseconds.
-44Extended Data Fig. 4 jAdditional Experimental Details, a, Items from critical mazes exper-
-iment. Blue obstacles are the location of obstacles during the navigation part of the trial. Orange
-obstacles with corresponding number are copies that were shown during location recall probes.
-During recall probes, participants only saw an obstacle paired with its copy. b,Example trial from
-process-tracing experiment. Participants could never see all the obstacles at once, but, before nav-
-igating, could use their mouse to reveal obstacles. We analyzed whether value-guided construal
-predicted which obstacles people tended to hover over and, if so, the duration of hovering.
-45Maze 0.15
-.05 .430.0
-.73
-0.00.0VGC
-2.7
-3.6 3.82.9
-3.1
-2.0.04Traj HS
-1.4
-3.0 4.0.82
-5.0
-2.00.0Graph HS
-7.0
-5.0 1.011.0
-7.0
-1.09.0Bottleneck
-.76
-1.3 1.4.32
-.62
-.01.12SR Overlap
-1.0
-1.1 1.04.0
-1.0
-1.03.6Opt DistMaze 1
-.25 .040.0.400.0
-0.00.0
-1.7 .360.01.20.0
-0.00.0
-4.0 .530.01.30.0
-0.00.0
-11.0 3.07.01.07.0
-11.012.0
-1.6 .051.5.421.4
-.81.01
-1.0 1.64.01.03.0
-2.08.0Maze 2.42
-0.0
-.170.0.85
-0.0
-0.03.1
-4.5
-1.83.13.1
-0.0
-.311.0
-5.0
-1.25.05.0
-0.0
-.096.0
-5.0
-1.05.09.0
-3.0
-5.01.0
-0.0
-0.00.00.0
-0.0
-0.01.0
-1.2
-1.01.41.0
-2.0
-1.8Maze 3.160.0
-.02
-.70.80
-.23.363.33.6
-3.0
-1.71.1
-1.72.40.01.1
-2.4
-2.52.0
-1.72.38.07.0
-5.0
-8.09.0
-5.01.0.61.46
-.62
-.84.20
-.25.833.07.0
-4.1
-1.01.0
-1.21.0Maze 4.45
-.03.47
-.17.20
-.31.01
-4.3
-1.93.2
-4.5.86
-1.6.13
-3.0
-1.04.5
-5.01.0
-2.1.14
-9.0
-5.01.0
-7.010.0
-3.05.0
-1.0
-0.00.0
-0.00.0
-0.00.0
-4.0
-1.01.0
-1.01.0
-1.02.3Maze 5.14
-.02
-0.0
-.450.0.730.0
-3.8
-3.4
-2.6
-3.53.53.14.1
-0.0
-2.4
-2.0
-5.04.05.00.0
-6.0
-6.0
-5.0
-1.03.08.09.0
-.78
-.75
-.47
-.57.64.67.37
-1.0
-4.0
-1.6
-1.01.01.03.0Maze 6.38
-.230.0
-0.00.0.01
-.32
-3.9
-3.80.0
-0.00.0.10
-.52
-4.0
-5.00.0
-0.00.0.15
-.63
-6.0
-7.08.0
-5.01.04.0
-4.0
-2.0
-1.1.84
-0.00.00.0
-1.7
-4.1
-1.01.0
-3.01.02.1
-1.2Maze 7.170.0
-.29
-0.00.0 0.0
-.63
-2.60.0
-.86
-0.00.0 0.0
-.69
-.750.0
-.57
-0.00.0 0.0
-1.0
-6.08.0
-2.0
-11.04.0 10.0
-1.0
-.50.13
-.38
-0.0.03 .03
-.25
-5.53.6
-1.0
-4.02.6 3.0
-1.0Extended Data Fig. 5 jModel predictions on mazes 0 through 7, Shown are the predictions
-for six of the eleven predictors we tested: fixed parameter value-guided construal modification
-46obstacle probability (VGC, our model); trajectory-based heuristic search obstacle hit score (Traj
-HS); graph-based heuristic search obstacle hit score (Graph HS); distance to optimal bottleneck
-(Bottleneck); successor representation overlap score (SR Overlap); and distance to optimal paths
-(Opt Dist) (see Methods, Model Implementations). Mazes 0 to 7 were all in the initial set of mazes.
-Darker obstacles correspond to greater predicted attention according to the model. Obstacle colors
-normalized by the minimum and maximum values for each model/maze.
-47Maze 80.0
-0.0.05
-.120.00.0
-.33VGC
-0.0
-0.01.5
-.970.00.0
-.98Traj HS
-0.0
-0.0.26
-1.60.00.0
-1.0Graph HS
-10.0
-2.06.0
-8.07.05.0
-1.0Bottleneck
-0.0
-0.0.97
-.810.00.0
-.26SR Overlap
-7.0
-1.03.5
-1.14.02.0
-1.0Opt DistMaze 9
-0.0
-0.0.46.58.45
-.28
-.143.3
-2.80.02.91.9
-4.0
-3.13.0
-2.0.675.01.0
-4.0
-4.07.0
-13.01.01.02.0
-8.0
-5.01.1
-.01.19.63.58
-.90
-1.34.0
-6.01.01.02.0
-5.0
-1.0Maze 10.19
-.43 .20
-0.0
-0.0.04 0.0.84
-2.6 4.1
-3.9
-1.9.28 .011.0
-4.4 1.1
-1.1
-1.3.36 .015.0
-1.0 8.0
-8.0
-6.08.0 11.0.06
-1.4 .90
-.58
-.59.29 1.51.2
-1.0 5.0
-6.9
-2.01.5 1.0Maze 11.32
-.220.0.54.68
-0.0.01
-3.7
-3.10.03.22.8
-0.0.22
-5.0
-3.00.05.05.0
-0.0.29
-4.0
-8.09.01.01.0
-12.07.0
-1.2
-.581.2.86.60
-.071.5
-1.0
-5.04.01.01.0
-7.91.0Maze 12
-.210.00.0.79
-.36
-3.50.03.73.4
-4.6
-3.00.05.05.0
-5.0
-8.08.06.04.0
-5.0
-.54.68.31.54
-.57
-6.04.02.01.0
-1.0Maze 13
-.190.00.0.38.84
-3.43.50.03.93.1
-4.05.00.04.05.0
-9.05.09.01.05.0
-.56.31.74.75.56
-6.02.05.01.01.0Maze 14.280.0
-0.0.29.82
-4.31.2
-3.83.63.1
-4.01.9
-4.03.05.0
-8.06.0
-6.01.010.0
-.93.02
-.73.64.58
-3.03.8
-4.01.01.0Maze 15.34
-0.00.0
-.30.87
-4.5
-3.51.5
-4.13.1
-5.0
-3.01.9
-4.05.0
-6.0
-10.07.0
-1.011.0
-1.0
-.02.02
-.61.56
-4.0
-6.53.7
-1.01.0Extended Data Fig. 6 jModel predictions on mazes 8 through 15, Shown are the predictions
-for six of the eleven predictors we tested (see Methods, Model Implementations). Mazes 8 to 11
-48were part of the initial set of mazes, while mazes 12 to 15 constituted the set of critical mazes.
-Darker obstacles correspond to greater predicted attention according to the model. Obstacle colors
-normalized by the minimum and maximum values for each model/maze.
-49R² = 0.50  
-0.0 0.50.00.51.0Initial Exp.
-Awareness JudgmentVGC
-R² = 0.05  
-0.0 2.5Traj HS
-R² = 0.28  
-0 5Graph HS
-R² = 0.32  
-5 10Bottleneck
-R² = 0.00  
-0 2SR Overlap
-R² = 0.55  
-2.5 5.0 7.5Opt Dist
-R² = 0.00  
-5 10 15Goal Dist
-R² = 0.00  
-5 10 15Start Dist
-R² = 0.06  
-2.5 5.0Wall Dist
-R² = 0.05  
-2.5 5.0 7.5Center Dist
-R² = 0.40  
-0.0 0.50.00.51.0Up-front Planning Exp.
-Awareness JudgmentR² = 0.01  
-0.0 2.5R² = 0.18  
-0 5R² = 0.39  
-5 10R² = 0.01  
-0 2R² = 0.53  
-2.5 5.0 7.5R² = 0.00  
-5 10 15R² = 0.00  
-5 10 15R² = 0.01  
-2.5 5.0R² = 0.01  
-2.5 5.0 7.5
-R² = 0.83  
-0.0 0.50.00.51.0Critical Maze Exp.
-Recall Accuracy
-R² = 0.25  
-0.0 2.5R² = 0.42  
-0 5R² = 0.06  
-5 10R² = 0.11  
-0 1R² = 0.44  
-2.5 5.0R² = 0.15  
-5 10 15R² = 0.12  
-10 20R² = 0.04  
-2.5 5.0R² = 0.01  
-5 10
-R² = 0.80  
-0.0 0.50.00.51.0Critical Mazes Exp.
-Recall ConfidenceR² = 0.05  
-0.0 2.5R² = 0.19  
-0 5R² = 0.05  
-5 10R² = 0.02  
-0 1R² = 0.42  
-2.5 5.0R² = 0.27  
-5 10 15R² = 0.21  
-10 20R² = 0.02  
-2.5 5.0R² = 0.07  
-5 10
-R² = 0.71  
-0.0 0.50.00.51.0Cricical Mazes Exp.
-Awareness JudgmentR² = 0.15  
-0.0 2.5R² = 0.27  
-0 5R² = 0.20  
-5 10R² = 0.05  
-0 1R² = 0.69  
-2.5 5.0R² = 0.11  
-5 10 15R² = 0.07  
-10 20R² = 0.00  
-2.5 5.0R² = 0.01  
-5 10
-R² = 0.38  
-0.0 0.50.00.51.0Process-Tracing
-(Initial Mazes 0-11)
-Hovering
-R² = 0.23  
-0.0 2.5R² = 0.33  
-0 5R² = 0.17  
-5 10R² = 0.02  
-0 2R² = 0.32  
-2.5 5.0 7.5R² = 0.01  
-5 10 15R² = 0.03  
-5 10 15R² = 0.07  
-2.5 5.0R² = 0.07  
-2.5 5.0 7.5
-R² = 0.29  
-0.0 0.5567Process-Tracing
-(Initial Mazes 0-11)
-Log-Hover Duration R² = 0.09  
-0.0 2.5R² = 0.17  
-0 5R² = 0.17  
-5 10R² = 0.00  
-0 2R² = 0.16  
-2.5 5.0 7.5R² = 0.00  
-5 10 15R² = 0.01  
-5 10 15R² = 0.00  
-2.5 5.0R² = 0.00  
-2.5 5.0 7.5
-R² = 0.52  
-0.0 0.50.00.51.0Process-Tracing
-(Critical Mazes 12-15)
-Hovering
-R² = 0.22  
-0.0 2.5R² = 0.30  
-0 5R² = 0.03  
-5 10R² = 0.00  
-0 1R² = 0.21  
-2.5 5.0R² = 0.18  
-5 10 15R² = 0.13  
-10 20R² = 0.07  
-2.5 5.0R² = 0.17  
-5 10
-R² = 0.42  
-0.0 0.55.56.06.57.0Process-Tracing
-(Critical Mazes 12-15)
-Log-Hover Duration R² = 0.12  
-0.0 2.5R² = 0.11  
-0 5R² = 0.04  
-5 10R² = 0.00  
-0 1R² = 0.13  
-2.5 5.0R² = 0.11  
-5 10 15R² = 0.08  
-10 20R² = 0.12  
-2.5 5.0R² = 0.24  
-5 10Extended Data Fig. 7 jSummaries of candidate models and data from planning experi-
-ments, Each row corresponds to a measurement of attention to obstacles from a planning exper-
-iment: Awareness judgments from the initial memory experiment, the up-front planning experi-
-ment, and the critical mazes experiment; recall accuracy and confidence from the critical mazes
-50experiment; and the binary hovering measure and hovering duration measure (in log milliseconds)
-from the two process-tracing experiments. Each column corresponds to candidate processes that
-could predict attention to obstacles: fixed parameter value-guided construal modification obsta-
-cle probability (VGC, our model), trajectory-based heuristic search hit score (Traj HS), graph-
-based heuristic search hit score (Graph HS), distance to bottleneck states (Bottleneck), successor-
-representation overlap (SR Overlap), expected distance to optimal paths (Opt Dist), distance to the
-goal location (Goal Dist), distance to the start location (Start Dist), distance to the invariant black
-walls (Wall Dist), and distance to the center of the maze (Center Dist). Note that for distance-based
-predictors, the x-axis is flipped. For each predictor, we quartile-binned the predictions across ob-
-stacles, and for each bin we plot (bright red lines) the mean and standard deviation of the predictor
-and mean by-obstacle response (overlapping bins were collapsed into a single bin). Black circles
-correspond to the mean response and prediction for each obstacle in each maze. Dashed dark red
-lines are simple linear regressions on the black circles, with R2values shown in the lower right
-of each plot. Across the nine measures, value-guided construal tracks attention to obstacles, while
-other candidate processes are less consistently associated with obstacle attention (data are based
-onn= 84215 observations taken from 825independent participants).
-51a
-b
-cExtended Data Table 1 jNecessity of different mechanisms for explaining attention to ob-
-stacles when planning, For each measure in each planning experiment, we fit hierarchical gener-
-alized linear models (HGLMs) that included the following predictors as fixed-effects: fixed param-
-eter value-guided construal modification obstacle probability (VGC, our model); trajectory-based
-heuristic search obstacle hit score (Traj HS); graph-based heuristic search obstacle hit score (Graph
-HS); distance to optimal bottleneck (Bottleneck); successor representation overlap score (SR Over-
-52lap); distance to path taken (Nav Dist); timestep of point closest along path taken (Nav Dist Step);
-distance to optimal paths (Opt Dist); distance to the goal state (Goal Dist); distance to the start
-state (Start Dist); distance to any part of the center walls (Wall Dist); and distance to the center of
-the maze (Center Dist) (Methods, Model Implementations). If the measure was taken before par-
-ticipants navigated, distance to the optimal paths was used, otherwise, distance to the path taken
-and its timestep were used. a, b, Estimated coefficients and standard errors for z-score normalized
-predictors in HGLMs fit to responses from the initial experiment, up-front planning experiment (F
-= full trials, E = early termination trials), the critical mazes experiment, and the process-tracing ex-
-periments. We found that value-guided construal was a significant predictor even when accounting
-for alternatives (likelihood ratio tests between full global models and models without value-guided
-construal: Initial Exp, Awareness: 2(1) = 501:11;p< 1:01016; Up-front Exp, Awareness (F):
-2(1) = 282:17;p< 1:01016; Up-front Exp, Awareness (E): 2(1) = 206:14;p< 1:01016;
-Critical Mazes Exp, Accuracy: 2(1) = 114:87;p < 1:01016; Critical Mazes Exp, Confi-
-dence:2(1) = 181:28;p < 1:01016; Critical Mazes Exp, Awareness: 2(1) = 486:99;p <
-1:01016; Process-Tracing Exp (Initial Mazes), Hovering: 2(1) = 294:40;p < 1:01016;
-Process-Tracing Exp (Initial Mazes), Duration: 2(1) = 177:58;p< 1:01016; Process-Tracing
-Exp (Critical Mazes), Hovering: 2(1) = 183:52;p< 1:01016; Process-Tracing Exp (Critical
-Mazes), Duration: 2(1) = 251:16;p < 1:01016).c,To assess the relative necessity of each
-predictor for the fit of a HGLM, we conducted lesioning analyses in which, for each predictor in a
-given global HGLM, we fit a new lesioned HGLM with only that predictor removed. Each entry of
-the table shows the change in AIC when comparing global and lesioned HGLMs, where larger pos-
-itive values indicate a greater reduction in fit as a result of removing a predictor. According to this
-criterion, across all experiments and measures, value-guided construal is either the first or second
-most important predictor.Largest increase in AIC after lesioning;ySecond-largest increase.
-53VGCTraj HSGraph HS Bottleneck SR OverlapNav Dist
-Nav Dist StepGoal Dist Start Dist Wall DistCenter DistVGC
-Traj HS
-Graph HS
-Bottleneck
-SR Overlap
-Nav Dist
-Nav Dist Step
-Goal Dist
-Start Dist
-Wall Dist
-Center Dist2110
-20704937
-204732463750
-1096309223573127
-20064938367231204993
-0990684113213041306
-2089486735363036494312744945
-20244926370929814986129249374988
-211149183602312949901305492849894995
-2105481537343122478511584761480647954815
-20994843374231274822119347924838482946954847Initial Exp.
-Awareness
-VGCTraj HSGraph HS Bottleneck SR OverlapGoal Dist Start Dist Opt Dist Wall DistCenter DistVGC
-Traj HS
-Graph HS
-Bottleneck
-SR Overlap
-Goal Dist
-Start Dist
-Opt Dist
-Wall Dist
-Center Dist1405
-13003312
-138720112557
-279144610721444
-11493267235014203287
-130833142551137332893317
-1403329124131441328332883303
-0673496326500731725731
-13113298254713923214329832747323296
-129833062541137332313306328573032123304Up-front Planning Exp.
-Awareness
-VGCTraj HSGraph HS Bottleneck SR OverlapNav Dist
-Nav Dist StepGoal Dist Start Dist Wall DistCenter DistVGC
-Traj HS
-Graph HS
-Bottleneck
-SR Overlap
-Nav Dist
-Nav Dist Step
-Goal Dist
-Start Dist
-Wall Dist
-Center Dist28
-24285
-26221225
-19285223350
-30271207321332
-22203180243223243
-16272220340334244364
-0209197252289222309313
-2219201261301224325276326
-27286227344330227352278297358
-28284227351308239364300317246368Critical Mazes Exp.
-Accuracy
-VGCTraj HSGraph HS Bottleneck SR OverlapNav Dist
-Nav Dist StepGoal Dist Start Dist Wall DistCenter DistVGC
-Traj HS
-Graph HS
-Bottleneck
-SR Overlap
-Nav Dist
-Nav Dist Step
-Goal Dist
-Start Dist
-Wall Dist
-Center Dist39
-38638
-32481536
-0622522639
-21636535634662
-26438408440440440
-33591497584637429638
-17414394325475328471475
-8459424366523348524320523
-16577477614538430628477524657
-8543450579429406598468510413624Critical Mazes Exp.
-Confidence
-VGCTraj HSGraph HS Bottleneck SR OverlapNav Dist
-Nav Dist StepGoal Dist Start Dist Wall DistCenter DistVGC
-Traj HS
-Graph HS
-Bottleneck
-SR Overlap
-Nav Dist
-Nav Dist Step
-Goal Dist
-Start Dist
-Wall Dist
-Center Dist394
-3671314
-39211091129
-011489321234
-3921297110212031453
-151687652715720740
-28013011126120414557331511
-13010971049782132070113241356
-99115210758351373712139710451411
-39512571096122613467421513134414061514
-393122510721196120673714981358141211221498Critical Mazes Exp.
-Awareness
-VGCTraj HSGraph HS Bottleneck SR OverlapGoal Dist Start Dist Opt Dist Wall DistCenter DistVGC
-Traj HS
-Graph HS
-Bottleneck
-SR Overlap
-Goal Dist
-Start Dist
-Opt Dist
-Wall Dist
-Center Dist274
-2271153
-197743743
-124674443902
-27611497448241360
-209115374490213531427
-1761136740782129812831337
-0127204493551550441563
-26111547438961337135312935271357
-256115574490013461366130453713051370Process-Tracing (Initial Mazes)
-Hovering
-VGCTraj HSGraph HS Bottleneck SR OverlapGoal Dist Start Dist Opt Dist Wall DistCenter DistVGC
-Traj HS
-Graph HS
-Bottleneck
-SR Overlap
-Goal Dist
-Start Dist
-Opt Dist
-Wall Dist
-Center Dist171
-142455
-167341414
-35246223246
-77421343229419
-169446402201409447
-144401323197383390399
-125298281206255286243297
-23406335150399394364247407
-0388315124386378350229306390Process-Tracing (Initial Mazes)
-Duration
-VGCTraj HSGraph HS Bottleneck SR OverlapGoal Dist Start Dist Opt Dist Wall DistCenter DistVGC
-Traj HS
-Graph HS
-Bottleneck
-SR Overlap
-Goal Dist
-Start Dist
-Opt Dist
-Wall Dist
-Center Dist157
-1141176
-119875897
-10811568611452
-26117089914521588
-3173172995512941292
-0824771103013887911386
-158857775103510409069301038
-95748699141114241294138510181566
-315605471253936121212849132401409Process-Tracing (Critical Mazes)
-Hovering
-VGCTraj HSGraph HS Bottleneck SR OverlapGoal Dist Start Dist Opt Dist Wall DistCenter DistVGC
-Traj HS
-Graph HS
-Bottleneck
-SR Overlap
-Goal Dist
-Start Dist
-Opt Dist
-Wall Dist
-Center Dist139
-140580
-72554552
-7524476530
-114582554529597
-0484511337526526
-5500521340540459541
-141414419412419393393417
-103367464481362513526384569
-682643934211724734843357513Process-Tracing (Critical Mazes)
-Duration
-01000200030004000
-050010001500200025003000
-050100150200250300350
-0100200300400500600
-0200400600800100012001400
-0200400600800100012001400
-0100200300400
-0200400600800100012001400
-0100200300400500Extended Data Figure 8 jSufficiency of individual and pairs of mechanisms for explaining
-attention to obstacles when planning, To assess the individual and pairwise sufficiency of each
-54predictor for explaining responses in the planning experiments, we fit hierarchical generalized
-linear models (HGLMs) that included pairs of predictors as fixed effects. Each lower-triangle plot
-corresponds to one of the experimental measures, where pairs of predictors included in a HGLM
-as fixed-effects are indicated on the x- and y-axes. Values are the 
AIC for each model relative
-to the best fitting model associated with an experimental measure (lower values indicate better
-fit). Values along the diagonals correspond to models fit with a single predictor. According to this
-criterion, across all experimental measures, value-guided construal is the first, second, or third best
-single-predictor HGLM, and is always in the best two-predictor HGLM.
-55Extended Data Table 2 jAlgorithm for Computing the Value of Representation Function
-To obtain predictions for our our ideal model of value-guided construal, we calculated the value of
-representation of all construals in a maze. This was done by enumerating all construals (subsets of
-obstacle effects) and then, for each construal, calculating its behavioral utility and cognitive cost.
-This allows us to obtain theoretically optimal value-guided construals. For a discussion of alterna-
-tive ways of calculating construals, see the Supplementary Discussion of Construal Optimization
-Algorithms.
-56
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