Planning, the evaluation of prospective future actions using a model of the environment, plays a critical role in sequential decision making (Hunt et al., 2021; Mattar and Lengyel, 2022). Two-step choice tasks have revealed quantitative evidence that humans are capable of flexible planning (Momennejad et al., 2017; Miller and Venditto, 2021; Wunderlich et al., 2012). Under unfamiliar or uncertain task conditions, planning may depend upon and occur in conjunction with active sensing, the cognitively motivated process of gathering information from the environment (Kaplan and Friston, 2018). After all, one cannot make decisions about the future without knowing what options are available. Humans and animals perform near-optimal active sensing via eye movements during binary decision making tasks (Yang et al., 2016; Renninger et al., 2007) and visual search tasks (Najemnik and Geisler, 2005; Ma et al., 2011; Hoppe and Rothkopf, 2019). Such tasks are typically characterized by an observation model, a mapping between states and observations, and visual information serves to reduce uncertainty about the state. In contrast, sequential decision-making tasks require knowledge about the structure of the environment characterized by state transitions, and visual information can additionally contribute to reducing uncertainty about this structure. Therefore, the principles of visually-informed decision making uncovered in simplified, discrete settings may not generalize to natural behaviors like real-world navigation, which entails planning a sequence of actions rather than a binary choice. How can we study visually-informed planning in structured, naturalistic sequential decision-making ventures such as navigation?

Theoretical work suggests that information acquisition and navigational planning can be simultaneously achieved through active inference – orienting the sensory apparati to reduce uncertainty about task variables in the service of decision making (Kaplan and Friston, 2018). Humans are fortuitously equipped with a highly evolved visual system to perform goal-oriented inference. By swiftly parsing a large, complex scene on a millisecond timescale, the eyes actively interrogate and efficiently gather information from different regions of space to facilitate complex computations (Leigh and Kennard, 2004; Schroeder et al., 2010). At the same time, eye movements are influenced by the contents of internal deliberation and the prioritization of goals in real-time, providing a faithful readout of important cognitive variables (Yang et al., 2018; Gottlieb and Oudeyer, 2018; Hutton, 2008; Ryan and Shen, 2020). Thus, eye tracking lends itself as a valuable tool for investigating how humans and animals gather information to plan action trajectories (Hoppe et al., 2018; Henderson et al., 2013; Eckstein et al., 2017; Yang et al., 2018).

Over the past few decades, research on eye movements has led to a growing consensus that the oculomotor system has evolved to prioritize top-down, cognitive guidance over image salience (Henderson and Hayes, 2017; Hayhoe and Ballard, 2005; Schütt et al., 2019). During routine activities such as making tea, we tend to foveate specifically upon objects relevant to the task being performed (e.g. boiling water) while ignoring salient distractors (Hayhoe and Ballard, 2005; Kowler, 2011). A current consensus about active sensing is that gaze elucidates how humans mitigate uncertainty in a goal-oriented manner (Yang et al., 2018). Therefore, we hypothesize that in the context of navigation, gaze will be directed towards the most informative regions of space, depending upon the specific relationship between the participant’s position and their goal. A candidate framework to formalize this hypothesis is reinforcement learning (RL), whereby the goal of behavior is cast in terms of maximizing total long-term reward (Sutton and Barto, 2018). For example, this framework has been previously used to provide a principled account of why neuronal responses in the hippocampal formation depend upon behavioral policies and environmental geometries (Gustafson and Daw, 2011; Stachenfeld et al., 2017), as well as a unifying account of how the hippocampus samples memories to replay (Mattar and Daw, 2018). Incidentally, RL provides a formal interpretation of active sensing, which can be understood as optimizing information sampling for the purpose of improving knowledge about the environment, allowing for better planning and ultimately greater long-term reward (Yang et al., 2018). Here, we invoke the RL framework and hypothesize that eye movements should be directed towards spatial locations where small changes in the local structure of the environment can drastically alter the expected reward.

While active sensing manifests as overt behavior, the planning algorithms which underlie action selection are thought to be more covert (Hunt et al., 2021). Researchers have proposed that certain neural codes, such as hierarchical representations, would support efficient navigational planning by exploiting structural redundancies in the environment (Tomov et al., 2020; Solway et al., 2014). There is also evidence for predictive sequential neural activations during sequence learning and visual motion viewing tasks (Liu et al., 2019; Ekman et al., 2017; Kurth-Nelson et al., 2016). This is reminiscent of replay, a well-documented phenomenon in rodents during navigation (Johnson and Redish, 2007; Pfeiffer and Foster, 2013; Dragoi and Tonegawa, 2011; Brown et al., 2016). The mechanism by which humans perform visually-informed planning may similarly involve simulating sequences of actions that chart out potential trajectories, and chunking a chosen trajectory into subgoals for efficient implementation. As recent evidence shows that eye movements reflect the dynamics of internal beliefs during sensorimotor tasks (Lakshminarasimhan et al., 2020), we hypothesize that participants’ gaze dynamics would also reveal sequential trajectory simulation, and thus reveal the strategies by which humans plan during navigation.

To test both hypotheses mentioned above, we designed a virtual reality navigation task where participants were asked to navigate to transiently visible targets using a joystick in unfamiliar arenas of varying degrees of complexity. We found that human participants balanced foveating the hidden reward location with viewing highly task-consequential regions of space both prior to and during active navigation, and that environmental complexity mediated a trade-off between the two modes of information sampling. The experiment also revealed that participants’ eyes indeed rapidly traced the trajectories which they subsequently embarked upon, with such sweeps being more prevalent in complex environments. Furthermore, participants seemed to decompose convoluted trajectories by focusing their gaze on one turn at a time until they reached their goal. Taken together, these results suggest that the spatiotemporal dynamics of gaze are significantly shaped by cognitive computations underlying sequential decision making tasks like navigation.

In this study, we highlight the crucial role of eye movements for flexible navigation. We found that humans took trajectories nearly optimal in length through unfamiliar arenas, and spent more time planning prior to navigation in more complex environments. The spatial distribution of gaze was largely concentrated at the hidden goal location in the simplest environment, but participants increasingly interrogated the task-relevant structure of the environment as the arena complexity increased. In the temporal domain, participants often rapidly traced their future trajectory to and from the goal with their eyes (sweeping), and generally concentrated their gaze upon one subgoal (turn) at a time until they reached their destination. In summary, we found evidence that the neural circuitry governing the oculomotor system optimally schedules and allocates resources to tackle the diverse cognitive demands of navigation, producing efficient eye movements through space and time.

Eye movements provide a natural means for researchers to understand information seeking strategies, in both experimental and real-world settings (Gottlieb et al., 2013; Gottlieb et al., 2014). Past studies using simple decision making tasks probed whether active sensing, specifically via eye movements, reduces uncertainty about the state of the environment (such as whether a change in an image has occurred) (Yang et al., 2016; Renninger et al., 2007; Ahmad and Yu, 2013). But in sequential decision making tasks such as navigation, there is added uncertainty about the task-contingent causal structure (model) of the environment (Kaplan and Friston, 2018; Mattar and Lengyel, 2022). Common paradigms for goal-oriented navigation occlude large portions of the environment from view, usually in the interest of distinguishing model-based strategies from conditioned responses (Smittenaar et al., 2013; Simon and Daw, 2011; de Cothi et al., 2020) or allow very restricted fields of view where eye movements have limited potential for sampling information (Javadi et al., 2017; Ghamari and Golshany, 2021). Occlusions eliminate the possibility of gathering information about the structure of the environment using active sensing. By removing such constraints, we allowed participants to acquire a model of the environment without physically navigating through it, which yielded new insights about how humans perform visually-informed planning.

In particular, we found that the gaze is distributed between the two components of the model required to plan a path – the transition function, which describes the relationship between states, and the reward function, which describes the relationship between the states and the reward – with the distribution skewed in favor of the former in more complex environments. When alternative paths were available, gaze tended to be directed towards them at the expense of looking at the hidden reward location. These findings suggest a context-dependent mechanism which dictates the dynamic arbitration between competing controllers of the oculomotor system that seek information about complementary aspects of the task. Neurally, this could be implemented by circuits that exert executive control over voluntary eye movements. Candidate substrates include the dorsolateral prefrontal cortex, which is known to be important for contextual information processing and memory-guided saccades (Pierrot-Deseilligny et al., 1995; Johnston and Everling, 2006; Pierrot-Deseilligny et al., 2005), and the anterior cingulate cortex, which is known to be involved in evaluating alternative strategies (Tervo et al., 2021; Gaymard et al., 1998). To better understand the precise neural mechanisms underlying the spatial gaze patterns we observed, it would be instructive to examine the direction of information flow between the oculomotor circuitry and brain regions with strong spatial and value representations during this task in animal models. Future research may also investigate multi-regional interactions in humans by building on recent advances in data analysis that allow for eye movements to be studied in fMRI scanners (Frey et al., 2021). Our analysis of spatial gaze patterns is grounded in the RL framework, which provides an objective way to measure the utility of sampling information from different locations. However, this measure was agnostic to the temporal ordering of those samples. Given that previous work demonstrated evidence for the planning of multiple saccades during simple tasks like visual search (Hoppe and Rothkopf, 2019), incorporating chronology into a normative theory of eye movements in sequential decision-making tasks presents an excellent opportunity for future studies.

Meanwhile, we found that the temporal pattern of eye movements revealed a fine-grained view of how planning computations unfold in time. In particular, participants made sequential eye movements sweeping forward and/or backward along the future trajectory, evocative of forward and reverse replay by place cells in the hippocampus (Diba and Buzsáki, 2007; Pfeiffer and Foster, 2013). Shortly after fixating on the goal, participants’ gaze often swept backwards along their future trajectory, mimicking reverse replay. Because these sweeps predominantly occurred before movement, they may reflect depth-first tree search, a model-based algorithm for path discovery (Zhou and Hansen, 2008). Then, during movement, participants were more likely to make forward sweeps when momentarily slowing down at turning points, analogous to finding that neural replay mainly occurs during periods of relative immobility (Sosa and Giocomo, 2021). Several recent studies have also supported that replay serves to consolidate memory and generalize information about rewards (Gillespie et al., 2021; Liu et al., 2021; Eldar et al., 2020). In light of the similarities between sweeps and sequential hippocampal activations, we predict that direct or indirect hippocampal projections to higher oculomotor controllers (e.g. the supplemental eye fields through the orbitofrontal cortex) may allow eye movements to embody the underlying activations of state representations (Larson and Loschky, 2009; Wilming et al., 2017; Hannula and Ranganath, 2009). This would allow replays to influence the active gathering of information. Alternatively, active sensing could be a result of rapid peripheral vision processing which drives saccade generation, such that the eye movements reflect the outcome of sensory processing rather than prior experience. Consistent with this idea, past studies have demonstrated that humans can smoothly trace paths through entirely novel 2D mazes (Crowe et al., 2000; Crowe et al., 2004). Interestingly, neural modulation does occur in this direction — the contents of gaze have been found to influence activity in the hippocampus and entorhinal cortex (Turk-Browne, 2019; Liu et al., 2017; Monaco et al., 2014; Jun et al., 2016; Fotowat et al., 2019; Ringo et al., 1994). Therefore, it is conceivable that sequential neural activity could emerge from consolidating temporally extended eye movements such as sweeps. We hope that in future, simultaneous recordings from brain areas involved in visual processing, eye movement control, and the hippocampal formation would uncover the mechanisms underlying trajectory sweeping eye movements and their relationship to perception and memory.

Value-based decisions are known to involve lengthy deliberation between similar alternatives (Bakkour et al., 2019; Tajima et al., 2016). Participants exhibited a greater tendency to deliberate between viable alternative trajectories at the expense of looking at the reward location. Likelihood of deliberation was especially high when approaching a turn, suggesting that some aspects of path planning could also be performed on the fly. More structured arena designs with carefully incorporated trajectory options could help shed light on how participants discover a near-optimal path among alternatives. However, we emphasize that deliberative processing accounted for less than one-fifth of the spatial variability in eye movements, such that planning largely involved searching for a viable trajectory.

Although we have analyzed strategies of active sensing and planning separately, these computations must occur simultaneously and influence each other. This is formalized by the framework of active inference that unifies planning and information seeking by integrating the RL framework, which describes exploiting rewards for their extrinsic value, and the information theoretic framework, which describes exploring new information for its epistemic value (Kaplan and Friston, 2018). Using this framework to simulate eye movements in a spatial navigation task, Kaplan and Friston, 2018 found that gaze is dominated by epistemic (curiosity) rather than pragmatic (reward) considerations in the first few trials, a prediction that is not supported by our results. However, it is possible that participants were able to rapidly resolve uncertainty about the arena structure in our experiments. Future studies must identify the constraints under which active inference models can provide quantitatively good fits to our data. In another highly relevant theoretical work, Mattar and Daw proposed that path planning and structure learning are variants of the same operation, namely the spatiotemporal propagation of memory (Mattar and Daw, 2018). The authors show that prioritization of reactivating memories about reward encounters and imminent choices depends upon its utility for future task performance. Through this formulation, the authors provided a normative explanation for the idiosyncrasies of forward and backward replay, the overrepresentation of reward locations and turning points in replayed trajectories, and many other experimental findings in the hippocampus literature. Given the parallels between eye movements and patterns of hippocampal activity, it is conceivable that gaze patterns can be parsimoniously explained as an outcome of such a prioritization scheme. But interpreting eye movements observed in our task in the context of the prioritization theory requires a few assumptions. First, we must assume that traversing a state space using vision yields information that has the same effect on the computation of utility as does information acquired through physical navigation. Second, peripheral vision allows participants to form a good model of the arena such that there is little need for active sensing. In other words, eye movements merely reflect memory access and have no computational role. Finally, long-term statistics of sweeps gradually evolve with exposure, similar to hippocampal replays. These assumptions can be tested in future studies by titrating the precise amount of visual information available to the participants, and by titrating their experience and characterizing gaze over longer exposures. We suspect that a pure prioritization-based account might be sufficient to explain eye movements in relatively uncluttered environments, whereas navigation in complex environments would engage mechanisms involving active inference. Developing an integrative model that features both prioritized memory-access as well as active sensing to refine the contents of memory, would facilitate further understanding of computations underlying sequential decision-making in the presence of uncertainty.

The tendency of humans to break larger problems into smaller, more tractable subtasks has been previously established in domains outside of navigation (Killian et al., 2012; Meister and Buffalo, 2018; Killian and Buffalo, 2018; Eckstein and Collins, 2020; Tomov et al., 2020). However, theoretical insights on clustered representations of space have not been empirically validated in the context of navigation (Balaguer et al., 2016; Rasmussen et al., 2017), primarily due to the difficulty in distinguishing between flat and hierarchical representations from behavior alone. Our observation that participants often gazed upon the upcoming turn during movement supports that participants viewed turns as subgoals of an overall plan. Future work could focus on designing more structured arenas to experimentally separate the effects of path length, number of subgoals, and environmental complexity on participants’ eye movement patterns.

We hope that the study of visually-informed planning during navigation will eventually generalize to understanding how humans accomplish a variety of sequential decision-making tasks. A major goal in the study of neuroscience is to elucidate the principles of biological computations which allow humans to effortlessly exceed the capabilities of machines. Such computations allow animals to learn environmental contingencies and flexibly achieve goals in the face of uncertainty. However, one of the main barriers to the rigorous study of active, goal-oriented behaviors is the complexity in estimating the participant’s prior knowledge, intentions, and internal deliberations which lead to the actions that they take. Luckily, eye movements reveal a wealth of information about ongoing cognitive processes during tasks as complex and naturalistic as spatial navigation.

Relevance simulations: Motivating the quantitative characterization of the task relevance of visual samples, we show an illustration of the consequence of mistaken beliefs about the passability of specific transitions on the subjective value function. Transition toggling can be defined as the act of removing an obstacle between two states if an obstacle was previously present, or adding an obstacle at that location if one was previously absent. In alignment with intuition, some transitions are more important to veridically represent (Appendix 1—figure 1A – middle), as toggling them results in a dramatic change to the value function (which is essential to computing the optimal set of actions to reach the goal), while toggling some other transitions causes a relatively minimal change (Appendix 1—figure 1A – right).

Appendix 1—figure 1

Download asset Open asset

By defining relevance of transitions according to Equation 1, we can thus capture multiple task-relevant attributes in a succinct manner. Theoretically investigating whether looking at task-relevant transitions improves navigational efficiency, we simulated artificial agents performing the same task that we imposed upon our human participants. One agent (‘perfect’) had a veridical subjective model of the environment, and thus was capable of computing the optimal trajectory (Appendix 1—figure 1f). Its antithesis (‘blind’) had an incorrect subjective model where half of the obstacle positions were ‘misremembered’ (toggled) to simulate a predicament where the agent had previous exposure to the arena, but were only halfway to learning the precise transition structure. The blind agent was incapable of using vision to correct their model prior to taking actions according to their subjectively computed value functions. Performance at these two extremes was compared against the performance of three agents that were allocated a fixed budget of ‘saccades’ to rectify their incorrect models. These agents either randomly interrogated transitions (‘random’), preferentially sampled transitions along the direction connecting the agent’s starting location to the goal location (‘goalward’), or chose the most task-relevant transitions as defined by the relevance metric in Equation 1 (‘smart’).

While all three agents showed an improvement over the ‘blind’ agent, the agent with knowledge about the most task-relevant transitions resulted in much shorter average path lengths than agents looking at transitions along the general direction of the goal or looking at random transitions (mean path length ±SE – perfect: 3.9 ± 0.1, blind: 9.6 ± 0.7, random: 8.9 ± 0.6, goalward: 8.6 ± 0.7, smart: 5.8 ± 0.3; Appendix 1—figure 1D). Moreover, the performance of the smart sampling agent quickly approached optimality as the number of sampled transitions increased (Appendix 1—figure 1E). The rate of performance improvement was substantially slower for the goalward and random samplers (linear rather than exponential). These results were robust to the precise algorithm used to compute the value function in Equation 1. In particular, the successor representation (SR) has been proposed as a computationally efficient, biologically plausible alternative to pure model-based algorithms like value iteration for responding to changing goal locations (Momennejad et al., 2017; Stachenfeld et al., 2017). We found that estimating the task-relevance of transitions using values implied by SR resulted in a similar performance improvement (Appendix 1—figure 2). Nevertheless, we emphasize that our objective was to use the relevance metric simply as a means to probe whether humans preferentially looked at task-relevant transitions. Understanding how the brain might compute such metrics is outside the scope of this study.

Appendix 1—figure 2

Download asset Open asset

Relevance derivation: In this section, we derive a general measure to quantify the relevance of transitions with respect to the task of navigating between two given states. The following derivation focuses on the general setting when external noise (stochastic transitions) is present and internal noise (model uncertainty) is inhomogeneous. As we will show, the measure used to quantify transition relevance in the main text (Equation 1) corresponds to the special case where transitions are deterministic and uncertainty is homogeneous. Let $T_k$ denote the status of the $k^{th}$ stochastic transition (1 or 0) and p_k be the parameter of the true probability distribution (p.d.) of that transition such that $P(T_k=1)=p_k$ and $P(T_k=0)=1-p_k$. Let ${\widehat{p}}_k$ be the parameter of the subjective probability distribution of the transition. That is the agent thinks that $P(T_k=1)={\widehat{p}}_k$ and $P(T_k=0)=1-{\widehat{p}}_k$. Given a particular goal state, let $V_s^k$ denote the value of the agent’s current state $s$ evaluated using the true transition status $T_k$ such that $V_s^k=V_s(T_k=1)$ if $T_k=1$ and $V_s^k=V_s(T_k=0)$ if $T_k=0$. Let ${\widehat{V}}_s^k$ denote the expectation of the value of state $s$ evaluated using the subjective transition p.d. of the $k^{th}$ transition such that ${\widehat{V}}_s^k={\widehat{p}}_k{V}_s(T_k=1)+(1-{\widehat{p}}_k)V_s(T_k=0)$. Since looking at a transition will dramatically reduce the uncertainty about the status of that transition, this can impact the subjective value of the current state, provided that transition is critical to the task at hand. For instance, discovering a subway line linking your neighborhood and downtown will increase the value of your neighborhood if your workplace is located downtown, but will have no impact if your workplace is located crosstown. Therefore, we define relevance (${\mathrm{\Omega }}_k$) of the $k^{th}$ transition as the expectation of the (log) change in subjective value about the current state $s$ induced by looking at that transition. Then, we have:

${\displaystyle {\mathrm{\Omega }}_k=\mathbb{E}[\mathrm{l}\mathrm{o}\mathrm{g}(|{\mathrm{V}}_{\mathrm{s}}^{\mathrm{k}}-{\hat{\mathrm{V}}}_{\mathrm{s}}^{\mathrm{k}}|){]}_{{\mathrm{p}}_{\mathrm{k}}}}$ where ${\displaystyle \mathbb{E}[.{]}_{p_k}}$ denotes expectation taken w.r.t. the true p.d.

where $\text{H}(X,Y)$ denotes the cross entropy between $X$ and $Y$

where $\text{H}(X)$ denotes the entropy of $X$

where ${\widehat{T}}_k$ denotes the subjective knowledge about the status of the $k^{th}$ transition

Observe that ${\mathrm{\Omega }}_k$ is comprised of four factors: (I) $\text{H}(p_k)$, the entropy of p_k, which captures transition volatility, (II) $D_{\text{KL}}(p_k||{\widehat{p}}_k)$, the Kullback-Leibler divergence between true and subjective p.d., which captures the degree of mismatch between the subjective and true transition models, (III) $\text{log}(\text{Var}[{\widehat{T}}_k])$, the log variance of the subjective status of the transition, which captures the agent’s uncertainty, and (IV) $\text{log}({|\mathrm{\Delta }V|}^2)=\text{log}({[V_s(T_k=1)-V_s(T_k=0)]}^2)$, the log change in the value of the current state induced by changing the transition status, which captures the sensitivity of the value function to the transition. The first and third terms suggest that an agent should prioritize looking at transitions with high volatility and high subjective uncertainty. The second term suggests that it is best to look at transitions whose subjective status is known to be wrong. Although this is mathematically correct, agents would not know the true model to begin with and therefore cannot direct their attention at such transitions. Therefore, if external and internal noise are homogeneous, the best strategy would be to look at transitions which the value function is highly sensitive to, as postulated by Equation 1 in the main text. Note that in deriving ${\mathrm{\Omega }}_k$, we have neglected the contribution of model mismatches that may exist at other transitions. This approximation will be valid if the model mismatch is small, and the solution works well in practice as demonstrated by the simulations (Figure 1).

Links to data and code are included in the manuscript.

1. 1. Zhu SL
   2. Lakshminarasimhan KJ
   3. Arfaei N
   4. Angelaki DE

   (2022) G-node

   ID neuro-sci/gaze-navigation. Gaze-navigation.

   https://gin.g-node.org/neuro-sci/gaze-navigation

1. Conference

   1. Ahmad S
   2. Yu AJ

   (2013)

   Active sensing as bayes-optimal sequential decision-making

   Uncertainty in Artificial Intelligence - Proceedings of the 29th Conference, UAI 2013. pp. 12–21.

   • Google Scholar
2. 1. Bakkour A
   2. Palombo DJ
   3. Zylberberg A
   4. Kang YH
   5. Reid A
   6. Verfaellie M
   7. Shadlen MN
   8. Shohamy D

   (2019) The hippocampus supports deliberation during value-based decisions

   eLife 8:e46080.

   https://doi.org/10.7554/eLife.46080

   • PubMed
   • Google Scholar
3. 1. Balaguer J
   2. Spiers H
   3. Hassabis D
   4. Summerfield C

   (2016) Neural Mechanisms of Hierarchical Planning in a Virtual Subway Network

   Neuron 90:893–903.

   https://doi.org/10.1016/j.neuron.2016.03.037

   • PubMed
   • Google Scholar
4. 1. Bellman R

   (1954) Some Problems in the Theory of Dynamic Programming

   Econometrica : Journal of the Econometric Society 22:37.

   https://doi.org/10.2307/1909830

   • Google Scholar
5. 1. Bermudez-Contreras E
   2. Clark BJ
   3. Wilber A

   (2020) The Neuroscience of Spatial Navigation and the Relationship to Artificial Intelligence

   Frontiers in Computational Neuroscience 14:1–16.

   https://doi.org/10.3389/fncom.2020.00063

   • PubMed
   • Google Scholar
6. 1. Brown TI
   2. Carr VA
   3. LaRocque KF
   4. Favila SE
   5. Gordon AM
   6. Bowles B
   7. Bailenson JN
   8. Wagner AD

   (2016) Prospective representation of navigational goals in the human hippocampus

   Science (New York, N.Y.) 352:1323–1326.

   https://doi.org/10.1126/science.aaf0784

   • PubMed
   • Google Scholar
7. 1. Buhry L
   2. Azizi AH
   3. Cheng S

   (2011) Reactivation, replay, and preplay: how it might all fit together

   Neural Plasticity 2011:203462.

   https://doi.org/10.1155/2011/203462

   • PubMed
   • Google Scholar
8. 1. Caspi A
   2. Beutter BR
   3. Eckstein MP

   (2004) The time course of visual information accrual guiding eye movement decisions

   PNAS 101:13086–13090.

   https://doi.org/10.1073/pnas.0305329101

   • PubMed
   • Google Scholar
9. 1. Crowe DA
   2. Averbeck BB
   3. Chafee MV
   4. Anderson JH
   5. Georgopoulos AP

   (2000) Mental maze solving

   Journal of Cognitive Neuroscience 12:813–827.

   https://doi.org/10.1162/089892900562426

   • PubMed
   • Google Scholar
10. 1. Crowe DA
    2. Chafee MV
    3. Averbeck BB
    4. Georgopoulos AP

    (2004) Neural activity in primate parietal area 7a related to spatial analysis of visual mazes

    Cerebral Cortex (New York, N.Y 14:23–34.

    https://doi.org/10.1093/cercor/bhg088

    • PubMed
    • Google Scholar
11. Preprint

    1. de Cothi W
    2. Nyberg N
    3. Griesbauer EM
    4. Ghanamé C
    5. Zisch F
    6. Lefort JM
    7. Fletcher L
    8. Newton C
    9. Renaudineau S
    10. Bendor D
    11. Grieves R
    12. Duvelle É
    13. Barry C
    14. Spiers HJ

    (2020) Predictive Maps in Rats and Humans for Spatial Navigation

    bioRxiv.

    https://doi.org/10.1101/2020.09.26.314815

    • Google Scholar
12. 1. Diba K
    2. Buzsáki G

    (2007) Forward and reverse hippocampal place-cell sequences during ripples

    Nature Neuroscience 10:1241–1242.

    https://doi.org/10.1038/nn1961

    • PubMed
    • Google Scholar
13. 1. Dragoi G
    2. Tonegawa S

    (2011) Preplay of future place cell sequences by hippocampal cellular assemblies

    Nature 469:397–401.

    https://doi.org/10.1038/nature09633

    • PubMed
    • Google Scholar
14. 1. Eckstein MK
    2. Guerra-Carrillo B
    3. Miller Singley AT
    4. Bunge SA

    (2017) Beyond eye gaze: What else can eyetracking reveal about cognition and cognitive development?

    Developmental Cognitive Neuroscience 25:69–91.

    https://doi.org/10.1016/j.dcn.2016.11.001

    • PubMed
    • Google Scholar
15. 1. Eckstein MK
    2. Collins AGE

    (2020) Computational evidence for hierarchically structured reinforcement learning in humans

    PNAS 117:29381–29389.

    https://doi.org/10.1073/pnas.1912330117

    • PubMed
    • Google Scholar
16. 1. Ekman M
    2. Kok P
    3. de Lange FP

    (2017) Time-compressed preplay of anticipated events in human primary visual cortex

    Nature Communications 8:1–9.

    https://doi.org/10.1038/ncomms15276

    • PubMed
    • Google Scholar
17. 1. Eldar E
    2. Lièvre G
    3. Dayan P
    4. Dolan RJ

    (2020) The roles of online and offline replay in planning

    eLife 9:e56911.

    https://doi.org/10.7554/eLife.56911

    • PubMed
    • Google Scholar
18. 1. Fotowat H
    2. Lee C
    3. Jun JJ
    4. Maler L

    (2019) Neural activity in a hippocampus-like region of the teleost pallium is associated with active sensing and navigation

    eLife 8:e44119.

    https://doi.org/10.7554/eLife.44119

    • PubMed
    • Google Scholar
19. 1. Frey M
    2. Nau M
    3. Doeller CF

    (2021) Magnetic resonance-based eye tracking using deep neural networks

    Nature Neuroscience 24:1772–1779.

    https://doi.org/10.1038/s41593-021-00947-w

    • PubMed
    • Google Scholar
20. 1. Gaymard B
    2. Rivaud S
    3. Cassarini JF
    4. Dubard T
    5. Rancurel G
    6. Agid Y
    7. Pierrot-Deseilligny C

    (1998) Effects of anterior cingulate cortex lesions on ocular saccades in humans

    Experimental Brain Research 120:173–183.

    https://doi.org/10.1007/s002210050391

    • PubMed
    • Google Scholar
21. 1. Ghamari H
    2. Golshany N

    (2021) Wandering Eyes: Using Gaze-Tracking Method to Capture Eye Fixations in Unfamiliar Healthcare Environments

    HERD 15:115–130.

    https://doi.org/10.1177/19375867211042344

    • PubMed
    • Google Scholar
22. 1. Gillespie AK
    2. Astudillo Maya DA
    3. Denovellis EL
    4. Liu DF
    5. Kastner DB
    6. Coulter ME
    7. Roumis DK
    8. Eden UT
    9. Frank LM

    (2021) Hippocampal replay reflects specific past experiences rather than a plan for subsequent choice

    Neuron 109:3149–3163.

    https://doi.org/10.1016/j.neuron.2021.07.029

    • PubMed
    • Google Scholar
23. 1. Gottlieb J
    2. Oudeyer PY
    3. Lopes M
    4. Baranes A

    (2013) Information-seeking, curiosity, and attention: computational and neural mechanisms

    Trends in Cognitive Sciences 17:585–593.

    https://doi.org/10.1016/j.tics.2013.09.001

    • PubMed
    • Google Scholar
24. 1. Gottlieb J
    2. Hayhoe M
    3. Hikosaka O
    4. Rangel A

    (2014) Attention, Reward, and Information Seeking

    Journal of Neuroscience 34:15497–15504.

    https://doi.org/10.1523/JNEUROSCI.3270-14.2014

    • PubMed
    • Google Scholar
25. 1. Gottlieb J
    2. Oudeyer PY

    (2018) Towards a neuroscience of active sampling and curiosity

    Nature Reviews. Neuroscience 19:758–770.

    https://doi.org/10.1038/s41583-018-0078-0

    • PubMed
    • Google Scholar
26. 1. Gustafson NJ
    2. Daw ND

    (2011) Grid cells, place cells, and geodesic generalization for spatial reinforcement learning

    PLOS Computational Biology 7:e1002235.

    https://doi.org/10.1371/journal.pcbi.1002235

    • PubMed
    • Google Scholar
27. 1. Hannula DE
    2. Ranganath C

    (2009) The eyes have it: hippocampal activity predicts expression of memory in eye movements

    Neuron 63:592–599.

    https://doi.org/10.1016/j.neuron.2009.08.025

    • PubMed
    • Google Scholar
28. 1. Hayhoe M
    2. Ballard D

    (2005) Eye movements in natural behavior

    Trends in Cognitive Sciences 9:188–194.

    https://doi.org/10.1016/j.tics.2005.02.009

    • PubMed
    • Google Scholar
29. 1. Henderson JM
    2. Shinkareva SV
    3. Wang J
    4. Luke SG
    5. Olejarczyk J
    6. Paterson K

    (2013) Predicting Cognitive State from Eye Movements

    PLOS ONE 8:e64937.

    https://doi.org/10.1371/journal.pone.0064937

    • Google Scholar
30. 1. Henderson JM
    2. Hayes TR

    (2017) Meaning-based guidance of attention in scenes as revealed by meaning maps

    Nature Human Behaviour 1:743–747.

    https://doi.org/10.1038/s41562-017-0208-0

    • PubMed
    • Google Scholar
31. 1. Hikosaka O
    2. Nakamura K
    3. Nakahara H

    (2006) Basal ganglia orient eyes to reward

    Journal of Neurophysiology 95:567–584.

    https://doi.org/10.1152/jn.00458.2005

    • PubMed
    • Google Scholar
32. 1. Hoppe S
    2. Loetscher T
    3. Morey SA
    4. Bulling A

    (2018) Eye Movements During Everyday Behavior Predict Personality Traits

    Frontiers in Human Neuroscience 12:1–8.

    https://doi.org/10.3389/fnhum.2018.00105

    • Google Scholar
33. 1. Hoppe D
    2. Rothkopf CA

    (2019) Multi-step planning of eye movements in visual search

    Scientific Reports 9:1–12.

    https://doi.org/10.1038/s41598-018-37536-0

    • PubMed
    • Google Scholar
34. 1. Hunt LT
    2. Daw ND
    3. Kaanders P
    4. MacIver MA
    5. Mugan U
    6. Procyk E
    7. Redish AD
    8. Russo E
    9. Scholl J
    10. Stachenfeld K
    11. Wilson CRE
    12. Kolling N

    (2021) Formalizing planning and information search in naturalistic decision-making

    Nature Neuroscience 24:1051–1064.

    https://doi.org/10.1038/s41593-021-00866-w

    • PubMed
    • Google Scholar
35. 1. Hutton SB

    (2008) Cognitive control of saccadic eye movements

    Brain and Cognition 68:327–340.

    https://doi.org/10.1016/j.bandc.2008.08.021

    • PubMed
    • Google Scholar
36. 1. Javadi AH
    2. Emo B
    3. Howard LR
    4. Zisch FE
    5. Yu Y
    6. Knight R
    7. Pinelo Silva J
    8. Spiers HJ

    (2017) Hippocampal and prefrontal processing of network topology to simulate the future

    Nature Communications 8:14652.

    https://doi.org/10.1038/ncomms14652

    • PubMed
    • Google Scholar
37. 1. Johnson A
    2. Redish AD

    (2007) Neural ensembles in CA3 transiently encode paths forward of the animal at a decision point

    The Journal of Neuroscience 27:12176–12189.

    https://doi.org/10.1523/JNEUROSCI.3761-07.2007

    • PubMed
    • Google Scholar
38. 1. Johnston K
    2. Everling S

    (2006) Monkey dorsolateral prefrontal cortex sends task-selective signals directly to the superior colliculus

    The Journal of Neuroscience 26:12471–12478.

    https://doi.org/10.1523/JNEUROSCI.4101-06.2006

    • PubMed
    • Google Scholar
39. 1. Jun JJ
    2. Longtin A
    3. Maler L

    (2016) Active sensing associated with spatial learning reveals memory-based attention in an electric fish

    Journal of Neurophysiology 115:2577–2592.

    https://doi.org/10.1152/jn.00979.2015

    • PubMed
    • Google Scholar
40. 1. Kaplan R
    2. Friston KJ

    (2018) Planning and navigation as active inference

    Biological Cybernetics 112:323–343.

    https://doi.org/10.1007/s00422-018-0753-2

    • PubMed
    • Google Scholar
41. 1. Killian NJ
    2. Jutras MJ
    3. Buffalo EA

    (2012) A map of visual space in the primate entorhinal cortex

    Nature 491:761–764.

    https://doi.org/10.1038/nature11587

    • PubMed
    • Google Scholar
42. 1. Killian NJ
    2. Buffalo EA

    (2018) Grid cells map the visual world

    Nature Neuroscience 21:161–162.

    https://doi.org/10.1038/s41593-017-0062-4

    • PubMed
    • Google Scholar
43. 1. Koenig S
    2. Kadel H
    3. Uengoer M
    4. Schubö A
    5. Lachnit H

    (2017) Reward Draws the Eye, Uncertainty Holds the Eye: Associative Learning Modulates Distractor Interference in Visual Search

    Frontiers in Behavioral Neuroscience 11:1–15.

    https://doi.org/10.3389/fnbeh.2017.00128

    • PubMed
    • Google Scholar
44. 1. Kowler E

    (2011) Eye movements: the past 25 years

    Vision Research 51:1457–1483.

    https://doi.org/10.1016/j.visres.2010.12.014

    • PubMed
    • Google Scholar
45. 1. Kurth-Nelson Z
    2. Economides M
    3. Dolan RJ
    4. Dayan P

    (2016) Fast Sequences of Non-spatial State Representations in Humans

    Neuron 91:194–204.

    https://doi.org/10.1016/j.neuron.2016.05.028

    • PubMed
    • Google Scholar
46. 1. Lakshminarasimhan KJ
    2. Avila E
    3. Neyhart E
    4. DeAngelis GC
    5. Pitkow X
    6. Angelaki DE

    (2020) Tracking the Mind’s Eye: Primate Gaze Behavior during Virtual Visuomotor Navigation Reflects Belief Dynamics

    Neuron 106:662–674.

    https://doi.org/10.1016/j.neuron.2020.02.023

    • PubMed
    • Google Scholar
47. 1. Larson AM
    2. Loschky LC

    (2009) The contributions of central versus peripheral vision to scene gist recognition

    Journal of Vision 9:6.

    https://doi.org/10.1167/9.10.6

    • PubMed
    • Google Scholar
48. 1. Leigh RJ
    2. Kennard C

    (2004) Using saccades as a research tool in the clinical neurosciences

    Brain 127:460–477.

    https://doi.org/10.1093/brain/awh035

    • PubMed
    • Google Scholar
49. 1. Liu ZX
    2. Shen K
    3. Olsen RK
    4. Ryan JD

    (2017) Visual Sampling Predicts Hippocampal Activity

    The Journal of Neuroscience 37:599–609.

    https://doi.org/10.1523/JNEUROSCI.2610-16.2016

    • PubMed
    • Google Scholar
50. 1. Liu Y
    2. Dolan RJ
    3. Kurth-Nelson Z
    4. Behrens TEJ

    (2019) Human Replay Spontaneously Reorganizes Experience

    Cell 178:640–652.

    https://doi.org/10.1016/j.cell.2019.06.012

    • PubMed
    • Google Scholar
51. 1. Liu Y
    2. Mattar MG
    3. Behrens TEJ
    4. Daw ND
    5. Dolan RJ

    (2021) Experience replay is associated with efficient nonlocal learning

    Science (New York, N.Y.) 372:eabf1357.

    https://doi.org/10.1126/science.abf1357

    • PubMed
    • Google Scholar
52. 1. Ma WJ
    2. Navalpakkam V
    3. Beck JM
    4. Berg R
    5. Pouget A

    (2011) Behavior and neural basis of near-optimal visual search

    Nature Neuroscience 14:783–790.

    https://doi.org/10.1038/nn.2814

    • PubMed
    • Google Scholar
53. 1. Mattar MG
    2. Daw ND

    (2018) Prioritized memory access explains planning and hippocampal replay

    Nature Neuroscience 21:1609–1617.

    https://doi.org/10.1038/s41593-018-0232-z

    • PubMed
    • Google Scholar
54. 1. Mattar MG
    2. Lengyel M

    (2022) Planning in the brain

    Neuron 110:914–934.

    https://doi.org/10.1016/j.neuron.2021.12.018

    • PubMed
    • Google Scholar
55. 1. Meister MLR
    2. Buffalo EA

    (2018) Neurons in Primate Entorhinal Cortex Represent Gaze Position in Multiple Spatial Reference Frames

    The Journal of Neuroscience 38:2430–2441.

    https://doi.org/10.1523/JNEUROSCI.2432-17.2018

    • PubMed
    • Google Scholar
56. 1. Miller KJ
    2. Venditto SJC

    (2021) Multi-step planning in the brain

    Current Opinion in Behavioral Sciences 38:29–39.

    https://doi.org/10.1016/j.cobeha.2020.07.003

    • Google Scholar
57. 1. Momennejad I
    2. Russek EM
    3. Cheong JH
    4. Botvinick MM
    5. Daw ND
    6. Gershman SJ

    (2017) The successor representation in human reinforcement learning

    Nature Human Behaviour 1:680–692.

    https://doi.org/10.1038/s41562-017-0180-8

    • PubMed
    • Google Scholar
58. 1. Monaco JD
    2. Rao G
    3. Roth ED
    4. Knierim JJ

    (2014) Attentive scanning behavior drives one-trial potentiation of hippocampal place fields

    Nature Neuroscience 17:725–731.

    https://doi.org/10.1038/nn.3687

    • PubMed
    • Google Scholar
59. 1. Najemnik J
    2. Geisler WS

    (2005) Optimal eye movement strategies in visual search

    Nature 434:387–391.

    https://doi.org/10.1038/nature03390

    • PubMed
    • Google Scholar
60. 1. Pfeiffer BE
    2. Foster DJ

    (2013) Hippocampal place-cell sequences depict future paths to remembered goals

    Nature 497:74–79.

    https://doi.org/10.1038/nature12112

    • PubMed
    • Google Scholar
61. 1. Pierrot-Deseilligny C
    2. Rivaud S
    3. Gaymard B
    4. Müri R
    5. Vermersch AI

    (1995) Cortical control of saccades

    Annals of Neurology 37:557–567.

    https://doi.org/10.1002/ana.410370504

    • PubMed
    • Google Scholar
62. 1. Pierrot-Deseilligny C
    2. Müri RM
    3. Nyffeler T
    4. Milea D

    (2005) The role of the human dorsolateral prefrontal cortex in ocular motor behavior

    Annals of the New York Academy of Sciences 1039:239–251.

    https://doi.org/10.1196/annals.1325.023

    • PubMed
    • Google Scholar
63. 1. Postle BR
    2. Idzikowski C
    3. Sala SD
    4. Logie RH
    5. Baddeley AD

    (2006) The selective disruption of spatial working memory by eye movements

    Quarterly Journal of Experimental Psychology 59:100–120.

    https://doi.org/10.1080/17470210500151410

    • PubMed
    • Google Scholar
64. 1. Rasmussen D
    2. Voelker A
    3. Eliasmith C

    (2017) A neural model of hierarchical reinforcement learning

    PLOS ONE 12:e0180234.

    https://doi.org/10.1371/journal.pone.0180234

    • PubMed
    • Google Scholar
65. 1. Redish AD

    (2016) Vicarious trial and error

    Nature Reviews Neuroscience 17:147–159.

    https://doi.org/10.1038/nrn.2015.30

    • PubMed
    • Google Scholar
66. 1. Renninger LW
    2. Verghese P
    3. Coughlan J

    (2007) Where to look next? Eye movements reduce local uncertainty

    Journal of Vision 7:1–17.

    https://doi.org/10.1167/7.3.6

    • PubMed
    • Google Scholar
67. 1. Ringo JL
    2. Sobotka S
    3. Diltz MD
    4. Bunce CM

    (1994) Eye movements modulate activity in hippocampal, parahippocampal, and inferotemporal neurons

    Journal of Neurophysiology 71:1285–1288.

    https://doi.org/10.1152/jn.1994.71.3.1285

    • PubMed
    • Google Scholar
68. 1. Ryan JD
    2. Shen K

    (2020) The eyes are a window into memory

    Current Opinion in Behavioral Sciences 32:1–6.

    https://doi.org/10.1016/j.cobeha.2019.12.014

    • Google Scholar
69. 1. Schroeder CE
    2. Wilson DA
    3. Radman T
    4. Scharfman H
    5. Lakatos P

    (2010) Dynamics of Active Sensing and perceptual selection

    Current Opinion in Neurobiology 20:172–176.

    https://doi.org/10.1016/j.conb.2010.02.010

    • PubMed
    • Google Scholar
70. 1. Schütt HH
    2. Rothkegel LOM
    3. Trukenbrod HA
    4. Engbert R
    5. Wichmann FA

    (2019) Disentangling bottom-up versus top-down and low-level versus high-level influences on eye movements over time

    Journal of Vision 19:1.

    https://doi.org/10.1167/19.3.1

    • Google Scholar
71. 1. Simon DA
    2. Daw ND

    (2011) Neural Correlates of Forward Planning in a Spatial Decision Task in Humans

    Journal of Neuroscience 31:5526–5539.

    https://doi.org/10.1523/JNEUROSCI.4647-10.2011

    • PubMed
    • Google Scholar
72. Preprint

    1. Sipatchin A
    2. Wahl S
    3. Rifai K

    (2020) Eye-Tracking for Low Vision with Virtual Reality (VR): Testing Status Quo Usability of the HTC Vive Pro Eye2

    bioRxiv.

    https://doi.org/10.1101/2020.07.29.220889

    • Google Scholar
73. 1. Smittenaar P
    2. FitzGerald THB
    3. Romei V
    4. Wright ND
    5. Dolan RJ

    (2013) Disruption of dorsolateral prefrontal cortex decreases model-based in favor of model-free control in humans

    Neuron 80:914–919.

    https://doi.org/10.1016/j.neuron.2013.08.009

    • PubMed
    • Google Scholar
74. 1. Solway A
    2. Diuk C
    3. Córdova N
    4. Yee D
    5. Barto AG
    6. Niv Y
    7. Botvinick MM

    (2014) Optimal behavioral hierarchy

    PLOS Computational Biology 10:e1003779.

    https://doi.org/10.1371/journal.pcbi.1003779

    • PubMed
    • Google Scholar
75. 1. Sosa M
    2. Giocomo LM

    (2021) Navigating for reward

    Nature Reviews. Neuroscience 22:472–487.

    https://doi.org/10.1038/s41583-021-00479-z

    • PubMed
    • Google Scholar
76. 1. Stachenfeld KL
    2. Botvinick MM
    3. Gershman SJ

    (2017) The hippocampus as a predictive map

    Nature Neuroscience 20:1643–1653.

    https://doi.org/10.1038/nn.4650

    • PubMed
    • Google Scholar
77. Book

    1. Sutton RS
    2. Barto AG

    (2018)

    Reinforcement Learning: An Introduction

    MIT Press.

    • Google Scholar
78. 1. Tajima S
    2. Drugowitsch J
    3. Pouget A

    (2016) Optimal policy for value-based decision-making

    Nature Communications 7:12400.

    https://doi.org/10.1038/ncomms12400

    • PubMed
    • Google Scholar
79. 1. Tervo DGR
    2. Kuleshova E
    3. Manakov M
    4. Proskurin M
    5. Karlsson M
    6. Lustig A
    7. Behnam R
    8. Karpova AY

    (2021) The anterior cingulate cortex directs exploration of alternative strategies

    Neuron 109:1876–1887.

    https://doi.org/10.1016/j.neuron.2021.03.028

    • PubMed
    • Google Scholar
80. 1. Tomov MS
    2. Yagati S
    3. Kumar A
    4. Yang W
    5. Gershman SJ
    6. Pascucci D

    (2020) Discovery of hierarchical representations for efficient planning

    PLOS Computational Biology 16:e1007594.

    https://doi.org/10.1371/journal.pcbi.1007594

    • Google Scholar
81. 1. Turk-Browne NB

    (2019) The hippocampus as A visual area organized by space and time: A spatiotemporal similarity hypothesis

    Vision Research 165:123–130.

    https://doi.org/10.1016/j.visres.2019.10.007

    • PubMed
    • Google Scholar
82. Preprint

    1. Wilming N
    2. König P
    3. König S
    4. Buffalo EA

    (2017) Entorhinal Cortex Receptive Fields Are Modulated by Spatial Attention, Even without Movement

    bioRxiv.

    https://doi.org/10.1101/183327

    • Google Scholar
83. 1. Wunderlich K
    2. Dayan P
    3. Dolan RJ

    (2012) Mapping value based planning and extensively trained choice in the human brain

    Nature Neuroscience 15:786–791.

    https://doi.org/10.1038/nn.3068

    • PubMed
    • Google Scholar
84. 1. Yang SCH
    2. Lengyel M
    3. Wolpert DM

    (2016) Active sensing in the categorization of visual patterns

    eLife 5:e12215.

    https://doi.org/10.7554/eLife.12215

    • PubMed
    • Google Scholar
85. 1. Yang SCH
    2. Wolpert DM
    3. Lengyel M

    (2018) Theoretical perspectives on active sensing

    Current Opinion in Behavioral Sciences 11:100–108.

    https://doi.org/10.1016/j.cobeha.2016.06.009

    • PubMed
    • Google Scholar
86. Conference

    1. Zhou R
    2. Hansen EA

    (2008)

    Combining breadth-first and depth-first strategies in searching for treewidth

    International Symposium on Combinatorial Search, SoCS 2008. pp. 162–168.

    • Google Scholar
87. Software

    1. Zhu S

    (2022) neuro-sci/gaze-navigation, version swh:1:rev:91870d7384c539b656f5dcab69bc24b83eece161

    GitHub.

    https://github.com/neuro-sci/gaze-navigation

Author details

1. Seren Zhu

   Center for Neural Science, New York University, New York, United States

   Contribution

   Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Software, Visualization, Writing – original draft, Writing – review and editing

   Contributed equally with

   Kaushik J Lakshminarasimhan

   For correspondence

   lt1686@nyu.edu

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0003-0555-9690

2. Kaushik J Lakshminarasimhan

   Center for Theoretical Neuroscience, Columbia University, New York, United States

   Contribution

   Conceptualization, Formal analysis, Methodology, Supervision, Visualization, Writing – original draft, Writing – review and editing

   Contributed equally with

   Seren Zhu

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0003-3932-2616

3. Nastaran Arfaei

   Department of Psychology, New York University, New York, United States

   Contribution

   Conceptualization, Methodology, Software

   Competing interests

   No competing interests declared

4. Dora E Angelaki

   1. Center for Neural Science, New York University, New York, United States
   2. Department of Mechanical and Aerospace Engineering, New York University, New York, United States

   Contribution

   Conceptualization, Funding acquisition, Methodology, Project administration, Resources, Supervision, Writing – review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-9650-8962

• 2,903

  views

• 518

  downloads

• 16

  citations

Views, downloads and citations are aggregated across all versions of this paper published by eLife.