Balancing safety and efficiency in human decision making

  1. Pranav Mahajan
  2. Shuangyi Tong
  3. Sang Wan Lee
  4. Ben Seymour

  • Curated by eLife

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    eLife Assessment

    This valuable work describes results from a set of simulation and empirical studies of a set-up assessing exploratory behavior in a potentially rewarding environment that contains danger. The core idea is that an instrumental agent can be helped to be both effective and safe, thus avoiding excessive danger, during exploratory behavior, if its influence is flexibly gated by an independent Pavlovian fear learning system. The conclusion that safe, but effective exploration can be achieved based on a flexibly weighted combination of a Pavlovian and an instrumental agent is solid.

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Abstract

The safety-efficiency dilemma describes the problem of maintaining safety during efficient exploration and is a special case of the exploration-exploitation dilemma in the face of potential dangers. Conventional exploration-exploitation solutions collapse punishment and reward into a single feedback signal, whereby early losses can be overcome by later gains. However, the brain has a separate system for Pavlovian fear learning, suggesting a possible computational advantage to maintaining a specific fear memory during exploratory decision-making. In a series of simulations, we show this promotes safe but efficient learning and is optimised by arbitrating Pavlovian avoidance of instrumental decision-making according to uncertainty. We provide a basic test of this model in a simple human approach-withdrawal experiment, and show that this flexible avoidance model captures choice and reaction times. These results show that the Pavlovian fear system has a more sophisticated role in decision-making than previously thought, by shaping flexible exploratory behaviour in a computationally precise manner.

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  1. eLife

    eLife Assessment

    This valuable work describes results from a set of simulation and empirical studies of a set-up assessing exploratory behavior in a potentially rewarding environment that contains danger. The core idea is that an instrumental agent can be helped to be both effective and safe, thus avoiding excessive danger, during exploratory behavior, if its influence is flexibly gated by an independent Pavlovian fear learning system. The conclusion that safe, but effective exploration can be achieved based on a flexibly weighted combination of a Pavlovian and an instrumental agent is solid.

  2. eLife

    Reviewer #1 (Public review):

    Summary:

    This paper provides a computational model of a synthetic task in which an agent needs to find a trajectory to a rewarding goal in a 2D-grid world, in which certain grid blocks incur a punishment. In a completely unrelated setup without explicit rewards, they then provide a model that explains data from an approach-avoidance experiment in which an agent needs to decide whether to approach or withdraw from, a jellyfish, in order to avoid a pain stimulus, with no explicit rewards. Both models include components that are labelled as Pavlovian; hence the authors argue that their data show that the brain uses a Pavlovian fear system in complex navigational and approach-avoid decisions.

    In the first setup, they simulate a model in which a component they label as Pavlovian learns about punishment in each grid block, whereas a Q-learner learns about the optimal path to the goal, using a scalar loss function for rewards and punishments. Pavlovian and Q-learning components are then weighed at each step to produce an action. Unsurprisingly, the authors find that including the Pavlovian component in the model reduces the cumulative punishment incurred, and this increases as the weight of the Pavlovian system increases. The paper does not explore to what extent increasing the punishment loss (while keeping reward loss constant) would lead to the same outcomes with a simpler model architecture, so any claim that the Pavlovian component is required for such a result is not justified by the modelling.

    In the second setup, an agent learns about punishments alone. "Pavlovian biases" have previously been demonstrated in this task (i.e. an overavoidance when the correct decision is to approach). The authors explore several models (all of which are dissimilar to the ones used in the first setup) to account for the Pavlovian biases.

    Strengths:

    Overall, the modelling exercises are interesting and relevant and incrementally expand the space of existing models.

    Weaknesses:

    I find the conclusions misleading, as they are not supported by the data.

    First, the similarity between the models used in the two setups appears to be more semantic than computational or biological. So it is unclear to me how the results can be integrated.

    Secondly, the authors do not show "a computational advantage to maintaining a specific fear memory during exploratory decision-making" (as they claim in the abstract). Making such a claim would require showing an advantage in the first place. For the first setup, the simulation results will likely be replicated by a simple Q-learning model when scaling up the loss incurred for punishments, in which case the more complex model architecture would not confer an advantage. The second setup, in contrast, is so excessively artificial that even if a particular model conferred an advantage here, this is highly unlikely to translate into any real-world advantage for a biological agent. The experimental setup was developed to demonstrate the existence of Pavlovian biases, but it is not designed to conclusively investigate how they come about. In a nutshell, who in their right mind would touch a stinging jellyfish 88 times in a short period of time, as the subjects do on average in this task? Furthermore, in which real-life environment does withdrawal from a jellyfish lead to a sting, as in this task?

    Crucially, simplistic models such as the present ones can easily solve specifically designed lab tasks with low dimensionality but they will fail in higher-dimensional settings. Biological behaviour in the face of threat is utterly complex and goes far beyond simplistic fight-flight-freeze distinctions (Evans et al., 2019). It would take a leap of faith to assume that human decision-making can be broken down into oversimplified sub-tasks of this sort (and if that were the case, this would require a meta-controller arbitrating the systems for all the sub-tasks, and this meta-controller would then struggle with the dimensionality j).

    On the face of it, the VR task provides higher "ecological validity" than previous screen-based tasks. However, in fact, it is only the visual stimulation that differs from a standard screen-based task, whereas the action space is exactly the same. As such, the benefit of VR does not become apparent, and its full potential is foregone.

    If the authors are convinced that their model can - then data from naturalistic approach-avoidance VR tasks is publicly available, e.g. (Sporrer et al., 2023), so this should be rather easy to prove or disprove. In summary, I am doubtful that the models have any relevance for real-life human decision-making.

    Finally, the authors seem to make much broader claims that their models can solve safety-efficiency dilemmas. However, a combination of a Pavlovian bias and an instrumental learner (study 1) via a fixed linear weighting does not seem to be "safe" in any strict sense. This will lead to the agent making decisions leading to death when the promised reward is large enough (outside perhaps a very specific region of the parameter space). Would it not be more helpful to prune the decision tree according to a fixed threshold (Huys et al., 2012)? So, in a way, the model is useful for avoiding cumulatively excessive pain but not instantaneous destruction. As such, it is not clear what real-life situation is modelled here.

    A final caveat regarding Study 1 is the use of a PH associability term as a surrogate for uncertainty. The authors argue that this term provides a good fit to fear-conditioned SCR but that is only true in comparison to simpler RW-type models. Literature using a broader model space suggests that a formal account of uncertainty could fit this conditioned response even better (Tzovara et al., 2018).

  3. eLife

    Reviewer #2 (Public review):

    Summary:

    The authors tested the efficiency of a model combining Pavlovian fear valuation and instrumental valuation. This model is amenable to many behavioral decision and learning setups - some of which have been or will be designed to test differences in patients with mental disorders (e.g., anxiety disorder, OCD, etc.).

    Strengths:

    (1) Simplicity of the model which can at the same time model rather complex environments.

    (2) Introduction of a flexible omega parameter.

    (3) Direct application to a rather advanced VR task.

    (4) The paper is extremely well written. It was a joy to read.

    Weaknesses:

    Almost none! In very few cases, the explanations could be a bit better.

  4. eLife

    Reviewer #3 (Public review):

    Summary:

    This paper aims to address the problem of exploring potentially rewarding environments that contain the danger, based on the assumption that an independent Pavlovian fear learning system can help guide an agent during exploratory behaviour such that it avoids severe danger. This is important given that otherwise later gains seem to outweigh early threats, and agents may end up putting themselves in danger when it is advisable not to do so.

    The authors develop a computational model of exploratory behaviour that accounts for both instrumental and Pavlovian influences, combining the two according to uncertainty in the rewards. The result is that Pavlovian avoidance has a greater influence when the agent is uncertain about rewards.

    Strengths:

    The study does a thorough job of testing this model using both simulations and data from human participants performing an avoidance task. Simulations demonstrate that the model can produce "safe" behaviour, where the agent may not necessarily achieve the highest possible reward but ensures that losses are limited. Interestingly, the model appears to describe human avoidance behaviour in a task that tests for Pavlovian avoidance influences better than a model that doesn't adapt the balance between Pavlovian and instrumental based on uncertainty. The methods are robust, and generally, there is little to criticise about the study.

    Weaknesses:

    The extent of the testing in human participants is fairly limited but goes far enough to demonstrate that the model can account for human behaviour in an exemplar task. There are, however, some elements of the model that are unrealistic (for example, the fact that pre-training is required to select actions with a Pavlovian bias would require the agent to explore the environment initially and encounter a vast amount of danger in order to learn how to avoid the danger later). The description of the models is also a little difficult to parse.

  5. eLife

    Author response:

    Public Reviews:

    Reviewer #1 (Public review):

    Summary:

    This paper provides a computational model of a synthetic task in which an agent needs to find a trajectory to a rewarding goal in a 2D-grid world, in which certain grid blocks incur a punishment. In a completely unrelated setup without explicit rewards, they then provide a model that explains data from an approach-avoidance experiment in which an agent needs to decide whether to approach or withdraw from, a jellyfish, in order to avoid a pain stimulus, with no explicit rewards. Both models include components that are labelled as Pavlovian; hence the authors argue that their data show that the brain uses a Pavlovian fear system in complex navigational and approach-avoid decisions.

    We thank the reviewer for their thoughtful comments. To clarify, the grid-world setup was used as a didactic tool/testbed to understand the interaction between Pavlovian and instrumental systems (lines 80-81) [Dayan et al., 2006], specifically in the context of safe exploration and learning. It helps us delineate the Pavlovian contributions during learning, which is key to understanding the safety-efficiency dilemma we highlight. This approach generates a hypothesis about outcome uncertainty-based arbitration between these systems, which we then test in the approach-withdrawal VR experiment based on foundational studies studying Pavlovian biases [Guitart-Masip et al., 2012, Cavanagh et al., 2013].

    Although the VR task does not explicitly involve rewards, it provides a specific test of our hypothesis regarding flexible Pavlovian fear bias, similar to how others have tested flexible Pavlovian reward bias without involving punishments (e.g., Dorfman & Gershman, 2019). Both the simulation and VR experiment models are derived from the same theoretical framework and maintain algebraic mapping, differing only in task-specific adaptations (e.g., differing in action sets and temporal difference learning for multi-step decisions in the grid world vs. Rescorla-Wagner rule for single-step decisions in the VR task). This is also true for Dayan et al. [2006] who bridge Pavlovian bias in a Go-No Go task (negative auto-maintenance pecking task) and a grid world task. Therefore, we respectfully disagree that the two setups are completely unrelated and that both models include components merely labelled as Pavlovian.

    We will rephrase parts of the manuscript to prevent the main message of our manuscript from being misconveyed. Particularly in the Methods and Discussion, to clarify that our main focus is on Pavlovian fear bias in safe exploration and learning (as also summarised by reviewers #2 and #3), rather than on its role in complex navigational decisions. We also acknowledge the need for future work to capture more sophisticated safe behaviours, such as escapes and sophisticated planning which span different aspects of the threat-imminence continuum [Mobbs et al., 2020], and we will highlight these as avenues for future research.

    In the first setup, they simulate a model in which a component they label as Pavlovian learns about punishment in each grid block, whereas a Q-learner learns about the optimal path to the goal, using a scalar loss function for rewards and punishments. Pavlovian and Q-learning components are then weighed at each step to produce an action. Unsurprisingly, the authors find that including the Pavlovian component in the model reduces the cumulative punishment incurred, and this increases as the weight of the Pavlovian system increases. The paper does not explore to what extent increasing the punishment loss (while keeping reward loss constant) would lead to the same outcomes with a simpler model architecture, so any claim that the Pavlovian component is required for such a result is not justified by the modelling.

    Thank you for this comment. We acknowledge that our paper does not compare the Pavlovian fear system to a purely instrumental system with varying punishment sensitivity. Instead, our model assumes the coexistence of these two systems and demonstrates the emergent safety-efficiency trade-off from their interaction. It is possible that similar behaviours could be modelled using an instrumental system alone. In light of the reviewer’s comment, we will soften our claims regarding the necessity of the Pavlovian system, despite its known existence.

    We also encourage the reviewer to consider the Pavlovian system as a biologically plausible implementation of punishment sensitivity. Unlike punishment sensitivity (scaling of the punishments), which has not been robustly mapped to neural substrates in fMRI studies, the neural substrates for the Pavlovian fear system (e.g., the limbic loop) are well known (see Supplementary Fig. 16).

    Additionally, we point out that varying reward sensitivities while keeping punishment sensitivity constant allows our PAL agent to differentiate from an instrumental agent that combines reward and punishment into a single feedback signal. As highlighted in lines 136-140 and the T-maze experiment (Fig. 3 A, B, C), the Pavlovian system maintains fear responses even under high reward conditions, guiding withdrawal behaviour when necessary (e.g., ω = 0.9 or 1), which is not possible with a purely instrumental model if the punishment sensitivities are fixed. This is a fundamental point.

    We will revise our discussion and results sections to reflect these clarifications.

    In the second setup, an agent learns about punishments alone. "Pavlovian biases" have previously been demonstrated in this task (i.e. an overavoidance when the correct decision is to approach). The authors explore several models (all of which are dissimilar to the ones used in the first setup) to account for the Pavlovian biases.

    Thank you, we respectfully disagree with the statement that our models used in the experimental setup are dissimilar to the ones used in the first setup. Due to differences in the nature of the task setup, the action set differs, but the model equations and the theory are the same and align closely, as described in our response above. The only additional difference is the use of a baseline bias in human experiments and the RLDDM model, where we also model reaction times with drift rates which is not a behaviour often simulated in grid world simulations. We will improve our Methods section to ensure that model similarity is highlighted.

    Strengths:

    Overall, the modelling exercises are interesting and relevant and incrementally expand the space of existing models.

    We thank reviewer #1 for acknowledging the relevance of our models in advancing the field. We would like to further highlight that, to the best of our knowledge, this is the first time reaction times in Pavlovian-Instrumental arbitration tasks have been modelled using RLDDM, which adds a novel dimension to our approach.

    Weaknesses:

    I find the conclusions misleading, as they are not supported by the data.

    First, the similarity between the models used in the two setups appears to be more semantic than computational or biological. So it is unclear to me how the results can be integrated.

    We acknowledge the dissimilarity between the task setups (grid-world vs. approach-withdrawal). However, we believe these setups are computationally similar and may be biologically related, as suggested by prior work like Dayan et al. [2006], which integrates Go-No Go and grid-world tasks. Just as that work bridged findings in the appetitive domain, we aim to integrate our findings in the aversive domain. We will provide a more integrated interpretation in the discussion section of the revised manuscript.

    Dayan, P., Niv, Y., Seymour, B., and Daw, N. D. (2006). The misbehavior of value and the discipline of the will. Neural networks, 19(8):1153–1160.

    Secondly, the authors do not show "a computational advantage to maintaining a specific fear memory during exploratory decision-making" (as they claim in the abstract). Making such a claim would require showing an advantage in the first place. For the first setup, the simulation results will likely be replicated by a simple Q-learning model when scaling up the loss incurred for punishments, in which case the more complex model architecture would not confer an advantage. The second setup, in contrast, is so excessively artificial that even if a particular model conferred an advantage here, this is highly unlikely to translate into any real-world advantage for a biological agent. The experimental setup was developed to demonstrate the existence of Pavlovian biases, but it is not designed to conclusively investigate how they come about. In a nutshell, who in their right mind would touch a stinging jellyfish 88 times in a short period of time, as the subjects do on average in this task? Furthermore, in which real-life environment does withdrawal from a jellyfish lead to a sting, as in this task?

    Thank you for your feedback. As mentioned above, we invite the reviewer to potentially think of Pavlovian fear systems as a way how the brain might implement punishment sensitivity. Secondly, it provides a separate punishment memory that cannot be overwritten with higher rewards (see also Elfwing and Seymour 2017, and Wang et al, 2021)

    Elfwing, S., & Seymour, B. (2017, September). Parallel reward and punishment control in humans and robots: Safe reinforcement learning using the MaxPain algorithm. In 2017 Joint IEEE International Conference on Development and Learning and Epigenetic Robotics (ICDL-EpiRob) (pp. 140-147). IEEE.

    Wang, J., Elfwing, S., & Uchibe, E. (2021). Modular deep reinforcement learning from reward and punishment for robot navigation. Neural Networks, 135, 115-126.

    The simulation setups such as the following grid-worlds are common test-beds for algorithms in reinforcement learning [Sutton and Barto, 2018].

    Any experimental setup faces the problem of having a constrained experiment designed to test and model a specific effect versus designing a lesser constrained exploratory experiment which is more difficult to model. Here we chose the former, building upon previous foundational experiments on Pavlovian bias in humans [Guitart-Masip et al., 2012, Cavanagh et al., 2013]. The condition where withdrawal from a jellyfish leads to a sting, though less realistic, was included for balancing the four cue-outcome conditions. Overall the task was designed to isolate the effect we wanted to test - Pavlovian fear bias in choices and reaction times, to the best of our ability. In a free operant task, it is very well likely that other components not included in our model could compete for control.

    Crucially, simplistic models such as the present ones can easily solve specifically designed lab tasks with low dimensionality but they will fail in higher-dimensional settings. Biological behaviour in the face of threat is utterly complex and goes far beyond simplistic fight-flight-freeze distinctions (Evans et al., 2019). It would take a leap of faith to assume that human decision-making can be broken down into oversimplified sub-tasks of this sort (and if that were the case, this would require a meta-controller arbitrating the systems for all the sub-tasks, and this meta-controller would then struggle with the dimensionality j).

    We agree that safe behaviours, such as escapes, involve more sophisticated computations. We do not propose Pavlovian fear bias as the sole computation for safe behavior, but rather as one of many possible contributors. Knowing about the existence about the Pavlovian withdrawal bias, we simply study its possible contribution. We will include in our discussion that such behaviours likely occupy different parts of the threat-imminence continuum [Mobbs et al., 2020].

    Dean Mobbs, Drew B Headley, Weilun Ding, and Peter Dayan. Space, time, and fear: survival computations along defensive circuits. Trends in cognitive sciences, 24(3):228–241, 2020.

    On the face of it, the VR task provides higher "ecological validity" than previous screen-based tasks. However, in fact, it is only the visual stimulation that differs from a standard screen-based task, whereas the action space is exactly the same. As such, the benefit of VR does not become apparent, and its full potential is foregone.

    We thank the reviewer for their comment. We selected the action space to build on existing models [Guitart-Masip et al., 2012, Cavanagh et al., 2013] that capture Pavlovian biases and we also wanted to minimize participant movement for EEG data collection. Unfortunately, despite restricting movement to just the arm, the EEG data was still too noisy to lead to any substantial results. We will explore more free-operant paradigms in future works.

    On the issue of the difference between VR and lab-based tasks, we note the reviewer's point. Note however that desktop monitor-based tasks lack the sensorimotor congruency between the action and the outcome. Second, it is also arguable, that the background context is important in fear conditioning, as it may help set the tone of the fear system to make aversive components easier to distinguish.

    If the authors are convinced that their model can - then data from naturalistic approach-avoidance VR tasks is publicly available, e.g. (Sporrer et al., 2023), so this should be rather easy to prove or disprove. In summary, I am doubtful that the models have any relevance for real-life human decision-making.

    We thank the reviewers for their thoughtful inputs. We do not claim our model is the best fit for all naturalistic VR tasks, as they require multiple systems across the threat-imminence continuum [Mobbs et al., 2020] and are currently beyond the scope of the current work. However, we believe our findings on outcome-uncertainty-based arbitration of Pavlovian bias could inform future studies and may be relevant for testing differences in patients with mental disorders, as noted by reviewer #2. At a general level, it can be said that most well-controlled laboratory-based tasks need to bridge a sizeable gap to applicabilty in real-life naturalistic behaviour; although the principle of using carefully designed tasks to isolate individual factors is well established

    Finally, the authors seem to make much broader claims that their models can solve safety-efficiency dilemmas. However, a combination of a Pavlovian bias and an instrumental learner (study 1) via a fixed linear weighting does not seem to be "safe" in any strict sense. This will lead to the agent making decisions leading to death when the promised reward is large enough (outside perhaps a very specific region of the parameter space). Would it not be more helpful to prune the decision tree according to a fixed threshold (Huys et al., 2012)? So, in a way, the model is useful for avoiding cumulatively excessive pain but not instantaneous destruction. As such, it is not clear what real-life situation is modelled here.

    We thank the reviewer for their comments and ideas. In our discussion lines 257-264, we discuss other works which identify similar safety-efficiency dilemmas, in different models. Here, we simply focus on the safety-efficiency trade-off arising from the interactions between Pavlovian and instrumental systems. It is important to note that the computational argument for the modular system with separate rewards and punishments explicitly protects (up to a point, of course) against large rewards leading to death because the Pavlovian fear response is not over-written by successful avoidance in recent experience. Note also that in animals, reward utility curves are typically convex. We will clarify this in the discussion section.

    We completely agree that in certain scenarios, pruning decision trees could be more effective, especially with a model-based instrumental agent. Here we utilise a model-free instrumental agent, which leads to a simpler model - which is appreciated by some readers such as reviewer #2. Future work can incorporate model-based methods.

    A final caveat regarding Study 1 is the use of a PH associability term as a surrogate for uncertainty. The authors argue that this term provides a good fit to fear-conditioned SCR but that is only true in comparison to simpler RW-type models. Literature using a broader model space suggests that a formal account of uncertainty could fit this conditioned response even better (Tzovara et al., 2018).

    We thank the reviewer for bringing this to our notice. We will discuss Tzovara et al., 2018 in our discussion in our revised manuscript.

    Reviewer #2 (Public review):

    Summary:

    The authors tested the efficiency of a model combining Pavlovian fear valuation and instrumental valuation. This model is amenable to many behavioral decision and learning setups - some of which have been or will be designed to test differences in patients with mental disorders (e.g., anxiety disorder, OCD, etc.).

    Strengths:

    (1) Simplicity of the model which can at the same time model rather complex environments.

    (2) Introduction of a flexible omega parameter.

    (3) Direct application to a rather advanced VR task.

    (4) The paper is extremely well written. It was a joy to read.

    Weaknesses:

    Almost none! In very few cases, the explanations could be a bit better.

    We thank reviewer #2 for their positive feedback and thoughtful recommendations. We will ensure that, in our revision, we clarify the explanations in the few instances where they may not be sufficiently detailed, as noted.

    Reviewer #3 (Public review):

    Summary:

    This paper aims to address the problem of exploring potentially rewarding environments that contain the danger, based on the assumption that an independent Pavlovian fear learning system can help guide an agent during exploratory behaviour such that it avoids severe danger. This is important given that otherwise later gains seem to outweigh early threats, and agents may end up putting themselves in danger when it is advisable not to do so.

    The authors develop a computational model of exploratory behaviour that accounts for both instrumental and Pavlovian influences, combining the two according to uncertainty in the rewards. The result is that Pavlovian avoidance has a greater influence when the agent is uncertain about rewards.

    Strengths:

    The study does a thorough job of testing this model using both simulations and data from human participants performing an avoidance task. Simulations demonstrate that the model can produce "safe" behaviour, where the agent may not necessarily achieve the highest possible reward but ensures that losses are limited. Interestingly, the model appears to describe human avoidance behaviour in a task that tests for Pavlovian avoidance influences better than a model that doesn't adapt the balance between Pavlovian and instrumental based on uncertainty. The methods are robust, and generally, there is little to criticise about the study.

    Weaknesses:

    The extent of the testing in human participants is fairly limited but goes far enough to demonstrate that the model can account for human behaviour in an exemplar task. There are, however, some elements of the model that are unrealistic (for example, the fact that pre-training is required to select actions with a Pavlovian bias would require the agent to explore the environment initially and encounter a vast amount of danger in order to learn how to avoid the danger later). The description of the models is also a little difficult to parse.

    We thank reviewer #3 for their thoughtful feedback and useful recommendations, which we will take into account while revising the manuscript.

    We acknowledge the complexity of specifying Pavlovian bias in the grid world and appreciate the opportunity to elaborate on how this bias is modelled. In the human experiment, the withdrawal action is straightforwardly biased, as noted, while in the grid world, we assume a hardwired encoding of withdrawal actions for each state/grid. This innate encoding of withdrawal actions could be represented in the dPAG [Kim et. al., 2013]. We implement this bias using pre-training, which we assume would be a product of evolution. Alternatively, this could be interpreted as deriving from an appropriate value initialization where the gradient over initialized values determines the action bias. Such aversive value initialization, driving avoidance of novel and threatening stimuli, has been observed in the tail of the striatum in mice, which is hypothesized to function as a Pavlovian fear/threat learning system [Menegas et. al., 2018].

    Additionally, we explored the possibility of learning the action bias on the fly by tracking additional punishment Q-values instead of pre-training, which produced similar cumulative pain and step plots. While this approach is redundant, and likely not how the brain operates, it demonstrates an alternative algorithm.

    We thank the reviewer for pointing out these potentially unrealistic elements, and we will revise the manuscript to clarify and incorporate these explanations and improve the model descriptions.

    Eun Joo Kim, Omer Horovitz, Blake A Pellman, Lancy Mimi Tan, Qiuling Li, Gal Richter-Levin, and Jeansok J Kim. Dorsal periaqueductal gray-amygdala pathway conveys both innate and learned fear responses in rats. Proceedings of the National Academy of Sciences, 110(36):14795–14800, 2013

    William Menegas, Korleki Akiti, Ryunosuke Amo, Naoshige Uchida, and Mitsuko Watabe-Uchida. Dopamine neurons projecting to the posterior striatum reinforce avoidance of threatening stimuli. Nature neuroscience, 21(10): 1421–1430, 2018

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