Curious Causality-Seeking Agents Learn Meta Causal World

We thank the reviewer n7bY for highlighting the strengths of our approach, especially the introduction of the Meta-Causal Graph for serving as the world model and our detailed analysis of identifiability for both meta states and causal subgraphs. Below are our responses to your comments and suggestions.

W1&Q1: Existence of state to meta state mapping when new variables appear during exploration in open-ended world. Would the observable assumption too strong?

• Firstly, we would like to highlight that the mapping from observation $x$ to meta state $C(x) = u$ necessarily exists when all variables are observable.
• This is because each state $x$ is governed by a unique underlying causal subgraph $\mathcal{G}_u$, and each meta state $u$ indexes a distinct subgraph.
• Secondly, our method can be naturally extended to open-world settings where new variables or objects are encountered during exploration.
• To support this, we added additional experiments (detailed setup and results below) showing performance across time steps as new variables are revealed. The results show that our method outperforms baselines, highlighting its strong exploratory and adaptive capabilities.

Setup

• We simulate the appearance of new variables by initially masking a subset of variables and gradually removing these masks during training, so that the set of observed variables increases over time.
• The metric is next-state prediction accuracy, evaluated under varying levels ($n$) of noise (lines 265–268).

Result

W2.a: What is the downstream task in the Chemical environment in paper

In the Chemical environment downstream task:

• The agent starts from a random color configuration and must transform a 10-node graph to match a target color pattern.
• Actions intervene on nodes, changing their color and that of all their descendants according to the hidden causal graph.
• The episode reward is the negative Hamming distance to the target (0 for a perfect match).

W2.b: The meaning of "predict transition dynamics for model-based reinforcement learning"

"Predict transition dynamics for model-based reinforcement learning" means predict future states with the learned model for decision making.

We will clarify these in the revised version.

Q1：The observable assumption too strong for get meta-state u

We detailedly discuss it in W1&Q1.

Q2: Clarification of assumptions to support causal discovery

• Our theoretical results are established under our stated assumptions, which are sufficient for our proofs (as also noted by Reviewer hzVP).
• We appreciate your suggestion and will consider the extension of our theory to more general conditions, including faithfulness and Markov assumptions, in next version.

Q3: Evaluate the causal discovery metrics (SHD, SID, F1 score, etc)

We add experimental results for these metrics. The results are shown below:

Q4: Intervention efficiency analysis when (1) the round of Algorithm 1 is limited, (2) the size of samples from the intervened distribution is small?

We added an experiment to evaluate the intervention efficiency by reducing the number of interventions.

• In this experimental setting, data is collected through interventions at each round; therefore, reducing the number of rounds corresponds to a direct reduction in available intervention data.
• The metric is the average episode reward from model-based planning on downstream tasks, evaluated under varying levels ($n$) of noise (lines 265–268). The results are shown below:

The results show that our method can achieve comparable performance with fewer interventions, demonstrating its efficiency in causal discovery.

Accessibility of the anonymous code repo

We have checked the anonymous code repository and confirmed that it is accessible. We kindly suggest trying again at a later time.

Dear Reviewer n7bY,

We are happy to hear that your concerns have been addressed sufficiently. Again, thank you for your valuable suggestions which have undoubtedly contributed to improving the quality of our paper.

Many thanks,

The authors of #20694

We thank the reviewer for highlighting that our curiosity-driven agent and meta-causal graph framework provide a theoretically grounded and practically effective approach to robust world modeling, with compelling empirical and theoretical results that advance causal learning beyond traditional single-graph or passive methods. Below are our responses to your comments and suggestions.

Discussion differences between MBRL under POMDP settings and intervention-based causal method [Winn et al.]

We appreciate the reviewer’s thoughtful suggestion.

Our framework can be viewed as a special case of MBRL, but more detailed differences are listed below:

• Unified World Representation: Our framework maintains a single meta-causal graph per environment, avoiding redundant definitions that arise from time-series changes in POMDPs.
• Explicit Causal Structure: Meta-causal graphs directly represent variable-level causal relationships in each context, whereas POMDPs only model transition probabilities without explicit causal structure.
• Identifiability Guarantees: The meta-causal graph framework provides theoretical guarantees for identifying both meta-states and causal structures, ensuring reliable causal discovery. In contrast, POMDPs generally lack such identifiability guarantees for their latent structure.

Compared to the intervention-based causal method mentioned by the reviewer (Winn et al.), their approach is not RL-based and does not incorporate curiosity-driven mechanisms to encourage intervention-based exploration, as our method does. A detailed discussion of the similarities and differences with more related works will be included in the revised version.

Efficiency and scalability of our method

To demonstrate the efficiency and scalability of our method, we added new experiments comparing it to non-causal baselines (MLP and GNN) across different model sizes and training rounds. The metrics are next-state prediction accuracy and the average episode reward obtained by model-based planning on downstream tasks, evaluated under varying levels ($n$) of noise (lines 265–268).

Comparison with Same Model Size

Comparison with Same Round

The results show that our method can achieve comparable performance with fewer training data and smaller model sizes, demonstrating its efficiency and scalability.

Scalability potential and challenges of our method

• Our theoretical framework is general and can, in principle, scale to more complex tasks, including those with delayed or partial observations.

  • We added a new experiment to demonstrate that our method can be naturally extended to open-world settings where variables are partially observable.
  • We simulate the appearance of new variables by initially masking a subset of variables and gradually removing these masks during training, so that the set of observed variables increases over time.
  • The metric is next-state prediction accuracy, evaluated under varying levels ($n$) of noise (lines 265–268). |Accuracy↑|Fork (n=2)|Fork (n=4)|Fork (n=6)|Chain (n=2)|Chain (n=4)|Chain (n=6)| |-|-|-|-|-|-|-| |FCDL|60.10|52.97|45.80|46.37|47.88|46.62| |MLP|31.56|31.67|31.93|25.95|24.71|21.66| |MCG|66.94|59.19|46.35|49.93|45.41|48.09|

• Engineering challenges such as model architecture design and efficient exploration strategies may require further adaptation as environments become larger or more complex. Addressing these challenges will be an important direction for future work.

  • We added a manipulation task with a more complex structure. Due to space constraints, we present only a subset of the graph. This experiment validates our method’s ability to recover causal structures in settings with 15 variables. We will extend this experiment to larger environments in next version.

    Causal graph recovered by MCG

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    Ground truth causal graph

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Increase emphasis of unique contribution compared with MBRL

Thank you for the valuable suggestion. Our framework can be viewed as a special case of MBRL, but more detailed differences are listed below:

• We agree that highlighting the importance of causal understanding distinguishes our approach from standard model-based RL methods, which often struggle to scale and to continually adapt to new causal structures in open-ended environments.
• Our method operates within an MBRL framework, but the meta-causal graph provides a structured, causal understanding of the world—enabling the agent to develop a causally grounded MDP that adapts to changing dynamics.
• We will include a more detailed discussion of connections to both standard MBRL and curiosity-driven latent variable models (e.g., POMDPs) in the revised version.

We thank the reviewer for acknowledging the importance of meta-causal graph (MCG), the effectiveness of our methodology, and the strength of our theoretical results on the identifiability of MCG. Below are our responses. Issues you specifically raised are marked with $\star$.

$\star$ W1: Simlarity with FCDL/NCD

FCDL and NCD are good works, but our method is totally different.

Different Motivation：

• FCDL & NCD are observation-based methods restricting themselves to passive learning and limits their capacity to truly explore or adapt in an open-ended world, while our method is intervention-based, which helps us to deal with the open-ended world problem.
• Our goal is to actively discover the unseen meta state in open-ended worlds to learn a MCG (line 39-40).

Different Formulation and theoretical contributions:

• FCDL & NCD do not model the minimal causal graph and cannot guarantee identifiability; their approach can lead to non-identifiable solutions due to infinite subgraph combinations. While we develop a theory framework to ensure identifiability of MCG.
• FCDL/NCD treats actions as part of observational data, which does not allow for active intervention. Our method treats actions as interventions, enabling true active intervention for causal discovery in open worlds.

$\star$ W2.a: Tractability of entropy computation and robustness to inaccurate posterior dist

The computation of entropy in Eq. 2 is tractable.

• Entropy is calculated as the sum of the entropies of Bernoulli variables, where each variable $M[i, j]$ represents the existence of an edge $i\to j$ in the causal subgraph and the corresponding Bernoulli probabilities $\hat{M}[i, j]=P(M[i, j]=1)$ are predicted by the neural network.
• Implementation details are provided in code file fcdl/utils/utils.py, function calculate_entropy.

We added experiments testing robustness to posterior inaccuracies by introducing disturbances. These results show the robustness of our method.

$\star$ W2.b: Discussion with other curiosity methods

Generally, curiosty-based RL methods require designing reward encouraging exploration, such as [Pathak et al., 2017], [Kim et al., 2020] and [Kauvar et al., 2023]. Compared with these methods, our curiosity-driven intervention is tailored for discovering new meta states in the MCG, which is unique to our framework, while traditional methods do not target unseen meta states.

We will discuss it more in the revised version.

W2.c: Move the reachability analysis from appendix to the main paper

Thank you for the suggestion. We will move the reachability analysis from appendix to the main paper in the revised version.

W3.a: Compared with traditional world models, why not use an observation function to obtain representations?

“World model” is a broad term. Not all world models operate directly from high-dimensional observations; some, including [e.g., Liu et al.], focus on extracting certain semantic representations from the state space. Similarly, we learn unknown meta state representations and their corresponding causal graphs directly from the state space.

$\star$ W3.b: Display the learned causal graphs in more complex tasks

We have added a manipulation task with a more complex structure. Due to space constraints, we present only a subset of the graph. This experiment validates our method’s ability to recover causal structures in settings with 15 variables. Larger one will be added in next version.

MCG

Ground truth

$\star$ W3.c: Add additional baselines

We added baselines you suggested: causal discovery using transformer attention weights ("transformer") and the Jacobian matrices of MLP layers ("sandy-mixture") from [Pitis et al., 2020] and [Urpí et al., 2024], for comparison. The results are shown below. Our method outperforms new baselines, demonstrating that our active intervention strategy improves the accuracy of the recovered causal graph.

$\star$ W3.d: Empirical validation of reachability

We added experiments comparing causal graphs under limited vs. full reachability. Limited reachability yields less accurate graphs (higher SHD, lower F1).

W4.a: Discussions on related works

We acknowledge the valuable contributions and inspiration of FCDL/NCD in causal discovery and will add more discussion in the revision. We believe that key conceptual differences have already been clarified in our response to Comment W1. We provide other comparisons here:

• Observation-based methods like FCDL and NCD are limited to Markov equivalence classes, while intervention-based methods (Ours) can actively reduce the Markov equivalence class and uniquely identify causal relations that are otherwise unidentifiable.
• We introduce $L_{mask}$ loss (line 197-198) that directly updates causal structure based on intervention outcomes while FCDL & NCD have no mechanism to verify or update causal beliefs through interventions.

W4.b: Citation for [Pitis et al., 2020]

Apologies for the citation error. The intended reference was another paper, [Pitis et al., 2022], which discusses methods that require domain knowledge or expert trajectories. We will correct this mistake in the revised version.

W5: Typos and clarification of theoretical aspects of the paper

Thank you for your careful reading. We will improve the clarity of the theoretical aspects of the paper and fix the typos.

Q1.a: How to integrate and learn context-specific causal discovery approach in world model efficiently

• Our approach uses a curiosity-driven exploration strategy to actively discover unknown meta states. Specifically, the agent maps each state to a learned representation that jointly captures the meta state and its corresponding causal graph.
• Based on the discovered causal graphs, we learn a transition model conditioned on meta states. Here, the MCG serves as structured world knowledge, while the learned transition model functions as the world model (see Definition 3 and line 204-205).
• We added experiments to show efficiency of our method. We compare other methods (GNN and MLP) with longer training rounds and more parameters. The result is shown below:

Comparison with Same Model Size

Comparison with Same Round

Our method achieves strong performance with less training data and smaller models, highlighting its efficiency.

Q1.b: How should actions be incorporated into the framework?

In our framework, actions are treated as interventions for causal discovery.

Q1.c: Additional structural assumptions needed?

While not all actions can intervene on every state (i.e., not all states are reachable by intervention), we explicitly make a reachability assumption to ensure identifiability of the underlying structure.

Q1.d: Can you leverage this structure discovery as part of reward learning?

Our curiosity-driven reward (Eq. 2) is explicitly designed to encourage MCG structure discovery of meta-states $u=C(x)$ and subgraphs $\mathcal{G}_u$.

Q2.a: Clarification of observation equivalence

Thank you for your comment. We believe there may be a slight misunderstanding. Observational equivalence refers to the condition where two mappings from states to meta states produce the same partitioning of observations, possibly up to relabeling. We will clarify this in the revised version.

Q2.b: How can imperfect representation affect the identifiability of meta-states and the causal graph?

Thank you for your comment. We agree that learned latents can be imperfect. Empirically and theoretically, our study on (Fig. 2 and Thm. 2) shows over‑parameterisation does not hurt performance much while under-parameterisation will lead to degradation of performance. We will add more discussions on this point in the revised version.

Yang Liu, et al. Learning world models with identifiable factorization. NeurIPS, 2023.

Silviu Pitis, et al. Mocoda: Model-based counterfactual data augmentation. NeurIPS, 2022.

Many thanks for the detailed response. I really appreciate the new experimental results and clarifications. That said I still have several concerns and would be glad to continue the discussion.

On W1: Yes, this is precisely what I meant in my original review: the core novelty lies in the added “active intervention” module based on entropy, while the rest of the pipeline remains quite similar to prior work. I understand the point of identifiability, but from a technical standpoint, the contribution still feels incremental. I would suggest spending more effort in future versions to explicitly position the work relative to prior methods and better highlight what is new.

On W2-a: Could you clarify how posterior accuracy was computed in the new experiment, was it over the full graph or limited to specific subgraphs?

On W2-b: I am not fully convinced by this. The cited methods are indeed reward-free, and the intrinsic signals they use (e.g., based on state properties such as uncertainty) serve similar purposes. In your case, entropy-based reward is a well-established form of intrinsic motivation. If the claim is about discovering novel meta-state representations, many of those methods can arguably do the same under different selection criteria. Happy to continue the discussion here.

On W3-a: I understand your argument, but I just checked [Liu et al.]—they do learn the world model from pixels. You may want to reconsider this citation. Also, please double-check your citation, looks like the author name may be incorrect

On W3-b: Thanks for the new results. It would be much better to also include a baseline for comparison, and report standard deviations (this setting can be sensitive to random seeds)

On Q1-b: Framing all actions in a world model as interventions feels too strong. In many real-world tasks, most actions do not intervene in a meaningful way (e.g., small or redundant movements). IMO, this assumption weakens the world model framing

On Q2-b: My point was not just about under- or over-parameterization, but more generally about lossy representations. This can arise from multiple sources. It would be wonderful to give more theoretical analysis on this point

Overall, I sincerely thank the authors for the thoughtful and thorough response. While I understand the framing around active interventions, I remain unconvinced about positioning this as a “world model” paper due to the concerns above. Also, the method feels incremental and lacks sufficient acknowledgement of related baselines (At the very least, I would suggest that in the next version, you explicitly state how your method builds on others, as the current presentation may give readers a misleading impression). Also, the entropy-based criteria for intervention are not entirely new. Framing it as a causal discovery work may be more appropriate. In that case, I would encourage more thorough discussion and comparison to active causal discovery and experimental design literature (I listed a few below).

I would look forward to further conversations and appreciate the effort and time the authors have put into the response.

Choo, Davin, Themistoklis Gouleakis, and Arnab Bhattacharyya. "Active causal structure learning with advice." International Conference on Machine Learning. PMLR, 2023.

Zhang, Zeyu, et al. "Bayesian active causal discovery with multi-fidelity experiments." Advances in Neural Information Processing Systems 36 (2023): 63957-63993.

Zhang, Jiaqi, et al. "Active learning for optimal intervention design in causal models." Nature Machine Intelligence 5.10 (2023): 1066-1075.

Elahi, Muhammad Qasim, et al. "Adaptive online experimental design for causal discovery." arXiv preprint arXiv:2405.11548 (2024).

Huang, Daolang, et al. "Amortized bayesian experimental design for decision-making." Advances in Neural Information Processing Systems 37 (2024): 109460-109486.

(Re: On Q2-b) Theoretical analysis of lossy representations

The lossy representation affects the probability of mapping a sample $x$ to the prototype embeddings.

We assume that for each state $x$ with true meta state $C(x) = u$, the probability that it is mapped by the encoder $E$ to the prototype embedding $\hat{u}_k$ is $p_k^u = P(\hat{C}(x) = \hat{u}_k \mid C(x) = u)$. This probability is determined by the representation power and discriminability of the encoder $E$, and it reflects the encoder’s tendency to assign samples with the same true meta state $u$ to different prototype embeddings.

From Definition 5, $\hat{C}(x)$ and $C(x)$ are observationally equivalent if, for all $\hat{u}_k \in \hat{U}$ and for all $x_1, x_2 \in \\{x \mid \hat{C}(x) = \hat{u}_k\\}$, $C(x_1) = C(x_2)$.

where $n$ is the number of samples.

The probability of $\hat{C}(x)$ and $C(x)$ are observationally equivalent is given by $\sum_{k} p_k \sum_{u \in U} \mu_u (1 - p_k + p_k^u \mu_u)^n.$

For a sample $x$, the probability that, for all $x' \in \\{x' \mid \hat{C}(x') = \hat{C}(x)\\}$, $C(x') = u' \neq C(x) = u$ is:

For a sample $x$, the probability of $x$ being misclassified as belonging to a representation entry $e_u$ that has multiple true meta states is:

Due to the lossy representation, the probability of misclassification is:

If $n(p_k + p_k^u \mu_u) \ll 1$, for representation entry $e_u$,

In a more accurate representation, for each prototype $k$ the vector $\{\mu_u p_k^u\}_u$ concentrates on a single true state—one $p_k^u$ increases while the others decrease—thereby increasing $\sum_u (\mu_u p_k^u)^2$ and thus reducing each bracketed term $\bigl[p_k^{2}-\sum_u (\mu_u p_k^u)^2\bigr]$. Consequently, higher representation accuracy monotonically lowers the error bound, reaching zero contribution per prototype when it is class-pure.

(Re: W3-a) Why this method can be regarded as a world models method?($\star$)

• The definition of world models remains an open topic of discussion in the literature, generally falling into two major perspectives: (i) understanding the world, and (ii) predicting the future [7], enabling AI agents to plan, reason, and make decisions.
• From a broad perspective, we consider world models is to include the state and a transition function from (state, action) to next state. Thus, world models are not limited to model-based RL frameworks with an added observation function. Rather, any approach that captures the regularities and dynamics of the world can be referred to as a world model [6].
• This broader interpretation in causality is also supported by Bernhard Schölkopf’s keynote at ICDM, Towards Causal World Models and Digital Twins, where he argues that causal models represent a form of world modeling. In particular, the transition function from (state, action) to next state can be derived from a structural causal model.
• Based on this view, methods that learn world dynamics, including FCDL, can be considered world models.

Under a narrower interpretation of world models as "learning from observations", we would like to highlight that

1. our method learns a meta state representation, which constitutes a mapping from high-dimensional state space to a lower-dimensional meta state space,
2. based on the meta-causal graph, we further learn a transition models show interaction dynamics of transition model, they are updated continuously by active agent exploration. This aligns with the goal of learning a compact, predictive model of the world.

[6] Marvin Minsky. A framework for representing knowledge, 1974.

[7] Jingtao Ding et al. Understanding World or Predicting Future? A Comprehensive Survey of World Models

(Re: On W3-b) It would be much better to also include a baseline for comparison, and report standard deviations (this setting can be sensitive to random seeds)

Thank you for your advice. We added more experiments to report standard deviations.

We added new experiment to evaluate SHD and F1 compared with FCDL. The results shows that causal graph recovered by MCG is more accurate.

(Re: On Q1-b) how to deal with if actions do not intervene in a meaningful way?

• We have considered this issue and discuss it explicitly in the paper.
• Specifically, we provide a theoretical discussion under the Reachability assumption, detailed in Theorem 3 (Appendix, Lines 671–697).
• The theorem shows that as long as a state can be directly or indirectly influenced by actions, the corresponding meta-causal graph is identifiable.
• We also acknowledge this as a limitation in our Limitations section, where we state that our current method assumes all states are reachable, either through direct or indirect interventions.
• We added a new experiment based on a manipulation task to demonstrate that our method can handle cases where actions cannot intervene on all variables. We also modified this environment to test generalization. The results show that our method maintains strong performance and generalizes well, even when only a subset of variables is directly intervenable.

We sincerely thank the reviewer for carefully reading our paper and rebuttal, and for expressing interest in further discussion. We truly appreciate the thoughtful engagement, and we also hope this exchange can lead to a deeper and more meaningful dialogue.

(Re: W1 W3-b) : Discussion on FCDL, Our Contributions, and Relation to Active Causal Methods ($\star$)

• We acknowledge that the primary algorithmic novelty of our work lies in the entropy-based curiosity feedback. However, the core contribution of our paper is theoretical: we are motivated by the challenge of causal dynamics in open-ended worlds, and we address whether it is possible to identify context-dependent causal graphs (meta-causal graphs) through interventions.

  In our previous response, due to limited space, we mainly highlighted the differences with FCDL. In fact, only in Section 4.1 (Learning from Experiences), we referenced and built upon FCDL. Therefore, it is understandable that the reviewer sees our method as an extension of FCDL. However, our main contribution goes beyond FCDL. We provide a theoretical framework for identifying context-dependent causal graphs under interventions (Section 4), and design a curiosity-driven agent to actively explore and distinguish meta states and their associated subgraphs. The key challenge is how to detect meta states and how to learn different causal structures conditioned on them continuously in open-ended world. We will clarify this in the revised version.

• The active interventions in our method connects our work to the literature on active causal discovery and experimental design. With reference to the papers suggested by the reviewers, we outline the key differences below. [1, 2, 4]: These works focus on active exploration to discover causal relations, but they do not model context-specific causal graphs. They assume that causal discovery accumulates into a single static graph as more data is observed. In contrast, we explicitly model context-dependence, where the agent must jointly learn the meta state and its corresponding subgraph. This requires a new theoretical treatment, which we provide.

  [3, 5]: These works propose intervention strategies, but their goal is not causal discovery. Instead, they aim to design effective interventions to facilitate scientific experimentation. In contrast, our method aims to learn the causal structure itself under context shifts through interaction.

To make it more clear, we put detailed discussion of our motivation and discussion with context-dependent like (FCDL) at the end of reply.

[1] Choo, Davin, Themistoklis Gouleakis, and Arnab Bhattacharyya. "Active causal structure learning with advice." International Conference on Machine Learning. PMLR, 2023.

[2] Zhang, Zeyu, et al. "Bayesian active causal discovery with multi-fidelity experiments." Advances in Neural Information Processing Systems 36 (2023): 63957-63993.

[3] Zhang, Jiaqi, et al. "Active learning for optimal intervention design in causal models." Nature Machine Intelligence 5.10 (2023): 1066-1075.

[4] Elahi, Muhammad Qasim, et al. "Adaptive online experimental design for causal discovery." arXiv preprint arXiv:2405.11548 (2024).

[5] Huang, Daolang, et al. "Amortized bayesian experimental design for decision-making." Advances in Neural Information Processing Systems 37 (2024): 109460-109486.

(Re: On W2-a): Could you clarify how posterior accuracy was computed in the new experiment, was it over the full graph or limited to specific subgraphs?

We added noise to the input to obtain an inaccurate posterior. It was over full graph.

(Re: On W2-b) On the Design of Entropy-Based Objective

• We would like to clarify that the use of entropy in our method serves primarily as a carrier of the exploration objective.
• The key idea lies in the construction of the meta-causal graph embedded inside the entropy calculation.
• In fact, entropy in our method could be replaced by other measures of uncertainty. The role of the intrinsic reward is to encourage the agent to explore previously unseen meta states.
• Each meta state is tightly associated with a distinct causal graph, so this exploration strategy effectively pushes the agent toward regions where causal structures are most uncertain or subject to change.
• While entropy-based exploration has been used in prior work, entropy also functions there as a proxy. What really matters is the goal encoded inside the entropy term. In our case, it is to identify causal changes across contexts.

(Re: W1, W3-b) Yes, I understand the motivation here. However, my concern remains regarding the writing, which could be more clearly structured in future versions. Specifically, it would help to formally distinguish which components are based on prior work and which technical parts are novel.

Thank you for the helpful suggestion. We will restructure the paper to clearly separate prior foundations from novel parts as we mentioned in Motivation and Comparison with Context-Dependent Causal Discovery.

• We built the learning-from-experience framework on top of prior work, which provides a strong initialization.
• Our novel contributions include:
  • The construction of a formal intervention-based meta-causal graph, with associated theorems and learning framework.
  • A progressive learning process through active intervention.

(Re: W2-b) Yes, this is precisely what I was trying to express in my previous feedback. It would be valuable to consider other exploration strategies as well. While I understand the rationale behind using entropy, since the goal is to propose a general framework, it would be ideal if it could accommodate other intrinsic terms that share high-level similarities with entropy.

Thank you. We added new experiments with different intrinsic terms.

We evaluated three intrinsic objectives:

• Prediction Uncertainty. $r_{\text{int}} = H\left[p_{\theta}(s_{t+1}\mid s_t,a_t)\right]$, i.e., the entropy of the model’s predictive distribution over the next state (or its feature representation).

• Feature Discrepancy. Let $z_{t+1}=f_{\phi}(s_{t+1})$ denote the feature representation of the next state, and let $\hat{s}\sim p_{\theta}(\cdot\mid s_t,a_t)$ with $\hat{z}=f_{\phi}(\hat{s})$. We set $r_{\text{int}}=\|\hat{z} - z_{t+1}\|_1$.

• Predictive-Distribution Discrepancy. $r_{\text{int}} = -\log p_{\theta}(s_{t+1}\mid s_t,a_t)$ (surprisal / negative log-likelihood). (For discrete $s_{t+1}$, one may alternatively use $1 - p_{\theta}(s_{t+1}\mid s_t,a_t)$, but we adopt the former for scale invariance.)

In all cases, $r_{\text{int}}$ serves as the curiosity signal guiding actions-as-interventions in the open-ended world.

(Re: W3-a) I understand this point. What I mentioned previously was indeed an incorrect citation to support your claim. However, regarding the framing of the world model, I believe the role of actions should be taken into account, which I assume will be discussed later in the paper.

Thank you for your comment. We will clarify the role of actions in the world model in the next revision.

• Sorry about the incorrect citation. We also note that Richens and Everitt operates directly on features rather than introducing an explicit high-dimensional observation function [1]; those features are treated as directly/partially observable and (in many cases) directly intervenable, which explains their action–intervention alignment.
• Our method identifies context-dependent causal graphs (meta-graphs) via interventions. Actions are how the curiosity-driven agent realizes those interventions.
• When actions can directly intervene each state (e.g., a chemical environment), we deploy targeted interventions to isolate edges and quickly distinguish meta states and their subgraphs.
• When not all interventions are feasible, we rely on the reachability assumption (Appendix A.8).
• We also added an experiment comparing causal graphs under limited vs. full reachability (W3.d).
• We will incorporate these clarifications in the next revision.

[1] Richens, J., & Everitt, T. (2024). Robust agents learn causal world models. arXiv preprint arXiv:2402.10877.

We thank the reviewer for highlighting our innovative Meta-Causal Graph framework, the effective curiosity-driven exploration strategy, and the strong theoretical guarantees for identifiability.

W1: More environments & experiments in generalization.

Thank you for your suggestion. We added new environment and adjusted magnetic force, density of ball and friction of the table to test the generalization ability of our method. The results are shown below and the metric is epsiode reward on downstream tasks:

We also added the new experiment to test the generalization ability of our method under varying levels ($n$) of noise (line 265-268) when some variables are not observed. The results are shown below and the metric is prediction accuracy:

W2: Improve clarity of the method part.

Thank you for your suggestion. Here is a clearer summary of the learning process:

• For each observed state, the agent predicts a compact meta-causal graph (MCG) representing the current context’s causal structure.
• The agent selects actions based on a curiosity-driven reward, which encourages exploration of uncertain or unseen contexts.
• The agent uses the learned MCG to model and predict environment dynamics.
• As the agent collects new experience, both the meta-state assignment and the corresponding causal graphs are iteratively updated.

We will improve the clarity of the method description in the revised version.

W3: Explanation of the Meta-causal graph.

• Yes, your understanding is correct. The meta-causal graph is a collection of causal subgraphs, each associated with a specific meta state indicator.
• We use the meta-causal graph for downstream tasks, where the agent learns to predict the transition dynamics based on the meta state and its corresponding causal subgraph.
• Importantly, these meta states are unknown to the agent and must be discovered through interaction, which makes the problem challenging. The joint identifiability of both the causal subgraphs and the underlying meta states requires rigorous theoretical justification, as it is a fundamentally difficult problem.

W4: Why is the Meta-Causal Graph considered a world model?

• The definition of a world model remains a subject of ongoing debate [Ding et al., 2024]. Generally, a world model is any system that models the environment’s dynamics—i.e., it learns the function mapping (state, action) pairs to next states. In this broad sense, CDL and Grader are also world models.
• Our approach aligns with the broader definition of a world model: we first infer a compact meta-causal graph from each input, capturing the context-specific causal structure, and then use this representation to predict future dynamics.
• This enables our model not only to predict transitions, like a dynamics model, but also to maintain an abstract and interpretable understanding of the environment’s underlying structure.

W5: More recent work should be discussed.

• We appreciate your suggestion and give a brief comparison here. We will include more recent works and discuss comparisons in the revised version.

  • [Wang et al., 2024]: This observation-based, passive learning method cannot actively explore or adapt in open-ended worlds. In contrast, our intervention-based approach actively discovers unseen meta-states to learn a Meta-Causal Graph, making it well-suited for open-ended environments.
  • [Cao et al., 2025]: Their causal structure is global and fixed, not adapting to state or meta-state changes. Our framework explicitly models multiple context-dependent causal graphs, allowing discovery of diverse causal mechanisms across meta-states.
  • [Yu et al., 2024]: OOCDM learns a shared causal structure for each object class through passive observation, without context-specific graphs or active exploration. Our method discovers multiple context-specific graphs via active, curiosity-driven interventions, enhancing exploration and identifiability.

• Additionally, We added new baselines: causal discovery using transformer attention weights ("transformer") and the Jacobian matrices of MLP layers ("sandy-mixture") from [Pitis et al., 2020] and [Urpí et al., 2024], for comparison. The results are shown below. The metrics used are next-state prediction accuracy and the average episode reward achieved by model-based planning on downstream tasks.

Pitis, Silviu, et al. Counterfactual data augmentation using locally factored dynamics. NeurIPS, 2020

Urpí, Núria, et al. Causal action influence aware counterfactual data augmentation. arXiv, 2024.

Yang Liu, et al. Learning world models with identifiable factorization. NeurIPS, 2023.

Zizhao Wang, et al. Building minimal and reusable causal state abstractions for reinforcement learning. AAAI, 2024.

Hongye Cao, et al. Towards empowerment gain through causal structure learning in model-based RL. arXiv, 2025.

Yu Zhongwei, et al. Learning causal dynamics models in object-oriented environments. arXiv, 2024.

Jingtao Ding, et al. Understanding world or predicting future? a comprehensive survey of world models. ACM Computing Surveys, 2024.

Thank you for the detailed response. I think you should conduct more experiments in more challenging environments (Meta-World/CausalWorld) to demonstrate that the proposed method is a genuine meta-cause-and-effect world in the future. I maintain my positive score.

Dear reviewer KoPL,

Thank you for maintaining a positive score and for suggesting Meta-World/CausalWorld. We agree they are compelling testbeds and view your pointer as a valuable direction beyond the present scope.

Many thanks,

The authors of #20694