Thank you for your valuable and detailed review. We're glad you engaged deeply with our work, and we address your concerns point by point below.

1. Novelty Beyond LLM-Based Rule/Knowledge Summarization: Here are the distinctive novelties of WALL-E: (1) a training-free world alignment framework that aligns pretrained LLMs with a specfic environment's dynamics, which leads to a precise neuro-symbolic world model; (2) an effective symbolic knowledge learning scheme (using LLM as an inductive reasoner); (3) a world model-grounded agent with efficient model-predictive control (MPC, using LLM as the optimizer).

These novelties are revolutionary to existing world modeling strategies as we only need to focus on the complementary symbolic and verifiable knowledge that cannot be covered by pretrained LLMs, which are much more efficient to learn than training a world model from scratch. In our method, we do not require any parameter training. We also replace the low-level optimization in classical MPC with high-level reasoning by LLMs under the symbolic constraints. This makes the planning more precise for long-horizon challenging tasks.

2. The Reliance of Code Rules on API Calling Limits Generalization Beyond 2D Environments: Executable code via API calls is a strength rather than a limitation—and it is increasingly becoming a popular design in recent 3D-embodied robotic systems, especially for hierarchical agents where high-level LLM planners call low-level controllers via API calls [1–4].

Our neurosymbolic MPC agent operates at a high level of abstraction (e.g., code rules execution), agnostic to the environment's dimensionality; the API layer serves to map these abstractions to environment-specific low-level controllers. This setting is important for maximizing the potential of pretrained LLMs as they are good at high-level inductive reasoning.

As a result, adapting our method from 2D to 3D or real-world scenarios only requires updating the API/controller bindings, without changing the neurosymbolic learning or planning mechanism.

3. Verification Code Rule Correctness (Syntax, Logic, Functionality): We verify the correctness by discarding any rule that contradicts ground-truth transitions from real trajectories $\tau^{\text{real}}$. For Syntax, we filter out any rule that raises an execution error during any run. For logical consistency and intended functionality, we do not manually inspect rules; instead, we rely on empirical validation: only rules that are correct, executable, and successfully cover/correct many LLM-mispredicted transitions are retained—these form the output of "Stage 4. code rules pruning". In practice, this pruning process consistently yields logically sound and functional rules (see the learned rules in Appendix D). We will further clarify this in "Stage 4: Code Rules Pruning" and the Appendix.

4. Efficiency and Storage of Symbolic Knowledge Learning: Symbolic knowledge learning is fast (<1h30min in Mars; <30min in ALFWorld), data-efficient (5 trajectories for Mars; 30 for ALFWorld), and lightweight—requiring <50kB of storage per environment (JSON format). Mars features high degrees of freedom and task complexity (≈240 steps/trajectory), so 5 trajectories reveal diverse transitions. In contrast, ALFWorld tasks are simpler and shorter (≈18 steps/trajectory), and categorized into different types, so we sample 5 trajectories per type across 6 types to ensure a broad coverage.

[1]. Liang, et al. "Code as Policies: Language Model Programs for Embodied Control." ICRA 2023.
[2]. Mao, et al. "Robomatrix: A skill-centric hierarchical framework for scalable robot task planning and execution in open-world." arXiv 2024.
[3]. Belkhale, et al. "RT-H: Action Hierarchies using Language." RSS 2024.
[4]. Shi, et al. "Hi robot: Open-ended instruction following with hierarchical vision-language-action models." ICML 2025.

Thank you for taking the time to evaluate our paper and provide thoughtful feedback. We value and appreciate your comments! In the following, we provide detailed responses and clarifications to each of your concerns.

1. Symbol Overload and Readability: We will remove non-essential symbols and annotate key ones directly in the figures to improve the clarity and readability.

2. Intuitive Explanation of Code Rule Pruning: Intuitively, Code Rules Pruning is to select a small subset of extracted rules that can cover and correct most mispredictions by LLM only. We formulate it as a classic maximum coverage problem (Eq.5 on Page 5) that can be addressed by the greedy algorithm (Alg.3 on Page 30). Specifically, we first collect all transitions where the LLM-only's predictions failed ($\mathcal{D}^{\text{inc}}$) —these mark LLM's misalignments with the real environment. Then, at each step, we select the rule that can cover/correct the most remaining mispredicted transitions and add it to the subset, remove its covered transitions from future consideration, and repeat the above procedure until the number of selected rules reach the budget size $l$. This yields a compact yet high‐impact rule set that best aligns the LLM's priors with environment dynamics.

3. WALL-E's Design is Complex: WALL-E's architecture is modular by design—it is principal and general. In WALL-E, the world model is an LLM augmented by a set of symbolic knowledge extracted from previous experiences. The agent planning is acheived by model-predictive control, in which an LLM agent interact with the world model for multiple rounds to determine the best action(s) to take in the following step(s).

The idea is to use LLMs for inductive reasoning of symbolic knowledge and proposing actions, while lightweight program modules encode symbolic knowledge and ensure transparent, verifiable execution of the rules. This follows a growing best practice in agentic AI: leveraging LLMs for generalization and abstraction, while using structured programs to ground and constrain LLMs' outputs, reducing hallucinations and uncertainty of LLM-only predictions. Compared to LLM-only or rigid rule-based systems, this neuro-symbolic approach offers greater robustness, efficiency, interpretability, and reliability, by combining the complementary strengths of LLMs and symbolic systems. Moreover, this is achieved without any parameter training or intensive human supervision.

4. Verification of Code Rule Correctness, Executability: We ensure the correctness by verifying each candidate code rule on ground-truth transitions from the real trajectory $\tau^{\text{real}}$ and discarding any rule that leads to wrong predictions. For executability, any rule that raises an execution error during any run is also removed. This filtering mechanism is simple but rigorous. We will further clarify this in "Stage 4: Code Rules Pruning."

Thank you for your thoughtful review and constructive comments. We're pleased that you recognized the potential of our approach, and we address your questions and suggestions in detail below.

1. Inflexibility of Symbolic Rule Structure: Our symbolic rule structure is highly flexible, as the rules are automatically derived by an LLM from previous experiences without relying on any domain-specific engineering. As noted in the main text (Lines 69–74, 100–103) and Appendix (Lines 455–459), WALL-E performs inductive reasoning by an LLM to extract symbolic rules directly from experiences—without handcrafted prompts, task-specific modeling, or any fine-tuning—enabling fast and scalable adaptation across diverse environments.

2. Clarify WALL-E's SotA Claim in Table 1 Given DreamerV3's Higher Score: WALL-E is the SOTA training-free method that does not require any finetuning of LLM parameters. While DreamerV3 achieves higher absolute rewards, it is trained for 1 million environment steps. Our bolding in Table 1 reflects WALL-E's leading performance within the training-free (LLM-based) category. DreamerV3's results are included for reference only, to highlight the contrast in sample efficiency and adaptation speed. We will revise Table 1's caption to make the evaluation and comparison setting clearer.

3. Why WALL-E Underperforms DreamerV3: This is because WALL-E does not finetune any model parameters and focus on high-level planning, while DreamerV3 fully finetunes a policy for 1M steps to produce low-level actions. These gaps in the training and modeling lead to their difference in performance. This gap also motivates hierarchical planning/control in recent works (LLM planner + trained controller) [1,2]. However, in our submission, we keep using the same setup as most LLM agent baselines for fair comparisons, where the LLM is not finetuned for specific tasks and takes the full control of the agent.

[1]. Shi, et al. "Hi robot: Open-ended instruction following with hierarchical vision-language-action models." ICML 2025.
[2]. Wang, et al. "Describe, explain, plan and select: interactive planning with large language models enables open-world multi-task agents." NeurIPS 2023.

Thank you for your careful assessment and valuable comments. We are pleased to respond to your concerns and further clarify the design and impact of our approach below.

1. Deterministic Rule Limitation vs. Probabilistic Dynamics: Our rule learning focuses on the deterministic part of dynamics because: (1) it is the backbone of many environments and complementary to the stochastic part that may have been captured by LLMs; (2) it enables stable and verifiable modeling of dynamics; and (3) many seemingly probabilistic outcomes collapse to deterministic when conditioned on the reasoning results of LLM on trajectories. For example, crafting an iron pickaxe may seem uncertain until one realizes that a furnace is a necessary precondition.

As noted in §Limitation and Future Work, extending our framework to handle explicit probabilistic transitions by allowing light-weight LLM finetuning is an important direction for our future work.

2. Code-Based vs. Natural Language Rules: Compared to natural language rules, code-based rules avoid possible ambiguity and lead to more precise and verifiable generalization. This is essential for stable and controllable decision-making. Moreover, they are also easier to be followed by LLMs.

Unlike natural language rules, our approach leverages LLM-induced symbolic patterns—e.g., abstracting both "table" and "desk" as functionally equivalent—to generalize safely without ambiguity. In contrast, natural language rules may lead to vague interpretation and reasoning that cause unsafe or inconsistent behaviors—an unacceptable risk in decision-making systems.

3. Extending the Method to Capture More General Abstraction of Transition Dynamics: We start with binary success/failure rules because they provide compact, straightforward, and verifiable instructions that various LLMs can easily understand and follow without further finetuning. The effectiveness is reflected by the strong long-horizon results in Tables 1–2. In §Limitation and Future Work, we plan to extend the framework to richer types of abstractions for future work.

4. Missing IfR in ALFWorld Comparison (Table 2): IfR [1] is not included in the ALFWorld Comparison (Table 2) because it was developed and evaluated specifically for Mars environment and has not been applied to any other environments. Direct comparison would be unfair and potentially misleading.

[1]. Tang, et al. "Mars: Situated inductive reasoning in an open-world environment." NeurIPS 2024.