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REVIEW 3 major objections 4 minor 2 cited by

Generating Symbolic World Models via Test-time Scaling of Large Language Models

T0 review · 3 major / 4 minor · reviewed 2026-08-08 · deepseek-v4-flash

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Pith's one-line read Spending more compute at test time lets LLMs write PDDL planning domains: Best-of-N sampling plus an LLM critique-correct loop lifts a 7B open-weights model to 85.2% on NL2Domain and 71.4% on Prob2Domain, beating o1-mini by over 41 and 33…

desk verdict BoN+iVML is a solid, training-free recipe for PDDL generation, but the headline numbers are VAL pass rates, not semantic correctness; worth engaging, not at face value. read the letter →

arxiv 2502.04728 v2 pith:VFQNJE4K submitted 2025-02-07 cs.AI

Zhouliang Yu , Yuhuan Yuan , Tim Z. Xiao , Fuxiang Frank Xia , Jie Fu , Ge Zhang , Ge Lin , Weiyang Liu This is my paper · ORCID
classification cs.AI
keywords PDDLdomainsynthesistest-timescalingBest-of-Nsamplingverbalizedmachinelearninginstancesymbolicworldmodelsclassicalplanninglargelanguage
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper argues that spending more computation at inference time can substitute for the missing training data that blocks large language models from writing PDDL, the formal planning language used in the International Planning Competition. The proposed recipe first samples many candidate PDDL domains and keeps the most likely ones, then runs a closed loop in which one LLM critiques the current domain in plain language and a second LLM rewrites it accordingly. On the two translation tasks—natural-language descriptions to domains and PDDL problems to domains—the method lifts a 7B open-weights coder model to 85.2% and 71.4% success, surpassing o1-mini by roughly 42 and 34 percentage points without any fine-tuning. If correct, this means reliably generating a formal world model is a test-time-compute problem rather than a data-collection problem, and the resulting PDDL lets classical search replace fragile natural-language planning.

What carries the argument

The mechanism is a two-phase optimization loop: Best-of-N (BoN) sampling for initialization and instance verbalized machine learning (iVML) for refinement. BoN explores the solution space by generating N diverse candidates and keeping the K with highest token log-likelihood, so iVML starts from a good point rather than a random one. iVML parameterizes the model as a text prompt containing the PDDL domain plus a natural-language chain of thought; the optimizer function produces critiques and the update function rewrites the domain, so the PDDL text itself is the learned parameter being improved. The loss being minimized is the match between the input description and the domain, computed entirely in natural language by the critique LLM.

What would settle it

Give the pipeline a set of NL2Domain tasks, take the VAL-passing domains it produces, and have human experts (or an oracle) compare each domain's action effects against the source description. If a large fraction of VAL-passing domains encode different state transitions than the description requires—for example, a blocks-world 'stack' action whose effect fails to clear the lower block, which VAL would still accept—then the reported success rates do not measure faithful world-model generation.

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Extended reading notes

Core claim

The paper's central claim is that test-time compute scaling can elicit PDDL generation ability from LLMs that they were not explicitly trained for, provided the effort is organized as exploration followed by exploitation. Exploration is Best-of-N sampling: the model generates N chain-of-thought-plus-PDDL candidates at temperature 0.7, scores each by total log-likelihood, and keeps the top K. Exploitation is iVML: an optimizer LLM reads the natural-language description, the current thoughts, and the current PDDL domain, and writes verbalized feedback; a learner LLM then rewrites thoughts and domain in response. Iterating this loop drives domains through VAL validation, and the resulting domains, paired with the Fast Downward planner, match or beat oracle-interaction baselines and LLM-as-planner systems on Barman, Floortile, Tyreworld, Grippers, and Termes.

Load-bearing premise

The whole method leans on the assumption that a domain passing VAL validation is genuinely the world model the natural-language description intends, since VAL only checks syntax and plan executability, not whether the domain matches the described semantics.

Editorial extensions

If this is right

  • Small open-weights models become competitive PDDL generators: Qwen2.5-Coder-7B with the two-phase loop outperforms o1-mini and o1-preview on domain synthesis, removing the need for proprietary large models.
  • PDDL domain synthesis no longer requires fine-tuning data or oracle environments; the same loop could apply to other formal languages where a verifier or critique signal exists.
  • Planning becomes robust again: once a valid domain is generated, classical heuristic search guarantees feasible and optimal plans, eliminating the rule-violation and state-tracking hallucinations of direct LLM planners.
  • The approach exposes a scaling behavior: increasing the sampling budget N and the iVML iteration count T both improve success rates, with iVML pushing past the saturation point that BoN alone reaches.
  • On the Planetarium problem generation benchmark, the method reaches 99.60% goal-correctness, beating fine-tuned baselines without any training.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the central claim holds, the scarce resource for symbolic modeling shifts from training data to verification signals; methods that can certify semantic alignment, not just syntax, would likely raise the ceiling further.
  • The sample-critique-rewrite template is a generic pattern that may transfer to other formal synthesis tasks, such as SMT constraint generation, grammar induction, or schema mapping, whenever an LLM judge can articulate what is wrong.
  • Because the optimizer LLM is the only feedback source, iVML could inherit the optimizer's blind spots; a testable extension is to inject external verifier signals, such as planner trace statistics or counterexample plans, as additional verbalized gradients.
  • The gap between VAL-passing and semantic correctness suggests the reported success rates may overstate faithful world-model generation; measuring plan agreement with ground truth, as the paper does in its planning experiments, is a stronger check and arguably the better future metric.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper proposes a two-stage test-time scaling method for PDDL domain synthesis. First, Best-of-N sampling with temperature 0.7 generates candidate PDDL domains and selects the top K by summed token log-likelihood. Second, instance verbalized machine learning (iVML) iteratively refines those candidates: an optimizer LLM critiques the current domain and chain-of-thought against the natural-language description, and a learner LLM produces a revised domain; this loop runs for T iterations. The method is evaluated on NL2Domain and Prob2Domain using IPC-derived datasets with VAL pass rate as the primary metric, on the Planetarium PDDL problem-generation benchmark with goal-matching accuracy, and on six planning domains with exact plan-matching accuracy after Fast Downward planning. The authors report that Qwen2.5-Coder-7B with iVML-5-BoN-8 reaches 85.2% on NL2Domain and 71.4% on Prob2Domain, outperforming o1-mini by 41.7 and 33.7 percentage points, and that PDDL-based planning with the synthesized domains outperforms LLM-as-planner baselines.

Significance. The central empirical claim is significant if it holds: it would show that an open 7B model, without fine-tuning or oracle interaction, can synthesize PDDL domains competitive with or better than much larger closed models, and that the synthesized domains can support classical planners on hard IPC domains. The method is simple, well described, and structurally reproducible: the prompts are given in full in the appendices, the benchmarks are standard IPC and Planetarium sets, and the evaluation uses external tools (VAL, Fast Downward). The iVML adaptation of verbalized machine learning to instance-level refinement is a genuine contribution. The main caveat is that the headline metric is only a necessary condition for correctness; the paper explicitly acknowledges this limitation, and the more semantically informative plan-matching evaluation is limited and unreplicated.

major comments (3)
  1. [Section 4.2, Table 2 and Section 5, limitation (1)] The headline success rates (85.2% on NL2Domain and 71.4% on Prob2Domain) are defined as the percentage of generated domains that pass VAL validation, and the paper itself concedes in Section 5 that VAL cannot detect semantic inconsistencies that violate domain intent or commonsense logic. A domain can pass VAL while omitting required actions, adding impossible ones, or encoding wrong preconditions or effects, so the primary metric does not establish the central claim that the method generates correct symbolic world models. The exact-plan-matching results in Table 5 are a more meaningful signal, but they cover only six domains and are not aggregated over the main benchmark. Please add a semantic evaluation on a sample of VAL-passing domains (e.g., human annotation or exact plan matching on a larger set), or revise the abstract and contribution claims to say "syntactically valid PDDL" rather than implying semantic correctness.
  2. [Section 4.6, Table 5] The exact-plan-matching results, which are the strongest evidence of semantic correctness, are reported for only six domains with no sample sizes, no repeated seeds, and non-monotonic behavior. For example, Blockworld shows 9.5 for BoN-4 versus 0.0 for BoN-16, and 71.4 for iVML-5-BoN-4 versus 81.0 for iVML-5-BoN-16; Grippers shows 100.0 for both BoN-4 and BoN-16. This pattern is consistent with high variance, so Table 5 cannot by itself rescue the domain-synthesis claim. Please report per-domain instance counts and repeated-seed variance, and consider aggregating the plan-matching metric over a larger subset of the NL2Domain and Prob2Domain benchmarks where ground-truth plans are available.
  3. [Section 4.2, Section 4.3, Eq. (2), Figures 3-5] No variance information is reported for any main result. BoN and iVML are stochastic (temperature 0.7), and Eq. (2) selects candidates by a raw sum of token log-likelihoods without length normalization, which may bias selection toward shorter candidates. The large margins over o1-mini are likely robust, but smaller claims (e.g., the "monotonic improvement" of iVML up to T=80, or the difference between N=8 and N=32 in Figure 3) would be more convincing with repeated runs and confidence intervals. At minimum, please report seed variance for the headline Table 2 rows and for the curves in Figure 3.
minor comments (4)
  1. [Section 4.1 and Table 2] The task name appears as "Prob2Domai" in Section 4.1, and Table 2 contains "Instrcut" for "Instruct"; the task name also alternates between "Problem2Domain" and "Prob2Domain." Please standardize these.
  2. [Table 3, Termes row] The natural-language description says "Create a block at the depot. The robot will have the block," but the PDDL action shown is remove-block and the critique discusses removing a block; this mismatch makes the qualitative example confusing.
  3. [Section 3.3, Eq. (4)] The indexing of feedback is inconsistent: Eq. (4) labels the output of the optimizer as F_i, but the f_update prompt template refers to "The error of the PDDL domain {F_{i-1}}"; please align the notation across the equation and the prompt templates.
  4. [Figures 3-5] The learning curves do not show error bars or shading, and the y-axis label "#Domains Pass VAL(%)" mixes a count symbol with a percentage unit; please clarify the metric and add interval information where possible.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the reported PDDL synthesis results are checked by external VAL, ground-truth goal, and plan-matching benchmarks; the VML self-citation is attribution rather than a load-bearing premise.

full rationale

The paper's derivation chain is empirical, not definitional. Best-of-N sampling (Eqs. 1-2) scores candidates by token log-likelihood and iVML (Eqs. 3-4) iteratively rewrites PDDL domains from LLM critiques; neither step fits a parameter to the evaluation set. The headline numbers in Table 2 are the percentages of synthesized domains that pass the external VAL validator, Table 4 uses Planetarium's ground-truth goal matching, and Table 5 uses exact matching against ground-truth reference plans found with Fast Downward. The evaluation is thus external to the method's own outputs, so no 'prediction' is forced by construction. The only self-citation is to VML [50], the authors' prior framework from which iVML is adapted; this is normal attribution and does not carry the central claim. The paper explicitly flags in Section 5 that VAL 'cannot detect semantic inconsistencies that violate domain intent or commonsense logic'; this is a metric-strength limitation, not a circular reduction, since a domain passing VAL is not defined in terms of iVML's self-critique. Central claims retain independent empirical content.

Assumptions & free parameters 4 free parameters · 3 assumptions · 0 invented entities

No new physical entities or fundamental constants are invented. The free parameters are algorithm hyperparameters (N, T, K, temperature) chosen by the authors. The axioms are domain assumptions about evaluation validity and the reliability of self-critique, both of which the paper partially acknowledges.

free parameters (4)
  • N (Best-of-N sample count) = 8 (main), 16 (Table 4 and 5), 4 (ablation)
    Number of candidate PDDL domains sampled in parallel; higher N improves BoN but saturates. Chosen per experiment, not fitted to a validation set.
  • T (iVML refinement iterations) = 5 (main), 1 (Table 4), up to 80 (Figure 3)
    Number of critique-update cycles. More iterations generally improve success rate but increase compute; set by the authors.
  • temperature tau = 0.7
    Sampling temperature for diversity in BoN and iVML. Set by hand and used across experiments.
  • K (top candidates retained for iVML) = not stated explicitly
    The paper says the top K candidates are retained but never specifies K, which affects compute and performance.
assumptions (3)
  • domain assumption VAL validation is a sufficient measure of correct PDDL domain generation.
    Used as the primary success metric in Tables 2-5. The paper's own limitation section (Section 5) states VAL cannot detect semantic inconsistencies, so this assumption is acknowledged to be imperfect.
  • domain assumption The LLM's self-critique in iVML provides reliable verbalized gradients without an oracle.
    iVML assumes the optimizer LLM (f_opt) produces useful feedback and the learner LLM (f_update) applies it correctly. This is an empirical assumption that is not independently proven and could fail for weaker models.
  • domain assumption Natural language descriptions and PDDL problems contain enough information to reconstruct the intended domain.
    Prob2Domain is under-specified in general (a problem alone does not define actions). The high success rates suggest the LLM exploits distributional priors rather than pure logical inference.

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Cite this review

Pith. "Pith review of Generating Symbolic World Models via Test-time Scaling of Large Language Models." pith.science (2026). https://pith.science/paper/VFQNJE4K

@misc{pith2026250204728,
  author       = {Pith},
  title        = {Pith review of: Generating Symbolic World Models via Test-time Scaling of Large Language Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VFQNJE4K}},
  note         = {Machine review of arXiv:2502.04728}
}
read the original abstract

Solving complex planning problems requires Large Language Models (LLMs) to explicitly model the state transition to avoid rule violations, comply with constraints, and ensure optimality-a task hindered by the inherent ambiguity of natural language. To overcome such ambiguity, Planning Domain Definition Language (PDDL) is leveraged as a planning abstraction that enables precise and formal state descriptions. With PDDL, we can generate a symbolic world model where classic searching algorithms, such as A*, can be seamlessly applied to find optimal plans. However, directly generating PDDL domains with current LLMs remains an open challenge due to the lack of PDDL training data. To address this challenge, we propose to scale up the test-time computation of LLMs to enhance their PDDL reasoning capabilities, thereby enabling the generation of high-quality PDDL domains. Specifically, we introduce a simple yet effective algorithm, which first employs a Best-of-N sampling approach to improve the quality of the initial solution and then refines the solution in a fine-grained manner with verbalized machine learning. Our method outperforms o1-mini by a considerable margin in the generation of PDDL domains, achieving over 50\% success rate on two tasks (i.e., generating PDDL domains from natural language description or PDDL problems). This is done without requiring additional training. By taking advantage of PDDL as state abstraction, our method is able to outperform current state-of-the-art methods on almost all competition-level planning tasks.

Figures

Figures reproduced from arXiv: 2502.04728 by the authors.

Figure 1
Figure 1. An overview of the proposed method. Our test-time compute scaling approach consists of two main [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. OpenAI-o1-preview plans for Termes: o1-preview frequently exhibits hallucination during the planning [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Left: The performance trend of BoN with increasing sampling numbers. Right: The performance trend of [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: The performance of iVML on NL2Domain tasks across different initialization settings. T:1 T:4 T:7 T:10 T:13 T:16 T:19 T:22 T:25 T:28 Num of iterations 0 20 40 60 80 100 #Domains Pass VAL(%) iVML under various initializations (Prob2Domain) prob_QwenCoder_BoN4 prob_QwenCo…
Figure 6
Figure 6. Figure 6: shows the planning graph that contains explicit state transition during planning for Termes [PITH_FULL_IMAGE:figures/full_fig_p030_6.png]

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Forward citations

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Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.