On Sample-Efficient Generalized Planning via Learned Transition Models

Biplav Srivastava; John A. Aydin; Nitin Gupta; Vishal Pallagani

REVIEW 3 major objections 6 minor 5 references

On Sample-Efficient Generalized Planning via Learned Transition Models

T0 review · 3 major / 6 minor · reviewed 2026-08-02 · deepseek-v4-flash

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Pith's one-line read Learning to predict successor states, not action sequences, is the stronger inductive bias for generalized planning, and small size-invariant models achieve it with far fewer parameters and training instances.

desk verdict The paper shows a promising hybrid pipeline, but the abstract overclaims: the OOD gains are likely driven by symbolic successor enumeration, not by the learned transition model itself. read the letter →

arxiv 2602.23148 v3 pith:DOLKO6BD submitted 2026-02-26 cs.AI

Nitin Gupta , Vishal Pallagani , John A. Aydin , Biplav Srivastava This is my paper · ORCID

classification cs.AI

keywords generalizedplanningtransition-modellearningneuro-symbolicWeisfeiler-Lemanembeddingsout-of-distributiongeneralizationsampleefficiencyplandecoding

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 tries to establish that generalized planning — finding one strategy that solves a whole family of planning problems — is better learned as a transition-modeling problem than as an action-sequence prediction problem. The authors train a small goal-conditioned model to predict the successor state in a fixed-dimensional embedding space, then decode the plan by selecting the valid symbolic successor closest to that prediction. With Weisfeiler–Leman state embeddings, these compact models extrapolate to planning instances with many more objects than seen in training: in Blocksworld and VisitAll they match or exceed published Transformer-based planners while using orders of magnitude fewer parameters and no data augmentation. The same method does not solve Logistics under strict extrapolation, and the decoding step relies on symbolic successor enumeration at every step. A sympathetic reader would care because the result suggests that learning domain dynamics, not scaling action-sequence models, is the more promising route to out-of-distribution generalization in planning.

What carries the argument

The load-bearing object is the residual transition model in WL embedding space plus the neuro-symbolic decoding rule. WL embeddings map any state–goal pair to a fixed-dimensional histogram of color-refinement classes, making input size independent of object count; residual prediction encodes STRIPS frame axioms; and the nearest-valid-successor rule converts the embedding-space prediction into a guaranteed-valid symbolic action. LSTM and XGBoost serve as the function approximators, demonstrating that neither architectural scale nor sequential memory is the source of the gains.

What would settle it

Replace the learned transition model with a trivial predictor (always predict zero delta, or a fixed random target) while keeping the same WL embeddings and symbolic successor decoding, and measure extrapolation success on the same splits. If the trivial predictor retains most of the 50% and 100% success on Blocksworld and VisitAll, the symbolic scaffolding is carrying the generalization; if success collapses, the learned model is load-bearing. A second check: decode by rounding the predicted embedding to a nearest state without enumerating symbolic successors — collapse would confirm that enu

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Extended reading notes

Core claim

The paper's discovery is a state-centric formulation of generalized planning: instead of modeling p(action sequence | problem), learn a goal-conditioned transition model fθ that predicts a residual Δ_t in a Weisfeiler–Leman embedding space, so that the predicted next-state embedding is φ(s_t) + Δ_t. At each step the planner computes all valid symbolic successors Succ(s_t) from the domain operators and selects the one whose embedding is closest to the prediction; this guarantees every executed action is applicable and corrects drift. The empirical claim is that this explicit transition-model bias, combined with permutation- and size-invariant WL embeddings, yields higher out-of-distribution s

Load-bearing premise

The load-bearing premise is that the extrapolation success is attributable to the learned transition model: at every step the method knows the true symbolic state, enumerates every valid successor, and only needs to rank them, so if the symbolic scaffolding — not the learned prediction — drives generalization, the paper's central claim about transition-model learning is not established.

Editorial extensions

If this is right

Small state-centric models can extrapolate to object counts far beyond training, so data and parameter scaling are not the only route to out-of-distribution planning.
Permutation- and size-invariant state encodings are a necessary ingredient: fixed-slot factored encodings obtain near-zero extrapolation success across all domains.
Residual (delta) transition prediction improves non-parametric models in sparse STRIPS domains, consistent with the add/delete semantics of transitions.
Symbolic successor decoding guarantees plan validity at every step, eliminating the invalid-action problem that action-sequence models face.
Hierarchical domains with multi-layer causal coupling remain out of reach for one-step learned transitions under strict extrapolation.

Reading between the lines

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

Because decoding always has the true symbolic state and the full successor set, the reported gains may be due to symbolic scaffolding rather than the learned model; a zero-residual control would separate these.
Using the transition model as a soft heuristic inside a classical search, rather than greedy nearest-neighbor rollouts, is a natural extension that might address the myopia behind the Logistics failure.
Training on multi-step or abstract transitions, while keeping the same decoding interface, could extend the approach to hierarchical and long-range dependency domains.
If a trivial predictor retains most of the extrapolation success, the practical lesson shifts to size-invariant representations plus symbolic decoding, with the model quality bar reduced to ranking near-miss successors.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The one thing to know about this paper: it's a well-run empirical study that overclaims its central result. The authors propose a state-centric approach to generalized planning—predict the next state's embedding rather than the next action—and then decode by enumerating all valid symbolic successors and picking the one closest to the prediction. In a few domains this beats action-sequence transformers on out-of-distribution extrapolation, with far smaller models and less data. If you're working on neural planning, this is worth reading.

What's actually new is the specific combination of goal-conditioned successor embedding prediction with WL features and nearest-neighbor symbolic decoding. The related work makes clear that WL features plus lightweight regressors already match GNNs for heuristic learning, and model-based RL is established, but nobody seems to have framed generalized planning this way. The empirical study is careful: they ablate representations (WL vs fixed-size factored), prediction modes (state vs delta), and model classes (LSTM vs XGBoost), and they report splits for validation, interpolation, and extrapolation. Code and data are promised. That's real work and it deserves credit.

The soft spot is the comparison. In Algorithm 1, the method maintains the true symbolic state at every step, enumerates every valid successor using the domain transition function γ, and only ranks those successors by embedding distance. So the learned model never has to produce an executable action or even a state outside the successor set. The action-centric baselines—Plansformer, PlanGPT, SymT—don't get that scaffolding; they have to generate action sequences from scratch. That means the reported gains could come from the neuro-symbolic decoding shell rather than from the learned transition model. The paper itself says the decoding 'guarantees that every generated action is applicable.' The stress-test note makes exactly this point, and I think it lands.

To support the attribution, the authors should include a control where the ranking is replaced by something trivial—random choice among valid successors, or a simple heuristic—and show that their transition model beats that. They also need to give an action-centric baseline a similar per-step validity filter or re-ranking to level the playing field. Without that, the abstract's assertion that 'learning explicit transition models yields higher OOD success than direct action-sequence prediction' is not established. The Logistics result (all models 0.00) reinforces the point: the scaffolding isn't sufficient.

Minor issues: the WL dimensions are inconsistent between Table 3 and Appendix E.4, the Plansformer baseline is run with a checkpoint trained only on Blocksworld and then used zero-shot on other domains, which is unfair but not central, and the beam-width implementation isn't described in enough detail.

Bottom line: this is a solid empirical paper with an interesting idea, but the headline claim gets ahead of the evidence. It deserves a proper referee, and with additional baselines and a more careful framing it could be a good contribution. I'd send it to peer review, and I'd ask for those controls. I would not cite its abstract claim in my own work until the controls are done.

Referee Report

3 major / 6 minor

Summary. The paper proposes a state-centric formulation of generalized planning: instead of predicting action sequences directly, a goal-conditioned model fθ maps WL graph embeddings of the current state and goal to a residual embedding delta, and plans are decoded by maintaining the true symbolic state, enumerating all valid successors Succ(s_t) via the exact transition function γ, and selecting the successor whose embedding is nearest to the predicted target (Algorithm 1). The authors evaluate LSTM and XGBoost transition models with WL and fixed-size factored representations on Blocksworld, Gripper, VisitAll, and Logistics, comparing against Plansformer, PlanGPT, and Symmetry-Aware Transformers. They report competitive or superior out-of-distribution extrapolation with far smaller models and fewer training instances, while acknowledging failure on Logistics.

Significance. If the central comparison were fair, the result would be practically significant: it would show that a compact, sample-efficient model can learn domain dynamics in embedding space and beat much larger action-sequence Transformers on size extrapolation. The paper is also well organized and unusually transparent about implementation details, with released code and appendices covering data generation, WL features, hyperparameters, and inference. However, the main comparison is confounded by the symbolic decoding scaffold, so the abstract's causal claim is not established. The significance is therefore conditional on additional controls and on evidence that fθ actually approximates γ.

major comments (3)

[Algorithm 1, lines 4–6; Appendix G.3] The evaluation is structurally unfair to action-centric baselines. At every step the method maintains the true symbolic state s_t, enumerates all valid successors Succ(s_t) using the exact transition function γ, and only ranks them by embedding distance. It can never emit an inapplicable action or an invalid successor state, whereas Plansformer, PlanGPT, and SymT generate action sequences without such per-step validity filtering. Consequently the abstract's claim that 'learning explicit transition models yields higher out-of-distribution satisficing-plan success than direct action-sequence prediction' is not supported by Table 1: the gains (e.g., WL-XGB delta 0.50 vs. SymT 0.13 in Blocksworld extrapolation) may reflect the symbolic scaffolding rather than fθ approximating γ. A minimal control is to give action-centric baselines the same per-step validity enumeration/reranking, or to run
[Section 'State-Centric Transition-Model Learning'; Table 1 (Logistics rows)] The paper overstates that fθ is a learned approximation of γ. No experiment measures how often the predicted embedding φ(s_t)+fθ(...) is closer to the true successor embedding than to other valid successors, nor reports prediction accuracy on extrapolation instances. The Logistics result (all learned models 0.00 extrapolation) and the statement in Appendix G.3 that decoding 'guarantees that every generated action is applicable' and 'performs online correction of neural prediction errors' indicate that the symbolic enumeration is doing essential work. Please report transition-prediction metrics (e.g., rank of the true successor among Succ(s_t), top-1 accuracy, or embedding distance to the true successor versus the candidate distribution) on interpolation and extrapolation splits. If the learned model's ranking accuracy is near chance, the method should be described as a learned ranker ove
[Appendix C.2; Table 4; sample-efficiency discussion] The data- and parameter-efficiency claims are also confounded by task difficulty. Ranking over a handful of γ-valid successors is an easier learning problem than open-ended action-sequence generation, so the 9-instance Blocksworld and 4-instance Gripper training sets do not by themselves demonstrate sample-efficient transition-model learning. The model-size ratios in Table 4 compare architectures solving different tasks; they are informative only after the scaffolding is controlled. At minimum, add (i) a state-centric variant without Succ(s_t) enumeration, or with noisy/partial successor sets, and (ii) an action-centric baseline with the same per-step validity enumeration, and report success rates and learning curves on equal footing.

minor comments (6)

[Equation (1) vs. Appendix G.2] The main text defines the training loss as squared error over successor embeddings, but Appendix G.2 states that LSTM state-mode training uses cosine embedding loss and delta-mode uses MSE. Please reconcile.
[Algorithm 1 line 5 vs. Table 7] Algorithm 1 writes the selection as argmin over Euclidean distance, while Appendix G.2 and Table 7 specify cosine distance for state mode. The distance metric should be stated consistently.
[Table 1 caption] The column labels 'SymTE*' and 'SymTED*' are not expanded in the table or its caption. Define them (presumably SymT encoder and SymT encoder-decoder variants).
[Baselines paragraph] Plansformer was not trained on Gripper, Logistics, or VisitAll; its 0.00 success in those domains is expected and should not be presented as evidence about action-centric sequence prediction without this caveat being prominent.
[Appendix E.4] The WL vocabulary is constructed from training graphs only. Out-of-vocabulary colors that appear in extrapolation instances are apparently dropped from the histogram. Discuss the potential impact of this on size extrapolation.
[Table 1 and repeated rollouts] The paper reports Mean±Std over 'successive rollouts (seeds)' but does not state how many seeds. Specify the number of independent decoding runs and, ideally, report confidence intervals for the headline extrapolation comparisons.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the transition-model pipeline is supervised on external expert trajectories and evaluated on held-out extrapolation; the symbolic decoding scaffold is a fairness confound, not a circular reduction.

full rationale

The paper's derivation chain is not circular. The learned model fθ is trained by supervised regression on successor-state targets extracted from Fast Downward/VAL expert trajectories (L = Σ_t ||φ̂(s_{t+1}) − φ(s_{t+1})||²), and all reported success rates are computed on held-out validation/interpolation/extrapolation splits using VAL as an external verifier; no test-time quantity is defined in terms of a fitted parameter or a training-set statistic. Algorithm 1's enumeration of Succ(s_t) via γ and nearest-embedding selection does provide strong symbolic scaffolding, and Appendix G.3's statement that 'Symbolic State Maintenance ... guarantees that every generated action is applicable' correctly identifies why the comparison to action-centric baselines may be unfair; however, this is a confound about what the experiments isolate, not a circular reduction, because the learned ranking must still identify a successor that leads to the goal and the final plans are externally validated. The only overlapping self-citation is Plansformer (Pallagani et al. 2022), used as a baseline with a publicly released checkpoint being compared against; the paper's central claim does not rest on that citation. Thus no load-bearing step reduces to its own inputs by construction.

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

No invented entities. Free parameters are architectural choices (k=2, horizon coefficients, beam width), not fitted to test outcomes. The main assumptions are about WL vocabulary coverage over OOD states, the feasibility of symbolic successor enumeration, and the transferability of expert-trajectory supervision.

free parameters (3)

WL refinement iterations k = 2
Hand-chosen for all domains; embedding fidelity and vocabulary size depend on it.
Inference horizon cap coefficients = T_max = max(100, 10|O|)
Set conservatively from training plan lengths; directly affects whether long extrapolation plans terminate.
Beam width = 3
Reported in Appendix Table 7 but not described in Algorithm 1 or Appendix G.3; affects search breadth.

assumptions (4)

domain assumption The WL color vocabulary collected from training states is sufficient to represent OOD test states; unseen colors at test time are ignored without loss.
Appendix E.3 constructs vocabulary from training graphs; extrapolation to much larger instances relies on this coverage, but the paper does not analyze out-of-vocabulary colors.
domain assumption At each planning step, all valid symbolic successors can be enumerated cheaply and completely from known γ.
Algorithm 1 line 4 requires Succ(s_t)={γ(s_t,a)|a applicable}; for high-branching or unknown-γ settings this fails, and the method's guarantees depend on it.
domain assumption Expert trajectories generated by Fast Downward on small instances are representative of goal-directed behavior that transfers to larger instances.
Supervised training target is these trajectories; if small-instance optimal plans mislead large-instance search, extrapolation fails.
standard math WL histograms are at least as expressive as 1-WL message-passing GNNs for planning states, so distance comparisons in embedding space rank successors meaningfully.
Cited from prior work (Chen et al. 2024; Xu et al. 2018); the paper relies on this for nearest-neighbor decoding to be meaningful.

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Cite this review

Pith. "Pith review of On Sample-Efficient Generalized Planning via Learned Transition Models." pith.science (2026). https://pith.science/paper/DOLKO6BD

@misc{pith2026260223148,
  author       = {Pith},
  title        = {Pith review of: On Sample-Efficient Generalized Planning via Learned Transition Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DOLKO6BD}},
  note         = {Machine review of arXiv:2602.23148}
}

abstract

Generalized planning studies the construction of solution strategies that generalize across families of planning problems sharing a common domain model, formally defined by a transition function $\gamma : S \times A \rightarrow S$. Classical approaches achieve such generalization through symbolic abstractions and explicit reasoning over $\gamma$. In contrast, recent Transformer-based planners, such as PlanGPT and Plansformer, largely cast generalized planning as direct action-sequence prediction, bypassing explicit transition modeling. While effective on in-distribution instances, these approaches typically require large datasets and model sizes, and often suffer from state drift in long-horizon settings due to the absence of explicit world-state evolution. In this work, we formulate generalized planning as a transition-model learning problem, in which a neural model explicitly approximates the successor-state function $\hat{\gamma} \approx \gamma$ and generates plans by rolling out symbolic state trajectories. Instead of predicting actions directly, the model autoregressively predicts intermediate world states, thereby learning the domain dynamics as an implicit world model. To study size-invariant generalization and sample efficiency, we systematically evaluate multiple state representations and neural architectures, including relational graph encodings. Our results show that learning explicit transition models yields higher out-of-distribution satisficing-plan success than direct action-sequence prediction in multiple domains, while achieving these gains with significantly fewer training instances and smaller models. This is an extended version of a short paper accepted at ICAPS 2026 under the same title.

Figures

Figures reproduced from arXiv: 2602.23148 by the authors.

**Figure 1.** State-Centric Generalized Planning Pipeline. From a symbolic planning instance Π, executable plans are generated using a learned transition model. (1) State Encoding: Symbolic state–goal pairs (st, g) are mapped to fixed-dimensional embeddings ϕ(st) using either WL graph kernels or fixed-size factored vectors. (2) Transition Modeling: A parametric model (LSTM) or a non-parametric model (XGBoost) learns residual sta… view at source ↗

**Figure 2.** Satisficing-plan success rates on the validation split across all domains, comparing PlanGPT, SymT, WL-based, and [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗

**Figure 3.** Satisficing-plan success rates on the interpolation split, comparing PlanGPT, SymT, WL-based, and FSF baselines for [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: Satisficing-plan success rates on the extrapolation split, comparing PlanGPT, SymT, WL-based, and FSF baselines [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

5 extracted references · 3 linked inside Pith

[2003]

Ha, D.; and Schmidhuber, J

Efficient solution algorithms for factored MDPs.Jour- nal of Artificial Intelligence Research, 19: 399–468. Ha, D.; and Schmidhuber, J. 2018. World models.arXiv preprint arXiv:1803.10122, 2(3). Hafner, D.; Lillicrap, T.; Fischer, I.; Villegas, R.; Ha, D.; Lee, H.; and Davidson, J. 2019. Learning latent dynamics for planning from pixels. InInternational co...

arXiv 2018
[2020]

Chen, Thi´ebaux, and Trevizan (2023) pro- posed GOOSE, a GNN-based heuristic learner that signifi- cantly outperformed STRIPS-HGN and generalized to much larger problem instances

learned domain-independent heuristics directly from planning graphs. Chen, Thi´ebaux, and Trevizan (2023) pro- posed GOOSE, a GNN-based heuristic learner that signifi- cantly outperformed STRIPS-HGN and generalized to much larger problem instances. Subsequent work (Chen, Trevizan, and Thi´ebaux 2024) showed that classical Weisfeiler-Leman (WL) graph kerne...

2023
[2022]

Richter, S.; and Westphal, M

Plansformer: Generating symbolic plans using trans- formers.arXiv preprint arXiv:2212.08681. Richter, S.; and Westphal, M. 2010. The LAMA planner: Guiding cost-based anytime planning with landmarks.Jour- nal of Artificial Intelligence Research, 39: 127–177. Rivlin, O.; Hazan, T.; and Karpas, E. 2020. Generalized planning with deep reinforcement learning.a...

arXiv 2010
[2023]

extends world-model learning to diverse RL domains, motivating explicit dynamics modeling. Positioning of Our Work.In contrast to prior action- sequence and heuristic-centric approaches, our work adopts astate-centric, model-based learningparadigm in which the planner is trained to predict state transitions directly. This enables explicit state grounding ...

2026
[2024]

InForty-first International Con- ference on Machine Learning

Position: LLMs can’t plan, but can help planning in LLM-modulo frameworks. InForty-first International Con- ference on Machine Learning. Liu, B.; Jiang, Y .; Zhang, X.; Liu, Q.; Zhang, S.; Biswas, J.; and Stone, P. 2023. Llm+ p: Empowering large language models with optimal planning proficiency.arXiv preprint arXiv:2304.11477. Pallagani, V .; Muppasani, B...

arXiv 2023

Pith tools

Reviewed August 2, 2026 · model on record in the stance chip above.

[1] [2003]

Ha, D.; and Schmidhuber, J

Efficient solution algorithms for factored MDPs.Jour- nal of Artificial Intelligence Research, 19: 399–468. Ha, D.; and Schmidhuber, J. 2018. World models.arXiv preprint arXiv:1803.10122, 2(3). Hafner, D.; Lillicrap, T.; Fischer, I.; Villegas, R.; Ha, D.; Lee, H.; and Davidson, J. 2019. Learning latent dynamics for planning from pixels. InInternational co...

arXiv 2018

[2] [2020]

Chen, Thi´ebaux, and Trevizan (2023) pro- posed GOOSE, a GNN-based heuristic learner that signifi- cantly outperformed STRIPS-HGN and generalized to much larger problem instances

learned domain-independent heuristics directly from planning graphs. Chen, Thi´ebaux, and Trevizan (2023) pro- posed GOOSE, a GNN-based heuristic learner that signifi- cantly outperformed STRIPS-HGN and generalized to much larger problem instances. Subsequent work (Chen, Trevizan, and Thi´ebaux 2024) showed that classical Weisfeiler-Leman (WL) graph kerne...

2023

[3] [2022]

Richter, S.; and Westphal, M

Plansformer: Generating symbolic plans using trans- formers.arXiv preprint arXiv:2212.08681. Richter, S.; and Westphal, M. 2010. The LAMA planner: Guiding cost-based anytime planning with landmarks.Jour- nal of Artificial Intelligence Research, 39: 127–177. Rivlin, O.; Hazan, T.; and Karpas, E. 2020. Generalized planning with deep reinforcement learning.a...

arXiv 2010

[4] [2023]

extends world-model learning to diverse RL domains, motivating explicit dynamics modeling. Positioning of Our Work.In contrast to prior action- sequence and heuristic-centric approaches, our work adopts astate-centric, model-based learningparadigm in which the planner is trained to predict state transitions directly. This enables explicit state grounding ...

2026

[5] [2024]

InForty-first International Con- ference on Machine Learning

Position: LLMs can’t plan, but can help planning in LLM-modulo frameworks. InForty-first International Con- ference on Machine Learning. Liu, B.; Jiang, Y .; Zhang, X.; Liu, Q.; Zhang, S.; Biswas, J.; and Stone, P. 2023. Llm+ p: Empowering large language models with optimal planning proficiency.arXiv preprint arXiv:2304.11477. Pallagani, V .; Muppasani, B...

arXiv 2023