arxiv: 2605.07248 · v1 · submitted 2026-05-08 · 💻 cs.CL · cs.LG

Recognition: 2 theorem links

· Lean Theorem

PaT: Planning-after-Trial for Efficient Test-Time Code Generation

Youngsik Yoon , Sungjae Lee , Seockbean Song , Siwei Wang , Wei Chen , Jungseul Ok

Authors on Pith no claims yet

Pith reviewed 2026-05-11 02:35 UTC · model grok-4.3

classification 💻 cs.CL cs.LG

keywords Planning-after-Trialtest-time computecode generationadaptive policiesheterogeneous modelsLLM inference efficiencyverification-guided scaling

0 comments

The pith

Planning-after-Trial invokes planning only after a code generation attempt fails verification, letting a cheap model plus targeted large-model planning match full large-model performance at 31 percent of the cost.

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

The paper introduces an adaptive policy called Planning-after-Trial that first lets a model attempt code generation and calls a planner only when verification fails. This avoids the overhead of always planning upfront on problems that a direct attempt can solve. The policy supports a heterogeneous setup in which a cost-efficient model handles routine generation while a stronger model intervenes selectively for planning. Experiments across benchmarks show this configuration reaches accuracy levels comparable to running the large model throughout, yet cuts total inference cost by roughly 69 percent. The result shifts the cost-performance trade-off for test-time compute in code generation.

Core claim

PaT is an adaptive policy for code generation that invokes a planner only upon verification failure. This naturally enables a heterogeneous model configuration: a cost-efficient model handles generation attempts, while a powerful model is reserved for targeted planning interventions. Empirically, across multiple benchmarks and model families, our approach significantly advances the cost-performance Pareto frontier. Notably, our heterogeneous configuration achieves performance comparable to a large homogeneous model while reducing inference cost by approximately 69%.

What carries the argument

The Planning-after-Trial (PaT) policy, which conditions planner invocation strictly on verification failure rather than always planning before the first trial.

If this is right

Planning overhead is incurred only on the subset of problems that actually need it, reducing wasted compute on directly solvable cases.
Smaller models can be used for the majority of attempts while still benefiting from occasional large-model planning.
The cost-performance frontier for test-time scaling in code generation moves outward compared with rigid planning-before-trial baselines.
Heterogeneous model mixtures become practical without requiring changes to training or fine-tuning.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same failure-triggered logic could be tested on other verifiable reasoning domains such as math word problems or program synthesis variants.
The approach implies that reliable, cheap verification functions are a higher-leverage research target than ever-stronger planners.
If verification is noisy, PaT could be extended with a lightweight second verification step before committing to the expensive planner.

Load-bearing premise

That a verification failure is a reliable signal that planning will improve the outcome without adding new errors or disproportionate extra cost.

What would settle it

A head-to-head run on the same benchmarks showing that the heterogeneous PaT setup either fails to reach the large model's accuracy or exceeds the large model's total inference cost.

Figures

Figures reproduced from arXiv: 2605.07248 by Jungseul Ok, Seockbean Song, Siwei Wang, Sungjae Lee, Wei Chen, Youngsik Yoon.

**Figure 1.** Figure 1: Cost (↓) - Pass@1 (↑) trade-off across diverse sizes. We plot the average Pass@1 across foundational benchmarks (HumanEval (Chen et al., 2021), MBPP (Austin et al., 2021) and their EvalPlus (Liu et al., 2023) variants) against the relative inference cost. PaT consistently advances the Pareto frontier across model sizes (Qwen34B,8B,14B and 32B). Detailed results are provided in Section 4.1.1 and [PITH_F… view at source ↗

**Figure 2.** Figure 2: Comparison with existing methods and PaT (Ours). Problems are grouped by difficulty (easy, mid, and hard). Boxes denote the key components: a Generator (creates code), a Planner (decomposes the problem), and an Executor (verifies the solution). (a) Standard directly generate and execute; works on easy problems but often fails on harder ones. (b) FunCoder (PbT) always plans first, so planning cost is paid e… view at source ↗

**Figure 3.** Figure 3: Distribution of incorrect test cases (false positives) per problem on HumanEval. The percentage of problems where the generated test cases contain 0, 1, 2, or 3+ incorrect test cases, given an average of 6.7 generated test cases per problem. inputs, selecting the one that achieves the broadest consensus. However, such consensus-based scoring is ill-suited for our framework, as its objective of selecting … view at source ↗

**Figure 4.** Figure 4: Adaptive decomposition probability and cost analysis for Qwen34B on xCodeEval. (a) Decomposition rate of FunCoder and PaT by problem difficulty. Per-difficulty cost distribution (solid line) and average cost (vertical dashed line) on (b) FunCoder and (c) PaT. higher cost than FunCoder. This is not a sign of inefficiency but a direct consequence of PaT’s adaptive strategy. Less capable models fail more fre… view at source ↗

**Figure 5.** Figure 5: Comparison of planning prompts. Excerpts from planning prompts for (a) FunCoder and (b) PaT. This behavioral divergence stems from the distinct prompt strategies shown in [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗

**Figure 6.** Figure 6: Trade-off curve for heterogeneous configurations. Corresponding to [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗

read the original abstract

Beyond training-time optimization, scaling test-time computation has emerged as a key paradigm to extend the reasoning capabilities of Large Language Models (LLMs). However, most existing methods adopt a rigid Planning-before-Trial (PbT) policy, which inefficiently allocates test-time compute by incurring planning overhead even on directly solvable problems. We propose Planning-after-Trial (PaT), an adaptive policy for code generation that invokes a planner only upon verification failure. This adaptive policy naturally enables a heterogeneous model configuration: a cost-efficient model handles generation attempts, while a powerful model is reserved for targeted planning interventions. Empirically, across multiple benchmarks and model families, our approach significantly advances the cost-performance Pareto frontier. Notably, our heterogeneous configuration achieves performance comparable to a large homogeneous model while reducing inference cost by approximately 69\%.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

PaT flips planning to after-trial only on verification failure and pairs cheap generation with strong planning to cut costs while matching big-model performance, but the gains rest on thin evidence about the trigger's reliability.

read the letter

The main things to know are that this paper swaps the usual rigid planning-before-trial for an adaptive Planning-after-Trial policy in code generation, and it pairs a small model for initial attempts with a larger one only when verification fails. That setup is presented as delivering comparable results to a single large model at about 69% lower inference cost across benchmarks and model families. The idea targets waste in test-time scaling by skipping planning on problems the cheap model can handle directly. It is a clean procedural change rather than a new architecture or training trick, and the experiments apparently move the cost-performance frontier in the reported setups. That counts as useful engineering progress in the subfield of efficient LLM inference for code tasks. The paper does well by keeping the method simple and testing it on multiple benchmarks, which gives the results some breadth. The heterogeneous configuration is a natural fit for the policy and avoids the overhead of always using the big model. The soft spots sit mainly in the assumptions behind the trigger and the net savings. The whole claim depends on verification failure being a precise signal that planning will help without the intervention adding new errors or enough extra tokens to erase the savings. The abstract supplies no breakdown of how often the planner is actually called, false-positive rates on the verifier, or detailed token accounting after planning. If those numbers do not hold up in the full results, the Pareto improvement shrinks or disappears. This is a real gap rather than a minor omission, because the central efficiency argument lives or dies on that mechanism. The paper is aimed at researchers and practitioners working on test-time compute allocation for LLMs, especially those focused on code generation and practical cost reductions. A reader looking for straightforward adaptive policies to try in their own inference pipelines would get value from the core idea and the reported direction of the results. It deserves a serious referee because the policy is well-motivated, the empirical direction is clear, and the potential practical impact is concrete even if the current evidence needs more scrutiny on the trigger and costs. I would send it to peer review rather than desk reject, with the expectation that reviewers will press for ablations on verification accuracy and full cost breakdowns.

Referee Report

3 major / 2 minor

Summary. The paper proposes Planning-after-Trial (PaT), an adaptive test-time policy for LLM code generation that performs an initial generation attempt with a cost-efficient model, verifies the output, and invokes a powerful planner model only upon verification failure. This contrasts with rigid Planning-before-Trial (PbT) approaches and enables heterogeneous model configurations. The central empirical claim is that PaT advances the cost-performance Pareto frontier, with a heterogeneous setup achieving performance comparable to a large homogeneous model at approximately 69% lower inference cost across multiple benchmarks and model families.

Significance. If the empirical results hold under rigorous controls, the work is significant for demonstrating a lightweight adaptive mechanism to allocate test-time compute more efficiently in code generation. It provides a practical demonstration of heterogeneous model use that avoids planning overhead on easy cases while reserving capacity for hard ones. The policy is simple, requires no additional training, and directly targets a known inefficiency in existing test-time scaling methods.

major comments (3)

[§4] §4 (Experiments) and associated tables/figures: The 69% inference cost reduction claim is load-bearing for the Pareto-frontier advance but is presented without a quantitative breakdown of net token costs (initial generation + verification + planner interventions on failure cases) or per-benchmark variance. This makes it impossible to verify whether planner overhead erodes the reported savings on realistic failure rates.
[§3] §3 (Method): The policy rests on the untested assumption that verification failure is a high-precision trigger for planner value (i.e., that the cheap model’s failures are exactly the cases where the large planner succeeds without introducing new errors). No precision/recall analysis of the trigger, no ablation of planner success rate conditional on failure, and no comparison of post-planning error modes versus the initial attempt are supplied.
[§4] §4: No statistical tests, confidence intervals, or multiple-run variance are reported for the benchmark gains or cost figures. Without these, the comparability claim to the large homogeneous model cannot be assessed for robustness.

minor comments (2)

[Abstract] The abstract and introduction would benefit from explicit naming of the benchmarks, model sizes, and verification method used, rather than the generic phrasing 'across multiple benchmarks and model families.'
[§3] Notation for the heterogeneous configuration (e.g., which model is used for generation vs. planning) should be introduced with a clear table or diagram early in §3 to avoid ambiguity when reading the results.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback. We address each major comment below, providing clarifications and committing to revisions that strengthen the manuscript without altering its core claims.

read point-by-point responses

Referee: [§4] §4 (Experiments) and associated tables/figures: The 69% inference cost reduction claim is load-bearing for the Pareto-frontier advance but is presented without a quantitative breakdown of net token costs (initial generation + verification + planner interventions on failure cases) or per-benchmark variance. This makes it impossible to verify whether planner overhead erodes the reported savings on realistic failure rates.

Authors: We appreciate the referee's emphasis on transparency. The reported 69% aggregate reduction reflects total observed token consumption across the heterogeneous PaT pipeline versus the large homogeneous baseline. To enable verification, we will revise Section 4 to include a detailed cost breakdown table (initial generation tokens, verification tokens, and planner intervention tokens) along with per-benchmark failure rates and cost savings. This addition will demonstrate that planner overhead does not erode the net savings under the observed failure distributions. revision: yes
Referee: [§3] §3 (Method): The policy rests on the untested assumption that verification failure is a high-precision trigger for planner value (i.e., that the cheap model’s failures are exactly the cases where the large planner succeeds without introducing new errors). No precision/recall analysis of the trigger, no ablation of planner success rate conditional on failure, and no comparison of post-planning error modes versus the initial attempt are supplied.

Authors: We acknowledge that the current manuscript lacks an explicit precision/recall analysis of the verification trigger. The overall Pareto improvement provides indirect support, but we will add a new ablation subsection in the revision that reports (i) planner success rate conditional on verification failure, (ii) trigger precision/recall where measurable, and (iii) a qualitative comparison of error modes before versus after planning. These results will directly test the assumption that the trigger selectively invokes the planner on cases it can usefully resolve. revision: yes
Referee: [§4] §4: No statistical tests, confidence intervals, or multiple-run variance are reported for the benchmark gains or cost figures. Without these, the comparability claim to the large homogeneous model cannot be assessed for robustness.

Authors: We agree that statistical reporting improves robustness assessment. In the revised manuscript we will re-execute the primary experiments across multiple random seeds, reporting means, standard deviations, and 95% confidence intervals for both performance and cost metrics. This will allow readers to evaluate the stability of the comparability claims to the large homogeneous model. revision: yes

Circularity Check

0 steps flagged

No circularity: procedural policy with empirical claims only

full rationale

The paper introduces Planning-after-Trial (PaT) as an adaptive, rule-based policy that triggers planning solely on verification failure, enabling heterogeneous model use. No equations, fitted parameters, or predictions are defined in the provided text. Performance claims (comparable results at ~69% lower cost) are presented as empirical outcomes across benchmarks rather than derivations. No self-citations are invoked as load-bearing uniqueness theorems, no ansatzes are smuggled, and no known results are renamed as new derivations. The method is a straightforward procedural modification without any reduction of outputs to inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The approach rests on standard assumptions about LLM generation, verification oracles, and model capability differences; no free parameters, new axioms, or invented entities are introduced in the abstract.

pith-pipeline@v0.9.0 · 5448 in / 1052 out tokens · 41629 ms · 2026-05-11T02:35:58.106389+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We propose Planning-after-Trial (PaT), an adaptive policy for code generation that invokes a planner only upon verification failure... heterogeneous model configuration... reducing inference cost by approximately 69%.
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

PaT initiates with standard inference and leverages execution feedback to verify this solution... only when the initial attempt fails.

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

45 extracted references · 45 canonical work pages · 14 internal anchors

[1]

The Thirty-eighth Annual Conference on Neural Information Processing Systems , year =

Divide-and-Conquer Meets Consensus: Unleashing the Power of Functions in Code Generation , author=. The Thirty-eighth Annual Conference on Neural Information Processing Systems , year =

work page
[2]

Findings of the Association for Computational Linguistics ACL 2024 , pages=

Debug like a Human: A Large Language Model Debugger via Verifying Runtime Execution Step by Step , author=. Findings of the Association for Computational Linguistics ACL 2024 , pages=

work page 2024
[3]

Evaluating Large Language Models Trained on Code

Evaluating large language models trained on code , author=. arXiv preprint arXiv:2107.03374 , year=

work page internal anchor Pith review Pith/arXiv arXiv
[4]

Program Synthesis with Large Language Models

Program synthesis with large language models , author=. arXiv preprint arXiv:2108.07732 , year=

work page internal anchor Pith review Pith/arXiv arXiv
[5]

arXiv preprint arXiv:2303.03004 (2023)

xcodeeval: A large scale multilingual multitask benchmark for code understanding, generation, translation and retrieval , author=. arXiv preprint arXiv:2303.03004 , year=

work page arXiv
[6]

CodeT : Code generation with generated tests

Codet: Code generation with generated tests , author=. arXiv preprint arXiv:2207.10397 , year=

work page arXiv
[7]

2025 , booktitle=

Revisit Self-Debugging with Self-Generated Tests for Code Generation , author=. 2025 , booktitle=

work page 2025
[8]

Qwen3 Technical Report

Qwen3 technical report , author=. arXiv preprint arXiv:2505.09388 , year=

work page internal anchor Pith review Pith/arXiv arXiv
[9]

Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks

Program of thoughts prompting: Disentangling computation from reasoning for numerical reasoning tasks , author=. arXiv preprint arXiv:2211.12588 , year=

work page internal anchor Pith review arXiv
[10]

Advances in neural information processing systems , volume=

Chain-of-thought prompting elicits reasoning in large language models , author=. Advances in neural information processing systems , volume=

work page
[11]

Advances in neural information processing systems , volume=

Tree of thoughts: Deliberate problem solving with large language models , author=. Advances in neural information processing systems , volume=

work page
[12]

Qwen2.5-Coder Technical Report

Qwen2. 5-coder technical report , author=. arXiv preprint arXiv:2409.12186 , year=

work page internal anchor Pith review Pith/arXiv arXiv
[13]

Measuring Mathematical Problem Solving With the MATH Dataset

Measuring mathematical problem solving with the math dataset , author=. arXiv preprint arXiv:2103.03874 , year=

work page internal anchor Pith review Pith/arXiv arXiv
[14]

Scaling Laws for Neural Language Models

Scaling laws for neural language models , author=. arXiv preprint arXiv:2001.08361 , year=

work page internal anchor Pith review Pith/arXiv arXiv 2001
[15]

ArXiv preprint , title =

Baptiste Rozi. ArXiv preprint , title =

work page
[16]

Advances in neural information processing systems , volume=

Language models are few-shot learners , author=. Advances in neural information processing systems , volume=

work page
[17]

Advances in Neural Information Processing Systems , volume=

Is your code generated by chatgpt really correct? rigorous evaluation of large language models for code generation , author=. Advances in Neural Information Processing Systems , volume=

work page
[18]

arXiv e-prints , pages=

The llama 3 herd of models , author=. arXiv e-prints , pages=

work page
[19]

DeepSeek-Coder-V2: Breaking the barrier of closed-source models in code intelligence.arXiv preprint arXiv:2406.11931,

Deepseek-coder-v2: Breaking the barrier of closed-source models in code intelligence , author=. arXiv preprint arXiv:2406.11931 , year=

work page arXiv
[20]

Science , volume=

Competition-level code generation with alphacode , author=. Science , volume=. 2022 , publisher=

work page 2022
[21]

GPT-4 Technical Report

GPT-4 technical report , author=. arXiv preprint arXiv:2303.08774 , year=

work page internal anchor Pith review Pith/arXiv arXiv
[22]

Toolformer: Language Models Can Teach Themselves to Use Tools

Toolformer: Language models can teach themselves to use tools , author=. arXiv preprint arXiv:2302.04761 , year=

work page internal anchor Pith review Pith/arXiv arXiv
[23]

Least-to-Most Prompting Enables Complex Reasoning in Large Language Models

Least-to-most prompting enables complex reasoning in large language models , author=. arXiv preprint arXiv:2205.10625 , year=

work page internal anchor Pith review arXiv
[24]

ACM Transactions on Software Engineering and Methodology , volume=

Self-planning code generation with large language models , author=. ACM Transactions on Software Engineering and Methodology , volume=. 2024 , publisher=

work page 2024
[25]

Advances in Neural Information Processing Systems , volume=

Reflexion: Language agents with verbal reinforcement learning , author=. Advances in Neural Information Processing Systems , volume=

work page
[26]

Outcome-Refining Process Supervision for Code Generation,

Reasoning Through Execution: Unifying Process and Outcome Rewards for Code Generation , author=. arXiv preprint arXiv:2412.15118 , year=

work page arXiv
[27]

Teaching Large Language Models to Self-Debug

Teaching large language models to self-debug , author=. arXiv preprint arXiv:2304.05128 , year=

work page internal anchor Pith review arXiv
[28]

Zhang, B

Repocoder: Repository-level code completion through iterative retrieval and generation , author=. arXiv preprint arXiv:2303.12570 , year=

work page arXiv
[29]

Juneja, Gurusha and Dutta, Subhabrata and Chakraborty, Tanmoy , journal=

work page
[30]

Learning when to plan: Efficiently allocating test-time compute for LLM agents,

Learning When to Plan: Efficiently Allocating Test-Time Compute for LLM Agents , author=. arXiv preprint arXiv:2509.03581 , year=

work page arXiv
[31]

The Thirteenth International Conference on Learning Representations , year=

Scaling LLM test-time compute optimally can be more effective than scaling parameters for reasoning , author=. The Thirteenth International Conference on Learning Representations , year=

work page
[32]

arXiv preprint arXiv:2504.04220 , year=

AdaCoder: An Adaptive Planning and Multi-Agent Framework for Function-Level Code Generation , author=. arXiv preprint arXiv:2504.04220 , year=

work page arXiv
[33]

The Thirteenth International Conference on Learning Representations , year=

Planning in Natural Language Improves LLM Search for Code Generation , author=. The Thirteenth International Conference on Learning Representations , year=

work page
[34]

ACL (Findings) , year=

INTERVENOR: Prompting the Coding Ability of Large Language Models with the Interactive Chain of Repair , author=. ACL (Findings) , year=

work page
[35]

ASE , year=

A Pair Programming Framework for Code Generation via Multi-Plan Exploration and Feedback-Driven Refinement , author=. ASE , year=

work page
[36]

Findings of the Association for Computational Linguistics: NAACL 2025 , pages=

Testeval: Benchmarking large language models for test case generation , author=. Findings of the Association for Computational Linguistics: NAACL 2025 , pages=

work page 2025
[37]

arXiv preprint arXiv:2502.01619 , year=

Learning to generate unit tests for automated debugging , author=. arXiv preprint arXiv:2502.01619 , year=

work page arXiv
[38]

ICLR , year=

CodeChain: Towards Modular Code Generation Through Chain of Self-revisions with Representative Sub-modules , author=. ICLR , year=

work page
[39]

Mixtral of Experts

Mixtral of experts , author=. arXiv preprint arXiv:2401.04088 , year=

work page internal anchor Pith review Pith/arXiv arXiv
[40]

rstar-coder: Scaling competitive code reasoning with a large-scale verified dataset

rStar-Coder: Scaling Competitive Code Reasoning with a Large-Scale Verified Dataset , author=. arXiv preprint arXiv:2505.21297 , year=

work page arXiv
[41]

Training language models to self-correct via reinforcement learning.arXiv preprint arXiv:2409.12917, 2024

Training language models to self-correct via reinforcement learning , author=. arXiv preprint arXiv:2409.12917 , year=

work page arXiv
[42]

Self-Play Fine-Tuning Converts Weak Language Models to Strong Language Models

Self-play fine-tuning converts weak language models to strong language models , author=. arXiv preprint arXiv:2401.01335 , year=

work page internal anchor Pith review arXiv
[43]

Advances in neural information processing systems , volume=

Training language models to follow instructions with human feedback , author=. Advances in neural information processing systems , volume=

work page
[44]

Code Llama: Open Foundation Models for Code

Code llama: Open foundation models for code , author=. arXiv preprint arXiv:2308.12950 , year=

work page internal anchor Pith review Pith/arXiv arXiv
[45]

arXiv preprint arXiv:2306.08568 , year=

Wizardcoder: Empowering code large language models with evol-instruct , author=. arXiv preprint arXiv:2306.08568 , year=

work page arXiv