arxiv: 2604.21764 · v2 · submitted 2026-04-23 · 💻 cs.AI

Recognition: unknown

Thinking with Reasoning Skills: Fewer Tokens, More Accuracy

Guangxiang Zhao , Qilong Shi , Xusen Xiao , Xiangzheng Zhang , Tong Yang , Lin Sun

Authors on Pith no claims yet

Pith reviewed 2026-05-09 21:58 UTC · model grok-4.3

classification 💻 cs.AI

keywords reasoning skillstoken efficiencyLLM reasoningchain-of-thoughtskill retrievalmathematical reasoningcoding tasksinference optimization

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The pith

Distilling reusable reasoning skills from prior deliberation lets models solve new problems with fewer tokens and higher accuracy.

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

The paper proposes that language models can summarize effective reasoning patterns distilled from extensive trial-and-error exploration on past problems, store them as reusable skills, and retrieve the relevant ones when facing a new query. Instead of generating long reasoning traces from scratch each time, the model first recalls these skills to steer toward productive solution paths and skip redundant steps. Evaluations on coding and mathematical reasoning tasks show shorter reasoning traces alongside gains in overall performance. The resulting drop in tokens per request points to lower computational costs for repeated use of the same model.

Core claim

By first recalling relevant skills distilled from prior deliberation and trial-and-error, the model avoids redundant detours and focuses on effective solution paths, yielding shorter reasoning traces and improved accuracy on coding and mathematical tasks compared with reasoning entirely from scratch.

What carries the argument

Reusable reasoning skills: compact summaries of effective solution strategies extracted from extensive prior deliberation and retrieved at inference time to guide the current reasoning process.

Load-bearing premise

Skills distilled from earlier problems remain general enough, accurately retrievable, and free of errors when applied to fresh problems.

What would settle it

A test set of coding and math problems where retrieving and applying the stored skills produces lower accuracy or longer token counts than standard chain-of-thought reasoning from scratch.

Figures

Figures reproduced from arXiv: 2604.21764 by Guangxiang Zhao, Lin Sun, Qilong Shi, Tong Yang, Xiangzheng Zhang, Xusen Xiao.

**Figure 1.** Figure 1: Above: The "Gist" of Thinking with Reasoning Skills. Below: Breaking the Efficiency-Accuracy Trade-off. (OpenAI, 2026)—lengthy traces dominate query costs and latency. Industry reports confirm that reasoning-heavy inference significantly amplifies infrastructure strain (Uptime Institute, 2025). Consequently, efficient reasoning is production-critical: we seek the benefits of deliberation without the cost… view at source ↗

**Figure 2.** Figure 2: The process of Thinking with Reasoning Skills (TRS). [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: A standard TRS prompt template that injects [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 4.** Figure 4: Performance comparison across difficulty [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

**Figure 5.** Figure 5: Compare to Direct on coding competitions. [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗

**Figure 7.** Figure 7: Impact of skill-injection prompts on accuracy [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗

**Figure 8.** Figure 8: Full prompt template for TRS-Normal. TRS prompt: Only You are a helpful and harmless assistant. You may be given an optional Solving Hints section. Use it only if it is relevant to the problem; otherwise, ignore it completely. [Solving Hints] SOLVING_HINTS [/Solving Hints] Only try to reduce the number of tokens used if the solution hints are useful; otherwise, please think normally. Problem: PROBLEM [PIT… view at source ↗

**Figure 9.** Figure 9: Full prompt template for TRS-Only. TRS prompt: Try-to You are a helpful and harmless assistant. You may be given an optional Solving Hints section. Use it only if it is relevant to the problem; otherwise, ignore it completely. [Solving Hints] SOLVING_HINTS [/Solving Hints] If you use the solving hints, please try to reduce the number of tokens used. Problem: PROBLEM [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗

**Figure 10.** Figure 10: Full prompt template for TRS-Try-to. TRS prompt: Short (budgeted) You are a helpful and harmless assistant. You may be given an optional Solving Hints section. Use it only if it is relevant to the problem; otherwise, ignore it completely. [Solving Hints] SOLVING_HINTS [/Solving Hints] Let’s think step by step and use less than [budget] tokens: PROBLEM [PITH_FULL_IMAGE:figures/full_fig_p011_10.png] view at source ↗

**Figure 11.** Figure 11: Full prompt template for TRS-Short (bud [PITH_FULL_IMAGE:figures/full_fig_p011_11.png] view at source ↗

**Figure 12.** Figure 12: Full prompt template for TRS-Draft (CoD [PITH_FULL_IMAGE:figures/full_fig_p011_12.png] view at source ↗

**Figure 14.** Figure 14: Full prompt template for CoD. No-Wait prompt Question: {QUESTION} Think step by step. Do not use any of the following words in your thinking process: “wait”, “alternatively”, “hmm”, “but”, “however”, “alternative”, “another”, “check”, “double-check”, “oh”, “maybe”, “verify”, “other”, “again”, “now”, “ah”, “any” [PITH_FULL_IMAGE:figures/full_fig_p012_14.png] view at source ↗

**Figure 15.** Figure 15: Full prompt template for No-Wait. H Extended Comparison with Chain-of-Draft (CoD) In this section, we extend the comparison between Thinking with Reasoning Skills (TRS) and the Chain-of-Draft (CoD) baseline to five additional models: GPT-5.2, Grok-4-Fast, Gemini-3-Pro, Gemini-3-Flash, and GPT-4o-mini. This analysis (visualized in [PITH_FULL_IMAGE:figures/full_fig_p012_15.png] view at source ↗

**Figure 13.** Figure 13: Full prompt template for TALE-EP (twophase: budget estimation and solve). CoD prompt Question: {QUESTION} Think step by step, but only keep a minimum draft for each thinking step, with 5 words at most. Return the answer at the end of the response after a separator #### [PITH_FULL_IMAGE:figures/full_fig_p012_13.png] view at source ↗

**Figure 16.** Figure 16: Main results compared with CoD at different thresholds (DeepMath-103K). [PITH_FULL_IMAGE:figures/full_fig_p013_16.png] view at source ↗

**Figure 17.** Figure 17: External contest-math transfer with the AoPS-derived skill bank. Left: TRS-minus-direct accuracy deltas. [PITH_FULL_IMAGE:figures/full_fig_p013_17.png] view at source ↗

**Figure 18.** Figure 18: Accuracy and cost-percentage deltas in the [PITH_FULL_IMAGE:figures/full_fig_p014_18.png] view at source ↗

read the original abstract

Reasoning LLMs often spend substantial tokens on long intermediate reasoning traces (e.g., chain-of-thought) when solving new problems. We propose to summarize and store reusable reasoning skills distilled from extensive deliberation and trial-and-error exploration, and to retrieve these skills at inference time to guide future reasoning. Unlike the prevailing \emph{reasoning from scratch} paradigm, our approach first recalls relevant skills for each query, helping the model avoid redundant detours and focus on effective solution paths. We evaluate our method on coding and mathematical reasoning tasks, and find that it significantly reduces reasoning tokens while improving overall performance. The resulting lower per-request cost indicates strong practical and economic potential for real-world deployment.

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

The paper sketches distilling reusable reasoning skills for token-efficient inference on coding and math but supplies no results or mechanism details to assess the claims.

read the letter

The main thing to know is that the authors want to replace long chain-of-thought traces with retrieved pre-distilled reasoning skills, claiming this cuts tokens while raising accuracy on coding and math tasks. The abstract frames it as moving beyond reasoning from scratch by recalling stored patterns from prior deliberation and trial-and-error. This has a clear practical hook for cost-sensitive deployments where token usage adds up quickly. The motivation lands: standard approaches often waste steps on redundant exploration for each new problem. The paper does a reasonable job spelling out why reusable skills could help focus the model on effective paths and lower per-request costs. That angle connects to real deployment needs without overclaiming theoretical novelty. The soft spots are substantial and central. No quantitative results, baselines, or error analysis appear in the text. The distillation process, storage format, and retrieval mechanism get no description at all, so it is impossible to judge whether the skills stay general enough or whether imprecise retrieval introduces new errors. The stress-test point about generalization risk holds up here because nothing in the available material tests or mitigates it. If the full manuscript contains controlled experiments with reproducible details, that would change the picture; as presented, the argument stays at the level of a high-level proposal. This work would interest readers building or optimizing reasoning systems for applied coding and math tools, where efficiency gains matter more than pure novelty. A serious referee could usefully press on the missing experiments and implementation choices. I would recommend sending it to peer review to see the actual data and methods rather than desk-rejecting on the abstract alone.

Referee Report

3 major / 1 minor

Summary. The manuscript proposes distilling reusable reasoning skills from extensive deliberation and trial-and-error exploration, storing them for later use, and retrieving relevant skills at inference time to guide reasoning on new problems. This is positioned as an alternative to 'reasoning from scratch' with long chain-of-thought traces, with the central claim being that the approach significantly reduces reasoning tokens while improving performance on coding and mathematical reasoning tasks.

Significance. If the empirical claims are substantiated with detailed results, the work could offer meaningful practical value by lowering per-request inference costs for reasoning LLMs, which has clear economic implications for deployment. The core idea of reusable skill distillation builds on existing concepts in knowledge reuse and could address inefficiencies in current reasoning paradigms, but its significance hinges on demonstrating reliable generalization.

major comments (3)

[Abstract] Abstract: The claim that the method 'significantly reduces reasoning tokens while improving overall performance' is presented without any quantitative metrics, baselines, error bars, task-specific results, or implementation details. This is load-bearing for the central empirical claim, as no evaluation data is supplied to allow verification or assessment of effect sizes.
[Method] Method description: The distillation of skills from deliberation, their summarization and storage, and the retrieval mechanism at inference time are described only at a high level with no algorithmic details, pseudocode, or formalization. This prevents evaluation of how token reduction is achieved in practice and whether retrieval introduces latency or errors.
[Evaluation] Evaluation section: Despite stating that the method was evaluated on coding and mathematical reasoning tasks, the manuscript provides no description of the experimental setup, models, datasets, number of stored skills, retrieval implementation, or comparison results. This directly undermines the ability to assess the accuracy improvement and generalization claims.

minor comments (1)

[Abstract] The abstract could be strengthened by including at least one key quantitative result (e.g., token reduction percentage or accuracy delta) to make the claims more concrete.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments, which identify opportunities to improve the clarity and verifiability of our claims. We address each major point below and will incorporate the requested details through substantial revisions to the manuscript.

read point-by-point responses

Referee: [Abstract] Abstract: The claim that the method 'significantly reduces reasoning tokens while improving overall performance' is presented without any quantitative metrics, baselines, error bars, task-specific results, or implementation details. This is load-bearing for the central empirical claim, as no evaluation data is supplied to allow verification or assessment of effect sizes.

Authors: We agree that the abstract would be strengthened by including concrete quantitative support for the central claims. In the revised version, we will add specific metrics drawn from our experiments (e.g., observed token reductions and accuracy gains on the coding and math tasks) together with baseline comparisons, so that the effect sizes are evident directly from the abstract. revision: yes
Referee: [Method] Method description: The distillation of skills from deliberation, their summarization and storage, and the retrieval mechanism at inference time are described only at a high level with no algorithmic details, pseudocode, or formalization. This prevents evaluation of how token reduction is achieved in practice and whether retrieval introduces latency or errors.

Authors: We acknowledge that the current method presentation remains conceptual. We will expand this section with algorithmic details, pseudocode for the distillation, summarization, storage, and retrieval steps, and a formal description of the overall process. We will also discuss any latency or error considerations introduced by retrieval. revision: yes
Referee: [Evaluation] Evaluation section: Despite stating that the method was evaluated on coding and mathematical reasoning tasks, the manuscript provides no description of the experimental setup, models, datasets, number of stored skills, retrieval implementation, or comparison results. This directly undermines the ability to assess the accuracy improvement and generalization claims.

Authors: We agree that the evaluation section requires a more complete description to substantiate the reported improvements. In the revision we will add a detailed experimental setup covering the models, datasets, number of stored skills, retrieval implementation, and full comparison results with baselines and task-specific breakdowns. revision: yes

Circularity Check

0 steps flagged

High-level empirical method proposal with no derivation chain or self-referential reductions

full rationale

The paper advances a practical proposal for distilling and retrieving reasoning skills to reduce token usage in LLMs, supported by evaluations on coding and mathematical tasks. No equations, fitted parameters, uniqueness theorems, or ansatzes are described in the provided text. The central claims rest on observed performance improvements rather than any derivation that reduces to its own inputs by construction. No self-citation load-bearing steps or renamings of known results appear. This is a standard non-circular empirical methods paper.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No free parameters, axioms, or invented entities are specified in the abstract; the method rests on the domain assumption that LLMs can reliably extract and apply generalizable reasoning skills.

pith-pipeline@v0.9.0 · 5417 in / 1117 out tokens · 26266 ms · 2026-05-09T21:58:34.120762+00:00 · methodology

discussion (0)

Reference graph

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