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arXiv 2603.02119cs.AIcs.GTcs.LG
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笔算谜题基准:多步骤可验证推理的基准

Pencil Puzzle Bench: A Benchmark for Multi-Step Verifiable Reasoning

Approximate Labs

Justin Waugh

AI总结:

Pencil Puzzle Bench通过笔算谜题评估大语言模型的多步骤可验证推理能力,揭示推理努力和代理迭代能力的差异。

摘要:

我们引入了Pencil Puzzle Bench,这是一个通过笔算谜题评估大型语言模型推理能力的框架,笔算谜题是一类与NP完全问题密切相关的约束满足问题,具有确定性的分步验证。从包含62,231个谜题的数据库中,涵盖94种类型且已验证唯一解的谜题中,我们选取了300个谜题,覆盖20种类型,并在两种模式下评估了来自11家提供商的51个模型:直接提问(单次)和代理(多轮带迭代验证)。我们基准的突出特点是,每个中间棋盘状态都可以根据特定类型的约束进行检查,将错误定位到确切违反的规则,为密集的每步奖励信号提供了基础设施,用于过程监督和强化学习。我们的评估揭示了两种不同的能力轴:(1)推理努力扩展,其中GPT-5.2从无推理提升81倍,从无推理到最大努力;(2)代理迭代,其中Claude Opus 4.6通过迭代检查从0.3%提升到30.0%,而GPT-5.2@xhigh从20.2%提升到56.0%。代理尝试的中位数为29轮,持续17分钟,最长超过1,221轮和14.3小时——对长上下文利用的严苛测试,不仅仅是推理。

英文摘要:

We introduce Pencil Puzzle Bench, a framework for evaluating large language model reasoning through pencil puzzles, a family of constraint-satisfaction problems closely related to NP-complete problems, with deterministic, step-level verification. From a database of 62,231 puzzles across 94 varieties with verified unique solutions, we select a benchmark of 300 puzzles spanning 20 varieties and evaluate 51 models from 11 providers in two modes: direct ask (single-shot) and agentic (multi-turn with iterative verification). A key differentiator of our benchmark is that every intermediate board state can be checked against variety-specific constraints, localizing errors to the exact rule violated, providing the infrastructure for dense, per-move reward signals for process supervision and reinforcement learning. Our evaluation reveals two distinct axes of capability: (1) reasoning effort scaling, where GPT-5.2 improves 81x from no reasoning to maximum effort; and (2) agentic iteration, where Claude Opus 4.6 rises from 0.3% to 30.0% through iterative checking, while GPT-5.2@xhigh improves from 20.2% to 56.0%. Agentic attempts span a median of 29 turns over 17 minutes, with the longest exceeding 1,221 turns and 14.3 hours - a demanding test of long-context utilization, not just reasoning.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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