WirelessMathLM：利用强化学习教授大语言模型无线通信中的数学推理
WirelessMathBench-XL: An Auditable Benchmark for Wireless Mathematical Reasoning
AI总结：
提出 WirelessMathLM，通过带可验证二元奖励的 GRPO 强化学习训练 0.5B–7B 模型，并构建 WirelessMathBench-XL，使其无线数学推理接近 GPT-4o 且正向迁移至通用数学。
摘要：
大语言模型（LLM）擅长通用数学推理，但在专业技术数学上会遭遇严重失败。在无线通信领域，问题需要对信息论界、优化约束和信号处理公式进行精确操作，即使是最先进的模型也难以取得合格性能。我们提出 WirelessMathLM，证明紧凑模型（0.5B–7B 参数）可通过带可验证奖励的领域特定强化学习，匹敌甚至超越大得多的模型。关键洞察在于：无线数学问题具有“可验证正确性”这一独特性质，使无需人工反馈的有效强化学习成为可能。我们构建了 WirelessMathBench-XL，这是一个来自 970 篇论文、包含 4,027 个问题的综合基准。采用带二元验证奖励的 Group Relative Policy Optimization（GRPO，组相对策略优化），我们直接从基础检查点训练模型，无需监督热启动。7B 模型在 WirelessMathBench-XL 上达到 39.5% 准确率，接近 GPT-4o（40.4%），而参数量约比 DeepSeek-R1（671B，57.4%）少 100 倍。值得注意的是，GRPO 训练在所有模型规模上几乎使性能翻倍（0.5B 提升 11%，3B 提升 103%，7B 提升 81%），并对通用数学基准产生正向迁移：在未接受任何这些任务训练的情况下，模型在 MATH、Minerva-Math、OlympiadBench、AMC 和 AIME 上平均提升 8.4 分。
英文摘要：
Technical-domain benchmarks constructed from arXiv papers can overlap the same public text used in LLM pretraining. Auditing this risk at training-corpus scale requires searching billions of corpus n-grams while retaining per-item evidence that users can inspect and recompute. We contribute a reverse-probe audit at a fixed 13-gram threshold: it indexes benchmark prompts, streams public pretraining corpora, and emits per-problem prompt-surface lexical-overlap metadata with memory that scales with the benchmark. We instantiate the protocol in WirelessMathBench-XL, a 4,027-problem wireless mathematical-reasoning benchmark built from 836 retained arXiv papers across 20 subfields. Against 12.9B streamed 13-grams from RedPajama-arXiv, the audit identifies a strict zero-hit view S0 covering 3,853 problems (95.7%). Filtering to S0 changes accuracy by less than 1 pp for every evaluated model; frontier calibration rows form one high-accuracy cluster between 86.5% and 91.3%, not a resolved rank order. Only 30/800 test items carry detected overlap. Under an all-flagged-correct counterfactual, their largest possible positive score inflation is 0.31-0.51 pp for the frontier rows, so full-versus-S0 is a bounded, structurally underpowered stability summary rather than a contamination-effect test or cleanliness claim. The audit channel does not cover paraphrase, target-answer, post-training, or closed-corpus exposure. The release includes source-paper identifiers, verifier-facing ground truths, audit and threshold metadata, filtered views, a paper-disjoint sensitivity view, evaluation traces, paired-bootstrap scripts, training recipes, Croissant metadata, and a Datasheet for Datasets.
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