用强化学习让小模型学会无线通信数学，准确率接近大模型。
WirelessMathLM: Teaching Mathematical Reasoning for LLMs in Wireless Communications with Reinforcement Learning
- 通过可验证正确性的奖励机制，无需人工标注训练小模型。
- 70亿参数模型在4027题基准上达39.5%准确率，接近GPT-4o。
- 训练后通用数学能力提升，零训练跨领域增8.4分。
大型语言模型在通用数学推理上表现优异，但在专业领域的技术数学中却表现灾难性失败。在无线通信领域，问题需精确处理信息论边界、优化约束和信号处理公式，即使最先进的模型也难以达到良好性能。本文提出WirelessMathLM，证明通过特定领域强化学习与可验证奖励，小型模型（0.5B–7B参数）可达到甚至超越更大模型的表现。关键洞察在于无线数学问题具有可验证正确性的独特属性，使强化学习无需人类反馈即可有效进行。我们构建了WirelessMathBench-XL，涵盖来自970篇论文的4,027道题目。采用组相对策略优化（GRPO）与二值验证奖励，从基础检查点直接训练模型，无需监督预热。我们的7B模型在WirelessMathBench-XL上达到39.5%准确率，接近GPT-4o（40.4%），而参数量仅为DeepSeek-R1（671B，57.4%）的约1/100。令人惊讶的是，GRPO训练使所有模型规模性能几乎翻倍（0.5B +11%，3B +103%，7B +81%），并展现出正向迁移：在MATH、Minerva-Math、OlympiadBench、AMC和AIME等通用数学基准上平均提升+8.4分，且未在此类任务上进行任何训练。
原文摘要 · Abstract (English)
Large language models (LLMs) excel at general mathematical reasoning but fail catastrophically on specialized technical mathematics. In wireless communications, where problems require precise manipulation of information-theoretic bounds, optimization constraints, and signal processing formulations, even state-of-the-art models struggle to achieve competent performance. We present WirelessMathLM, demonstrating that compact models (0.5B-7B parameters) can match or exceed much larger models through domain-specific reinforcement learning with verifiable rewards. Our key insight is that wireless mathematics problems possess a unique property--verifiable correctness--that enables effective reinforcement learning without human feedback. We construct WirelessMathBench-XL, a comprehensive benchmark of 4,027 problems from 970 papers. Using Group Relative Policy Optimization (GRPO) with binary verification rewards, we train models directly from base checkpoints without supervised warm-start. Our 7B model achieves 39.5% accuracy on WirelessMathBench-XL, approaching GPT-4o (40.4%) while using about 100 times fewer parameters than DeepSeek-R1 (671B, 57.4%). Remarkably, GRPO training nearly doubles performance across all model scales (0.5B +11%, 3B +103%, 7B +81%), with positive transfer to general mathematics benchmarks--our models gain +8.4 points on average across MATH, Minerva-Math, OlympiadBench, AMC, and AIME without any training on these tasks.
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