WirelessMathLM: Teaching Mathematical Reasoning for LLMs in Wireless Communications with Reinforcement Learning

• URL: http://arxiv.org/abs/2509.23219v1
• Date: Sat, 27 Sep 2025 09:58:03 GMT
• Title: WirelessMathLM: Teaching Mathematical Reasoning for LLMs in Wireless Communications with Reinforcement Learning
• Authors: Xin Li, Mengbing Liu, Yiyang Zhu, Wenhe Zhang, Li Wei, Jiancheng An, Chau Yuen,
• Abstract summary: Large language models (LLMs) excel at general mathematical reasoning but fail catastrophically on specialized technical mathematics.<n>In wireless communications, where problems require precise manipulation of information-theoretic bounds, even state-of-the-art models struggle to achieve competent performance.<n>We present WirelessMathLM, demonstrating that compact models (0.5B-7B parameters) can match or exceed much larger models through domain-specific reinforcement learning.
• Score: 51.13280433665446
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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