WirelessMathLM: Teaching Mathematical Reasoning for LLMs in Wireless
  Communications with Reinforcement Learning
Authors: name: Xin Li, name: Mengbing Liu, name: Yiyang Zhu, name: Wenhe Zhang, name: Li Wei, name: Jiancheng An, name: Chau Yuen

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.