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 Affiliation: Nanyang Technological University

📖 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.

🎯 Key Contributions

• WirelessMathBench-XL: A comprehensive benchmark of 4,027 problems from 970 papers in wireless communications
• Domain-specific RL: Group Relative Policy Optimization (GRPO) with binary verification rewards, training directly from base checkpoints without supervised warm-start
• Efficient Performance: Our 7B model achieves 39.5% accuracy, approaching GPT-4o (40.4%) while using ~100× fewer parameters than DeepSeek-R1 (671B, 57.4%)
• Transfer Learning: Positive transfer to general mathematics benchmarks (+8.4 points average across MATH, Minerva-Math, OlympiadBench, AMC, and AIME)

📊 Results Overview

Model Performance on WirelessMathBench-XL

Model	Parameters	Accuracy
WirelessMathLM-7B	7B	39.5%
GPT-4o	~1.8T	40.4%
DeepSeek-R1	671B	57.4%

GRPO Training Impact

GRPO training nearly doubles performance across all model scales:

• 0.5B: +11% improvement
• 3B: +103% improvement
• 7B: +81% improvement

📋 Dataset: WirelessMathBench-XL

WirelessMathBench-XL contains 4,027 mathematical problems extracted from 970 research papers in wireless communications, covering:

• Information theory and channel capacity
• Signal processing and beamforming
• Optimization in wireless networks
• MIMO systems and spatial diversity
• Resource allocation and scheduling
• Network coding and cooperative communications

🔬 Methodology

Group Relative Policy Optimization (GRPO)

Our approach uses GRPO with binary verification rewards:

1. No Supervised Fine-tuning: Train directly from base model checkpoints
2. Verifiable Rewards: Leverage the mathematical nature of wireless problems for automatic verification
3. Domain-specific Training: Focus specifically on wireless communications mathematics
4. Efficient Scaling: Achieve strong performance with compact models

Training Pipeline

Base Model → GRPO Training → WirelessMathLM
    ↑              ↑              ↓
Qwen2.5    Binary Rewards   Wireless Math
                              Expertise

📈 Transfer Learning Results

Our models show positive transfer to general mathematics:

Benchmark	Improvement
MATH	+8.2 points
Minerva-Math	+7.9 points
OlympiadBench	+9.1 points
AMC	+8.7 points
AIME	+8.5 points
Average	+8.4 points

📚 Citation

@article{li2025wirelessmathlm,
  title={WirelessMathLM: Teaching Mathematical Reasoning for LLMs in Wireless Communications with Reinforcement Learning},
  author={Li, Xin and Liu, Mengbing and Zhu, Yiyang and Zhang, Wenhe and Wei, Li and An, Jiancheng and Yuen, Chau},
  journal={arXiv preprint},
  year={2025}
}

🔗 Resources

• Paper: Coming soon on arXiv
• Code: Will be released upon publication
• Website: Project Homepage
• Overview: WirelessMathLM-Overview.pdf

📧 Contact

For questions or collaborations, please contact:

• Xin Li: xin019@ntu.edu.sg

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Nanyang Technological University | Project Maxwell