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<!DOCTYPE html>
<html lang="en">
<head>
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<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>WirelessMathLM: Teaching Mathematical Reasoning for LLMs in Wireless Communications</title>
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<nav class="navbar">
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<div class="nav-links">
<a href="#abstract">Abstract</a>
<a href="#highlights">Highlights</a>
<a href="#results">Results</a>
<a href="#dataset">Dataset</a>
<a href="#experiments">Experiments</a>
<a href="#transfer">Transfer Learning</a>
<a href="#qualitative">Analysis</a>
<a href="#citation">Citation</a>
<a href="#resources">Resources</a>
</div>
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</nav>
<header class="hero">
<div class="container">
<div class="hero-content">
<div class="institution-logo">
<a href="https://project-maxwell.github.io/">
<img src="maxwell_logo.png" alt="Nanyang Technological University" class="logo">
</a>
</div>
<h1 class="paper-title">
WirelessMathLM: Teaching Mathematical Reasoning for LLMs in Wireless Communications with Reinforcement Learning
</h1>
<div class="authors">
<span class="authors-label">Authors:</span>
<ul class="authors-list">
<li class="author-item">
<a href="https://lixin.ai/" class="author-link" target="_blank" rel="noopener noreferrer">
<strong>Xin Li</strong>
</a><span class="author-separator">,</span>
</li>
<li class="author-item">
<a href="https://liumengbing.com/" class="author-link" target="_blank" rel="noopener noreferrer">
<strong>Mengbing Liu</strong>
</a><span class="author-separator">,</span>
</li>
<li class="author-item">
<a href="https://scholar.google.com/citations?user=LWh42_8AAAAJ" class="author-link" target="_blank" rel="noopener noreferrer">
<strong>Yiyang Zhu</strong>
</a><span class="author-separator">,</span>
</li>
<li class="author-item">
<a href="https://scholar.google.com/citations?user=x" class="author-link" target="_blank" rel="noopener noreferrer">
<strong>Wenhe Zhang</strong>
</a><span class="author-separator">,</span>
</li>
<li class="author-item">
<a href="https://scholar.google.com.sg/citations?user=zdSz9-gAAAAJ" class="author-link" target="_blank" rel="noopener noreferrer">
<strong>Li Wei</strong>
</a><span class="author-separator">,</span>
</li>
<li class="author-item">
<a href="https://scholar.google.com/citations?user=QbTi47kAAAAJ" class="author-link" target="_blank" rel="noopener noreferrer">
<strong>Jiancheng An</strong>
</a><span class="author-separator">,</span>
</li>
<li class="author-item">
<a href="https://blogs.ntu.edu.sg/chau-yuen/" class="author-link" target="_blank" rel="noopener noreferrer">
<strong>Chau Yuen</strong>
</a>
</li>
</ul>
</div>
<div class="affiliation">
Nanyang Technological University
</div>
<div class="paper-links">
<a href="https://arxiv.org/pdf/2509.23219" class="btn btn-primary">
<i class="fas fa-file-pdf"></i> arXiv Paper
</a>
<a href="#" class="btn btn-secondary" onclick="alert('Code will be released upon publication')">
<i class="fab fa-github"></i> Code
</a>
<!-- <a href="WirelessMathLM-Overview.pdf" class="btn btn-secondary" target="_blank">
<i class="fas fa-presentation"></i> Overview
</a> -->
</div>
</div>
<!-- <div class="hero-visual">
<img src="teaser_wireless_math_lm.pdf" alt="WirelessMathLM Overview" class="teaser-image">
</div> -->
</div>
</header>
<main class="main-content">
<section id="abstract" class="section">
<div class="container">
<h2>Abstract</h2>
<div class="abstract-content">
<p>
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.
</p>
<p>
We present <strong>WirelessMathLM</strong>, 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.
</p>
<p>
We construct <strong>WirelessMathBench-XL</strong>, 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.
</p>
<p>
Our 7B model achieves <strong>39.5% accuracy</strong> on WirelessMathBench-XL, approaching GPT-4o (40.4%) while using ≈100× fewer parameters than DeepSeek-R1 (671B, 57.4%). Remarkably, GRPO training nearly doubles performance across all model scales, with positive transfer to general mathematics benchmarks.
</p>
</div>
</div>
</section>
<section id="highlights" class="section bg-light">
<div class="container">
<h2>Key Highlights</h2>
<div class="highlights-grid">
<div class="highlight-card">
<div class="highlight-icon">
<i class="fas fa-rocket"></i>
</div>
<h3>Verification-Based RL</h3>
<p>First to use binary verification rewards for domain-specific mathematical reasoning without human feedback</p>
</div>
<div class="highlight-card">
<div class="highlight-icon">
<i class="fas fa-compress-alt"></i>
</div>
<h3>Compact Models</h3>
<p>7B model approaches GPT-4o performance while using ≈100× fewer parameters than DeepSeek-R1</p>
</div>
<div class="highlight-card">
<div class="highlight-icon">
<i class="fas fa-database"></i>
</div>
<h3>WirelessMathBench-XL</h3>
<p>4,027 problems from 970 papers spanning 6 communication eras with automated verification</p>
</div>
<div class="highlight-card">
<div class="highlight-icon">
<i class="fas fa-chart-line"></i>
</div>
<h3>Positive Transfer</h3>
<p>Domain-specific training improves general math performance by +8.4 points on average</p>
</div>
</div>
</div>
</section>
<section id="results" class="section">
<div class="container">
<h2>Key Results</h2>
<div class="results-grid">
<div class="result-card">
<div class="result-number">39.5%</div>
<div class="result-description">WirelessMathLM-7B accuracy on WirelessMathBench-XL</div>
</div>
<div class="result-card">
<div class="result-number">100×</div>
<div class="result-description">Fewer parameters than DeepSeek-R1 while approaching performance</div>
</div>
<div class="result-card">
<div class="result-number">+103%</div>
<div class="result-description">Performance improvement for 3B model with GRPO training</div>
</div>
<div class="result-card">
<div class="result-number">+8.4</div>
<div class="result-description">Average point improvement on general math benchmarks</div>
</div>
</div>
<div class="figures-grid">
<div class="figure-container">
<img src="figure1_model_performance.png" alt="Model Performance Comparison" class="figure-image">
<div class="figure-caption">
<strong>Figure 1:</strong> Performance comparison across different model sizes and training methods on WirelessMathBench-XL.
</div>
</div>
<div class="figure-container">
<img src="figure2_grpo_impact.png" alt="GRPO Training Impact" class="figure-image">
<div class="figure-caption">
<strong>Figure 2:</strong> Impact of Group Relative Policy Optimization (GRPO) training on model performance across scales.
</div>
</div>
</div>
</div>
</section>
<section id="dataset" class="section">
<div class="container">
<h2>WirelessMathBench-XL Dataset</h2>
<div class="dataset-content">
<div class="dataset-stats">
<div class="stat-item">
<div class="stat-number">4,027</div>
<div class="stat-label">Problems</div>
</div>
<div class="stat-item">
<div class="stat-number">970</div>
<div class="stat-label">Source Papers</div>
</div>
<div class="stat-item">
<div class="stat-number">6</div>
<div class="stat-label">Communication Eras</div>
</div>
</div>
<div class="dataset-description">
<p>
WirelessMathBench-XL is a comprehensive benchmark for evaluating mathematical reasoning in wireless communications. The dataset spans six major communication eras and covers diverse problem types including information theory, signal processing, optimization, and network analysis.
</p>
</div>
<div class="dataset-figures">
<div class="figure-container">
<img src="techniques_distribution_vertical.png" alt="Techniques Distribution" class="figure-image">
<div class="figure-caption">
Distribution of mathematical techniques and problem types in the dataset.
</div>
</div>
</div>
</div>
</div>
</section>
<section id="experiments" class="section bg-light">
<div class="container">
<h2>Experimental Setup & Results</h2>
<div class="experiments-content">
<div class="experiment-section">
<h3>Comprehensive Baseline Comparison</h3>
<p>We benchmark against comprehensive baselines spanning proprietary and open-source models:</p>
<div class="baseline-categories">
<div class="baseline-category">
<h4>Proprietary Models</h4>
<ul>
<li><strong>GPT-5</strong> (57.87% overall) - Best proprietary performance</li>
<li><strong>GPT-4o</strong> (40.37%) - Close to our 7B model performance</li>
<li><strong>Claude-4.0-Sonnet</strong> (53.75%)</li>
<li><strong>Gemini-2.5-Flash</strong> (54.25%)</li>
<li><strong>Grok-4-Fast</strong> (54.89%)</li>
</ul>
</div>
<div class="baseline-category">
<h4>Open-Source General</h4>
<ul>
<li><strong>DeepSeek-R1</strong> (671B, 57.37%) - Massive but best open model</li>
<li><strong>DeepSeek-V3.1</strong> (671B, 56.87%)</li>
<li><strong>Llama-3.3-70B</strong> (38.37%)</li>
<li><strong>Qwen2.5-72B</strong> (37.50%)</li>
</ul>
</div>
<div class="baseline-category">
<h4>Math-Specialized</h4>
<ul>
<li><strong>Qwen2.5-Math-72B</strong> (42.13%)</li>
<li><strong>DeepSeekMath-7B-RL</strong> (21.50%)</li>
</ul>
</div>
</div>
</div>
<div class="performance-breakdown">
<h3>Performance by Question Type</h3>
<div class="question-types">
<div class="question-type">
<h4>Multiple Choice Questions (MCQ)</h4>
<div class="performance-comparison">
<div class="model-perf">WirelessMathLM-7B: <span class="perf-score">53.4%</span></div>
<div class="model-perf">GPT-4o: <span class="perf-score">54.1%</span></div>
<div class="model-perf">DeepSeek-R1: <span class="perf-score">65.4%</span></div>
</div>
</div>
<div class="question-type">
<h4>Fill-in-the-Blank</h4>
<div class="performance-comparison">
<div class="model-perf">WirelessMathLM-7B: <span class="perf-score">37.0%</span></div>
<div class="model-perf">Base Model: <span class="perf-score">14.3%</span></div>
<div class="improvement">+159% improvement</div>
</div>
</div>
<div class="question-type">
<h4>Full Equation Completion</h4>
<div class="performance-comparison">
<div class="model-perf">WirelessMathLM-7B: <span class="perf-score">36.1%</span></div>
<div class="model-perf">GPT-5-mini: <span class="perf-score">40.3%</span></div>
</div>
</div>
</div>
</div>
<div class="training-details">
<h3>Training Configuration</h3>
<div class="training-specs">
<div class="training-spec">
<h4>Hardware & Time</h4>
<ul>
<li>4 × NVIDIA A6000 GPUs</li>
<li>0.5B model: 14 hours</li>
<li>3B model: 40 hours</li>
<li>7B model: 61 hours</li>
</ul>
</div>
<div class="training-spec">
<h4>Hyperparameters</h4>
<ul>
<li>40 epochs (240 steps)</li>
<li>Learning rate: 10⁻⁶</li>
<li>Temperature: 0.6 (validation), 1.0 (training)</li>
<li>KL penalty β = 0.01</li>
</ul>
</div>
</div>
</div>
</div>
</div>
</section>
<section id="transfer" class="section">
<div class="container">
<h2>Transfer Learning Results</h2>
<div class="transfer-content">
<div class="transfer-intro">
<h3>Positive Transfer to General Mathematics</h3>
<p>Surprisingly, domain-specific training on wireless mathematics enhances general mathematical reasoning without catastrophic forgetting.</p>
</div>
<div class="transfer-results">
<div class="transfer-comparison">
<h4>WirelessMathLM-7B Performance Gains</h4>
<div class="benchmark-results">
<div class="benchmark-result">
<div class="benchmark-name">MATH 500</div>
<div class="benchmark-scores">
<span class="base-score">52.0%</span>
<span class="arrow">→</span>
<span class="final-score">67.0%</span>
<span class="improvement">+28.8%</span>
</div>
</div>
<div class="benchmark-result">
<div class="benchmark-name">Minerva-Math</div>
<div class="benchmark-scores">
<span class="base-score">12.1%</span>
<span class="arrow">→</span>
<span class="final-score">14.3%</span>
<span class="improvement">+18.2%</span>
</div>
</div>
<div class="benchmark-result">
<div class="benchmark-name">OlympiadBench</div>
<div class="benchmark-scores">
<span class="base-score">25.3%</span>
<span class="arrow">→</span>
<span class="final-score">30.2%</span>
<span class="improvement">+19.4%</span>
</div>
</div>
<div class="benchmark-result">
<div class="benchmark-name">AMC</div>
<div class="benchmark-scores">
<span class="base-score">27.7%</span>
<span class="arrow">→</span>
<span class="final-score">41.0%</span>
<span class="improvement">+48.0%</span>
</div>
</div>
<div class="benchmark-result">
<div class="benchmark-name">AIME24</div>
<div class="benchmark-scores">
<span class="base-score">6.7%</span>
<span class="arrow">→</span>
<span class="final-score">13.3%</span>
<span class="improvement">+98.5%</span>
</div>
</div>
</div>
</div>
<div class="transfer-analysis">
<h4>Key Insights</h4>
<ul>
<li><strong>No Catastrophic Forgetting:</strong> Specialized training strengthens rather than degrades fundamental mathematical capabilities</li>
<li><strong>Consistent Gains:</strong> Improvements across diverse mathematical domains suggest robust transfer</li>
<li><strong>Scale-Dependent Effects:</strong> 3B model shows even larger relative improvements (+39.9% on MATH 500)</li>
<li><strong>Average Improvement:</strong> +8.4 points across all general mathematics benchmarks</li>
</ul>
</div>
</div>
</div>
</div>
</section>
<section id="qualitative" class="section bg-light">
<div class="container">
<h2>Qualitative Analysis</h2>
<div class="qualitative-content">
<div class="analysis-overview">
<h3>Solution Quality Assessment</h3>
<p>Comprehensive analysis of 800 solutions from WirelessMathLM-7B reveals sophisticated mathematical reasoning capabilities developed through GRPO training.</p>
</div>
<div class="quality-indicators">
<div class="quality-metric">
<div class="metric-stat">99.1%</div>
<div class="metric-desc">Solutions demonstrate clear step-by-step reasoning with logical connectives</div>
</div>
<div class="quality-metric">
<div class="metric-stat">87%</div>
<div class="metric-desc">Correct responses properly identify underlying problem types and select appropriate methodologies</div>
</div>
<div class="quality-metric">
<div class="metric-stat">100%</div>
<div class="metric-desc">Solutions maintain dimensional consistency in matrix operations and physical constraints</div>
</div>
</div>
<div class="reasoning-capabilities">
<h3>Advanced Reasoning Capabilities</h3>
<div class="capabilities-grid">
<div class="capability">
<h4>Domain-Specific Knowledge Integration</h4>
<p>Strong competency in applying wireless-specific mathematical frameworks including conjugate beamforming, information-theoretic bounds, and signal processing formulations.</p>
</div>
<div class="capability">
<h4>Constraint Awareness</h4>
<p>Automatically incorporates non-negativity constraints for power allocations, maintains causality in signal processing, and respects dimensionality requirements.</p>
</div>
<div class="capability">
<h4>Physical Intuition Integration</h4>
<p>Solutions frequently connect mathematical expressions to underlying physical phenomena, demonstrating deep understanding beyond pattern matching.</p>
</div>
<div class="capability">
<h4>Method Justification</h4>
<p>Correct solutions routinely include explicit rationales for chosen approaches with detailed step-by-step derivations.</p>
</div>
</div>
</div>
</div>
</div>
</section>
<section id="citation" class="section">
<div class="container">
<h2>Citation</h2>
<div class="citation-content">
<div class="citation-intro">
<p>If you use WirelessMathLM, WirelessMathBench-XL, or our methodology in your research, please cite our paper:</p>
</div>
<div class="citation-box">
<pre id="citation-text">@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}
}</pre>
<div class="citation-actions">
<button id="copy-citation" class="btn btn-primary">
<i class="fas fa-copy"></i> Copy Citation
</button>
<button id="download-bib" class="btn btn-secondary">
<i class="fas fa-download"></i> Download .bib
</button>
</div>
</div>
</div>
</div>
</section>
<section id="resources" class="section bg-light">
<div class="container">
<h2>Resources</h2>
<div class="resources-grid">
<div class="resource-card">
<div class="resource-icon">
<i class="fas fa-file-pdf"></i>
</div>
<h3>Paper</h3>
<p>Read the full paper on arXiv (coming soon)</p>
<a href="https://arxiv.org/pdf/2509.23219" class="resource-link">Access Paper</a>
</div>
<div class="resource-card">
<div class="resource-icon">
<i class="fab fa-github"></i>
</div>
<h3>Code</h3>
<p>Source code and training scripts (will be released upon publication)</p>
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<h3>Dataset</h3>
<p>WirelessMathBench-XL benchmark dataset</p>
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