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3B Models Show Significant Gains in Signal Mathematical Reasoning

Guozheng Sun· August 19, 2026 View original

Key takeaways

  • Smaller 3B parameter LLMs can achieve significant mathematical reasoning improvements in specialized domains.
  • Domain-aware chain-of-thought supervised fine-tuning is an effective initialization for reinforcement learning.
  • Reinforcement learning with verifiable rewards substantially boosts accuracy in signal mathematical problems.
  • This approach offers a cost-effective way to deploy capable LLMs for niche technical applications.

Who benefits

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Summary

This report investigates reinforcement fine-tuning strategies for adapting Qwen2.5-3B-Base to graduate-level signal mathematical problems, achieving a more than threefold improvement in accuracy. It explores direct reinforcement learning and supervised fine-tuning with a distilled chain-of-thought corpus, demonstrating the potential of smaller models in specialized mathematical reasoning.

While large language models (LLMs) have shown significant improvements in mathematical reasoning through techniques like supervised chain-of-thought fine-tuning and reinforcement learning, their application to specialized domains like signal processing remains less explored. This study focuses on adapting a smaller 3-billion-parameter model, Qwen2.5-3B-Base, to tackle graduate-level signal mathematical problems using the WirelessMATHBench-XL benchmark. The research examined two primary training paradigms: direct reinforcement learning (RL) with verifiable rewards on WirelessMATHBench-XL, and a combination of supervised fine-tuning (SFT) on a distilled wireless-domain chain-of-thought corpus followed by the same domain-specific RL stage. Various policy optimization methods were benchmarked within these paradigms. The best performing model achieved an overall accuracy of 39.12%, representing a substantial improvement of over three times compared to the untrained Base model's 12.37%. This demonstrates that even smaller LLMs, when subjected to domain-aware chain-of-thought SFT and targeted reinforcement fine-tuning, can achieve significant capabilities in complex, specialized mathematical reasoning tasks.

Why it matters

For professionals working with specialized technical domains, this research shows that smaller, more efficient LLMs can be fine-tuned to achieve impressive mathematical reasoning capabilities, potentially reducing computational costs and enabling deployment in resource-constrained environments.

How to implement this in your domain

  1. 1Explore fine-tuning smaller LLMs (e.g., 3B parameters) for specialized mathematical or technical reasoning tasks within your domain.
  2. 2Develop or acquire domain-specific chain-of-thought corpora for supervised fine-tuning to enhance model performance.
  3. 3Implement reinforcement learning with verifiable rewards to further improve the accuracy of LLMs in complex problem-solving.
  4. 4Benchmark the performance of fine-tuned smaller models against larger, general-purpose models for cost-efficiency and deployment considerations.

Original post by Guozheng Sun

"arXiv:2608.17301v1 Announce Type: new Abstract: Post-training with supervised chain-of-thought fine-tuning and reinforcement learning from verifiable rewards has substantially improved the mathematical reasoning capabilities of large language models (LLMs). However, their applica…"

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