🤖 AI Summary
This study addresses the low efficiency and unstable performance of open-source large language models (LLMs) on mathematical reasoning tasks. We propose the first cross-architecture, systematic parameter optimization framework, jointly tuning temperature (0.1–0.5), reasoning steps (4–12), planning cycles (1–4), and nucleus sampling threshold (0.85–0.98), while incorporating stochasticity control and dynamic depth adjustment. The framework achieves 100% optimization success across five state-of-the-art models: Qwen2.5-72B, Llama-3.1-70B, DeepSeek-V3, Mixtral-8x22B, and Yi-Lightning. Experiments demonstrate an average 29.4% reduction in computational cost, a 23.9% increase in inference speed, a 98% accuracy for DeepSeek-V3, and peak token efficiency for Mixtral-8x22B (361.5 tokens per correct response). The work establishes a reusable, standardized optimization paradigm and plug-and-play configuration protocol, providing both theoretical foundations and practical engineering guidance for efficient LLM deployment in mathematical reasoning.
📝 Abstract
This paper presents a practical investigation into fine-tuning model parameters for mathematical reasoning tasks through experimenting with various configurations including randomness control, reasoning depth, and sampling strategies, careful tuning demonstrates substantial improvements in efficiency as well as performance. A holistically optimized framework is introduced for five state-of-the-art models on mathematical reasoning tasks, exhibiting significant performance boosts while maintaining solution correctness. Through systematic parameter optimization across Qwen2.5-72B, Llama-3.1-70B, DeepSeek-V3, Mixtral-8x22B, and Yi-Lightning, consistent efficiency gains are demonstrated with 100% optimization success rate. The methodology achieves an average 29.4% reduction in computational cost and 23.9% improvement in inference speed across all tested models. This framework systematically searches parameter spaces including temperature (0.1-0.5), reasoning steps (4-12), planning periods (1-4), and nucleus sampling (0.85-0.98), determining optimal configurations through testing on mathematical reasoning benchmarks. Critical findings show that lower temperature regimes (0.1-0.4) and reduced reasoning steps (4-6) consistently enhance efficiency without compromising accuracy. DeepSeek-V3 achieves the highest accuracy at 98%, while Mixtral-8x22B delivers the most cost-effective performance at 361.5 tokens per accurate response. Key contributions include: (1) the first comprehensive optimization study for five diverse SOTA models in mathematical reasoning, (2) a standardized production-oriented parameter optimization framework, (3) discovery of universal optimization trends applicable across model architectures, and (4) production-ready configurations with extensive performance characterization.