通过优化提示词，让大模型数学推理更高效，节省80%以上成本。
PREMISE: Scalable and Strategic Prompt Optimization for Efficient Mathematical Reasoning in Large Models
- 用诊断+梯度启发式方法优化提示词，减少冗余推理步骤。
- 在GSM8K等数据集上准确率持平或提升，推理令牌减少87.5%。
- 无需改模型，可直接用于商用大模型，适合高并发低延迟场景。
大型推理模型（如Claude 3.7 Sonnet和OpenAI o1）在数学基准测试中表现优异，但其链式思维（CoT）推理过程冗长，导致令牌消耗高、成本上升，限制了在延迟敏感或API受限场景的部署。我们提出PREMISE（PRompt-based Efficient Mathematical Inference with Strategic Evaluation），一种仅通过提示词优化实现高效推理的框架，不修改模型权重。PREMISE结合轨迹级诊断与梯度启发式提示优化，最小化冗余计算同时保持答案准确性。该方法通过多目标文本搜索，在令牌长度与答案正确性间取得平衡。相比以往工作，PREMISE采用单次遍历的黑箱接口，可直接应用于商业LLM。在GSM8K、SVAMP和Math500上，其准确率与基线相当（Claude：96%→96%，Gemini：91%→92%），推理令牌减少最高达87.5%，美元成本降低69%–82%。结果表明，提示词层面优化是无需牺牲推理质量即可实现高效推理的可行且可扩展路径。
原文摘要 · Abstract (English)
Large reasoning models (LRMs) such as Claude 3.7 Sonnet and OpenAI o1 achieve strong performance on mathematical benchmarks using lengthy chain-of-thought (CoT) reasoning, but the resulting traces are often unnecessarily verbose. This inflates token usage and cost, limiting deployment in latency-sensitive or API-constrained settings. We introduce PREMISE (PRompt-based Efficient Mathematical Inference with Strategic Evaluation), a prompt-only framework that reduces reasoning overhead without modifying model weights. PREMISE combines trace-level diagnostics with gradient-inspired prompt optimization to minimize redundant computation while preserving answer accuracy. The approach jointly optimizes brevity and correctness through a multi-objective textual search that balances token length and answer validity. Unlike prior work, PREMISE runs in a single-pass black-box interface, so it can be applied directly to commercial LLMs. On GSM8K, SVAMP, and Math500 we match or exceed baseline accuracy ($96\%\rightarrow96\%$ with Claude, $91\%\rightarrow92\%$ with Gemini) while reducing reasoning tokens by up to $87.5\%$ and cutting dollar cost by $69$--$82\%$. These results show that prompt-level optimization is a practical and scalable path to efficient LRM inference without compromising reasoning quality.
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