PREMISE: Scalable and Strategic Prompt Optimization for Efficient Mathematical Reasoning in Large Models

TL;DR

PREMISE is a prompt-only framework that significantly reduces reasoning trace length and cost in large reasoning models while maintaining high accuracy, enabling more efficient deployment in resource-constrained settings.

Contribution

It introduces a novel prompt optimization method that minimizes reasoning verbosity and cost without altering model weights, applicable directly to commercial large language models.

Findings

Reduces reasoning tokens by up to 87.5%

Maintains or improves accuracy on mathematical benchmarks

Cuts dollar cost of inference by 69-82%

Abstract

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.