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

arXiv: https://arxiv.org/abs/2506.10716 · HTML: https://mlsanity.com/paper/2506.10716/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 29 of its 36 references that are in the map.
- First posted on arXiv 12 Jun 2025.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 29 of 29)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [Training Large Language Models to Reason in a Continuous Latent Space](https://mlsanity.com/paper/2412.06769/) (2024)
- [Do NOT Think That Much for 2+3=? On the Overthinking of o1-Like LLMs](https://mlsanity.com/paper/2412.21187/) (2024)
- [Chain of Draft: Thinking Faster by Writing Less](https://mlsanity.com/paper/2502.18600/) (2025)
- [Towards Large Reasoning Models: A Survey of Reinforced Reasoning with Large Language Models](https://mlsanity.com/paper/2501.09686/) (2025)
- [Token-Budget-Aware LLM Reasoning](https://mlsanity.com/paper/2412.18547/) (2024)
- [CODI: Compressing Chain-of-Thought into Continuous Space via Self-Distillation](https://mlsanity.com/paper/2502.21074/) (2025)
- [Compressed Chain of Thought: Efficient Reasoning Through Dense Representations](https://mlsanity.com/paper/2412.13171/) (2024)
- [C3oT: Generating Shorter Chain-of-Thought without Compromising Effectiveness](https://mlsanity.com/paper/2412.11664/) (2024)
- [Towards Thinking-Optimal Scaling of Test-Time Compute for LLM Reasoning](https://mlsanity.com/paper/2502.18080/) (2025)
- [Sketch-of-Thought: Efficient LLM Reasoning with Adaptive Cognitive-Inspired Sketching](https://mlsanity.com/paper/2503.05179/) (2025)
- [Fast Best-of-N Decoding via Speculative Rejection](https://mlsanity.com/paper/2410.20290/) (2024)
- [Reward-Guided Speculative Decoding for Efficient LLM Reasoning](https://mlsanity.com/paper/2501.19324/) (2025)
- [LightThinker: Thinking Step-by-Step Compression](https://mlsanity.com/paper/2502.15589/) (2025)
- [Self-Training Elicits Concise Reasoning in Large Language Models](https://mlsanity.com/paper/2502.20122/) (2025)
- [How Well do LLMs Compress Their Own Chain-of-Thought? A Token Complexity Approach](https://mlsanity.com/paper/2503.01141/) (2025)
- [Token Assorted: Mixing Latent and Text Tokens for Improved Language Model Reasoning](https://mlsanity.com/paper/2502.03275/) (2025)
- [Sampling-Efficient Test-Time Scaling: Self-Estimating the Best-of-N Sampling in Early Decoding](https://mlsanity.com/paper/2503.01422/) (2025)
- [Can Language Models Learn to Skip Steps?](https://mlsanity.com/paper/2411.01855/) (2024)
- [Efficiently Scaling LLM Reasoning with Certaindex](https://mlsanity.com/paper/2412.20993/) (2024)
- [InftyThink: Breaking the Length Limits of Long-Context Reasoning in Large Language Models](https://mlsanity.com/paper/2503.06692/) (2025)
- [Dynamic Parallel Tree Search for Efficient LLM Reasoning](https://mlsanity.com/paper/2502.16235/) (2025)
- [REVOLVE: Optimizing AI Systems by Tracking Response Evolution in Textual Optimization](https://mlsanity.com/paper/2412.03092/) (2024)
- [Prompt Stability Matters: Evaluating and Optimizing Auto-Generated Prompt in General-Purpose Systems](https://mlsanity.com/paper/2505.13546/) (2025)

## Built on by (most cited first, 5 of 5)

- [A Survey of Context Engineering for Large Language Models](https://mlsanity.com/paper/2507.13334/) (2025)
- [Neural Chain-of-Thought Search: Searching the Optimal Reasoning Path to Enhance Large Language Models](https://mlsanity.com/paper/2601.11340/) (2026)
- [Synthetic Data-Driven Prompt Tuning for Financial QA over Tables and Documents](https://mlsanity.com/paper/2511.06292/) (2025)
- [C-MOP: Integrating Momentum and Boundary-Aware Clustering for Enhanced Prompt Evolution](https://mlsanity.com/paper/2602.10874/) (2026)
- [MetaCtrl: Your Large Language Models Can Reason Better and More Concisely with a Metacognitive Controller](https://mlsanity.com/paper/2609.37304/) (2026)

## Abstract (arXiv)

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.