# Steering LLM Thinking with Budget Guidance

arXiv: https://arxiv.org/abs/2506.13752 · HTML: https://mlsanity.com/paper/2506.13752/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 22 of its 31 references that are in the map.
- First posted on arXiv 16 Jun 2025.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 22 of 22)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Fine-tuning Aligned Language Models Compromises Safety, Even When Users Do Not Intend To!](https://mlsanity.com/paper/2310.03693/) (2023)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Training Large Language Models to Reason in a Continuous Latent Space](https://mlsanity.com/paper/2412.06769/) (2024)
- [Chain of Draft: Thinking Faster by Writing Less](https://mlsanity.com/paper/2502.18600/) (2025)
- [Token-Budget-Aware LLM Reasoning](https://mlsanity.com/paper/2412.18547/) (2024)
- [FOLIO: Natural Language Reasoning with First-Order Logic](https://mlsanity.com/paper/2209.00840/) (2022)
- [Dynamic Early Exit in Reasoning Models](https://mlsanity.com/paper/2504.15895/) (2025)
- [Efficient Guided Generation for Large Language Models](https://mlsanity.com/paper/2307.09702/) (2023)
- [ThinkPrune: Pruning Long Chain-of-Thought of LLMs via Reinforcement Learning](https://mlsanity.com/paper/2504.01296/) (2025)
- [Reasoning Models Can Be Effective Without Thinking](https://mlsanity.com/paper/2504.09858/) (2025)
- [TableBench: A Comprehensive and Complex Benchmark for Table Question Answering](https://mlsanity.com/paper/2408.09174/) (2024)
- [SEAL: Steerable Reasoning Calibration of Large Language Models for Free](https://mlsanity.com/paper/2504.07986/) (2025)
- [Z1: Efficient Test-time Scaling with Code](https://mlsanity.com/paper/2504.00810/) (2025)

## Built on by (most cited first, 30 of 33)

- [Base Models Know How to Reason, Thinking Models Learn When](https://mlsanity.com/paper/2510.07364/) (2025)
- [BIRD-INTERACT: Re-imagining Text-to-SQL Evaluation for Large Language Models via Lens of Dynamic Interactions](https://mlsanity.com/paper/2510.05318/) (2025)
- [Towards Concise and Adaptive Thinking in Large Reasoning Models: A Survey](https://mlsanity.com/paper/2507.09662/) (2025)
- [ContextBudget: Budget-Aware Context Management for Long-Horizon Search Agents](https://mlsanity.com/paper/2604.01664/) (2026)
- [DiffAdapt: Difficulty-Adaptive Reasoning for Token-Efficient LLM Inference](https://mlsanity.com/paper/2510.19669/) (2025)
- [Confucius Code Agent: Scalable Agent Scaffolding for Real-World Codebases](https://mlsanity.com/paper/2512.10398/) (2025)
- [ROI-Reasoning: Rational Optimization for Inference via Pre-Computation Meta-Cognition](https://mlsanity.com/paper/2601.03822/) (2026)
- [Neural Chain-of-Thought Search: Searching the Optimal Reasoning Path to Enhance Large Language Models](https://mlsanity.com/paper/2601.11340/) (2026)
- [Are Large Reasoning Models Interruptible?](https://mlsanity.com/paper/2510.11713/) (2025)
- [Exploring Efficiency Frontiers of Thinking Budget in Medical Reasoning: Scaling Laws between Computational Resources and Reasoning Quality](https://mlsanity.com/paper/2508.12140/) (2025)
- [BAMAS: Structuring Budget-Aware Multi-Agent Systems](https://mlsanity.com/paper/2511.21572/) (2025)
- [Putting on the Thinking Hats: A Survey on Chain of Thought Fine-tuning from the Perspective of Human Reasoning Mechanism](https://mlsanity.com/paper/2510.13170/) (2025)
- [Certainty-Guided Reasoning in Large Language Models: A Dynamic Thinking Budget Approach](https://mlsanity.com/paper/2509.07820/) (2025)
- [When Reasoning Meets Its Laws](https://mlsanity.com/paper/2512.17901/) (2025)
- [Prefix Sliding for efficient test-time scaling](https://mlsanity.com/paper/2608.26070/) (2026)
- [Buy versus Build an LLM: A Decision Framework for Governments](https://mlsanity.com/paper/2602.13033/) (2026)
- [Reasoning as Compression: Unifying Budget Forcing via the Conditional Information Bottleneck](https://mlsanity.com/paper/2603.08462/) (2026)
- [DOVA: Deliberation-First Multi-Agent Orchestration for Autonomous Research Automation](https://mlsanity.com/paper/2603.13327/) (2026)
- [Agentic Chain-of-Thought Steering for Efficient and Controllable LLM Reasoning](https://mlsanity.com/paper/2606.03965/) (2026)
- [Shorter Reasoning, Earlier Answers? An Evaluation of Reasoning Interfaces](https://mlsanity.com/paper/2608.03401/) (2026)
- [Thinking Hard, Not Smart: Reasoning Models Fail to Ration Test-Time Compute Across Questions](https://mlsanity.com/paper/2608.07968/) (2026)
- [Do Math Reasoning LLMs Help Predict the Impact of Public Transit Events?](https://mlsanity.com/paper/2511.00808/) (2025)
- [Supervised Fine-Tuning Needs to Unlock the Potential of Token Priority](https://mlsanity.com/paper/2602.01227/) (2026)
- [Decoding the Critique Mechanism in Large Reasoning Models](https://mlsanity.com/paper/2603.16331/) (2026)
- [Efficient Reasoning on the Edge](https://mlsanity.com/paper/2603.16867/) (2026)
- [STEM Agent: A Self-Adapting, Tool-Enabled, Extensible Architecture for Multi-Protocol AI Agent Systems](https://mlsanity.com/paper/2603.22359/) (2026)
- [Avoiding Overthinking and Underthinking: Curriculum-Aware Budget Scheduling for LLMs](https://mlsanity.com/paper/2604.19780/) (2026)
- [When Less is Enough: Efficient Inference via Collaborative Reasoning](https://mlsanity.com/paper/2605.01111/) (2026)
- [HRBench: Benchmarking and Understanding Thinking-Mode Switch Strategies in Hybrid-Reasoning LLMs](https://mlsanity.com/paper/2605.28398/) (2026)
- [OS-Pruner: Pruning Chains-of-Thought of Reasoning Models via Optimal Stopping](https://mlsanity.com/paper/2607.11089/) (2026)

## Abstract (arXiv)

Recent deep-thinking large language models often reason extensively to improve performance, but such lengthy reasoning is not always desirable, as it incurs excessive inference costs with disproportionate performance gains. Controlling reasoning length without sacrificing performance is therefore important, but remains challenging, especially under tight thinking budgets. We propose budget guidance, a simple yet effective method for steering the reasoning process of LLMs toward a target budget without requiring any LLM fine-tuning. Our approach introduces a lightweight predictor that models a Gamma distribution over the remaining thinking length during next-token generation. This signal is then used to guide generation in a soft, token-level manner, ensuring that the overall reasoning trace adheres to the specified thinking budget. Budget guidance enables natural control of the thinking length, along with significant token efficiency improvements over baseline methods on challenging math benchmarks. For instance, it achieves up to a 26% accuracy gain on the MATH-500 benchmark under tight budgets compared to baseline methods, while maintaining competitive accuracy with only 63% of the thinking tokens used by the full-thinking model. Budget guidance also generalizes to broader task domains and exhibits emergent capabilities, such as estimating question difficulty. The source code is available at: https://github.com/UMass-Embodied-AGI/BudgetGuidance.