# Adaptive Rectification Sampling for Test-Time Compute Scaling

arXiv: https://arxiv.org/abs/2504.01317 · HTML: https://mlsanity.com/paper/2504.01317/

## Key facts

- Cited by 3 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 28 of its 42 references that are in the map.
- First posted on arXiv 2 Apr 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, 28 of 28)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (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)
- [Code Llama: Open Foundation Models for Code](https://mlsanity.com/paper/2308.12950/) (2023)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Teaching Large Language Models to Self-Debug](https://mlsanity.com/paper/2304.05128/) (2023)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [CRITIC: Large Language Models Can Self-Correct with Tool-Interactive Critiquing](https://mlsanity.com/paper/2305.11738/) (2023)
- [Do NOT Think That Much for 2+3=? On the Overthinking of o1-Like LLMs](https://mlsanity.com/paper/2412.21187/) (2024)
- [O1-Pruner: Length-Harmonizing Fine-Tuning for O1-Like Reasoning Pruning](https://mlsanity.com/paper/2501.12570/) (2025)
- [RLHF Workflow: From Reward Modeling to Online RLHF](https://mlsanity.com/paper/2405.07863/) (2024)
- [Token-Budget-Aware LLM Reasoning](https://mlsanity.com/paper/2412.18547/) (2024)
- [Making Large Language Models Better Reasoners with Step-Aware Verifier](https://mlsanity.com/paper/2206.02336/) (2022)
- [Self-Evaluation Guided Beam Search for Reasoning](https://mlsanity.com/paper/2305.00633/) (2023)
- [CoT-Valve: Length-Compressible Chain-of-Thought Tuning](https://mlsanity.com/paper/2502.09601/) (2025)
- [Can 1B LLM Surpass 405B LLM? Rethinking Compute-Optimal Test-Time Scaling](https://mlsanity.com/paper/2502.06703/) (2025)
- [Let's Sample Step by Step: Adaptive-Consistency for Efficient Reasoning and Coding with LLMs](https://mlsanity.com/paper/2305.11860/) (2023)
- [Escape Sky-high Cost: Early-stopping Self-Consistency for Multi-step Reasoning](https://mlsanity.com/paper/2401.10480/) (2024)
- [Make Every Penny Count: Difficulty-Adaptive Self-Consistency for Cost-Efficient Reasoning](https://mlsanity.com/paper/2408.13457/) (2024)
- [Think Smarter not Harder: Adaptive Reasoning with Inference Aware Optimization](https://mlsanity.com/paper/2501.17974/) (2025)
- [Iterative Deepening Sampling as Efficient Test-Time Scaling](https://mlsanity.com/paper/2502.05449/) (2025)

## Built on by (most cited first, 3 of 3)

- [Scaling over Scaling: Exploring Test-Time Scaling Plateau in Large Reasoning Models](https://mlsanity.com/paper/2505.20522/) (2025)
- [Strategic Scaling of Test-Time Compute: A Bandit Learning Approach](https://mlsanity.com/paper/2506.12721/) (2025)
- [Adaptive Test-Time Compute Allocation with Evolving In-Context Demonstrations](https://mlsanity.com/paper/2604.21018/) (2026)

## Abstract (arXiv)

The newly released OpenAI-o1 and DeepSeek-R1 have demonstrated that test-time scaling can significantly improve model performance, especially in complex tasks such as logical reasoning. Common test-time scaling methods involve generating more chains of thought (CoTs) or longer CoTs with self-correction. However, while self-correction can improve performance, it may lead to significant token waste and reduce readability of the CoT if the reasoning steps are already correct. To demonstrate that large language models (LLMs) can rectify errors at a more fine-grained level, we propose Adaptive Rectification Sampling (AR-Sampling), which can guide the LLMs to self-correction at the appropriate step. AR-Sampling leverages a process-supervised reward model (PRM) as a verifier and constructed trigger sentences to guide the model in adaptive step-level rethinking. Through the experiments on GSM8K and MATH500, it indicates that our approach enables the models to rethink in more fine-grained level, improving the accuracy of solutions, while generating a reasonable number of additional tokens.