# SCOPE: Compress Mathematical Reasoning Steps for Efficient Automated Process Annotation

arXiv: https://arxiv.org/abs/2505.14419 · HTML: https://mlsanity.com/paper/2505.14419/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 25 of its 29 references that are in the map.
- First posted on arXiv 20 May 2025.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)
- LLM alignment / RLHF / preference optimisation / [Process reward models for reasoning](https://mlsanity.com/alignment/process-reward-models-for-reasoning/)

## Builds on (most cited first, 25 of 25)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [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)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Qwen2.5-Coder Technical Report](https://mlsanity.com/paper/2409.12186/) (2024)
- [SGLang: Efficient Execution of Structured Language Model Programs](https://mlsanity.com/paper/2312.07104/) (2023)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [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)
- [Process Reinforcement through Implicit Rewards](https://mlsanity.com/paper/2502.01456/) (2025)
- [Improve Mathematical Reasoning in Language Models by Automated Process Supervision](https://mlsanity.com/paper/2406.06592/) (2024)
- [DeepSpeed Inference: Enabling Efficient Inference of Transformer Models at Unprecedented Scale](https://mlsanity.com/paper/2207.00032/) (2022)
- [ProcessBench: Identifying Process Errors in Mathematical Reasoning](https://mlsanity.com/paper/2412.06559/) (2024)
- [Free Process Rewards without Process Labels](https://mlsanity.com/paper/2412.01981/) (2024)
- [Do NLP Models Know Numbers? Probing Numeracy in Embeddings](https://mlsanity.com/paper/1909.07940/) (2019)
- [MathScale: Scaling Instruction Tuning for Mathematical Reasoning](https://mlsanity.com/paper/2403.02884/) (2024)
- [MARIO: MAth Reasoning with code Interpreter Output -- A Reproducible Pipeline](https://mlsanity.com/paper/2401.08190/) (2024)
- [AntiLeakBench: Preventing Data Contamination by Automatically Constructing Benchmarks with Updated Real-World Knowledge](https://mlsanity.com/paper/2412.13670/) (2024)
- [AKEW: Assessing Knowledge Editing in the Wild](https://mlsanity.com/paper/2402.18909/) (2024)
- [Are LLMs Good Zero-Shot Fallacy Classifiers?](https://mlsanity.com/paper/2410.15050/) (2024)

## Built on by (most cited first, 1 of 1)

- [When Tokenization is Secretly Output Supervision](https://mlsanity.com/paper/2609.01386/) (2026)

## Abstract (arXiv)

Process Reward Models (PRMs) have demonstrated promising results in mathematical reasoning, but existing process annotation approaches, whether through human annotations or Monte Carlo simulations, remain computationally expensive. In this paper, we introduce Step COmpression for Process Estimation (SCOPE), a novel compression-based approach that significantly reduces annotation costs. We first translate natural language reasoning steps into code and normalize them through Abstract Syntax Tree, then merge equivalent steps to construct a prefix tree. Unlike simulation-based methods that waste numerous samples on estimation, SCOPE leverages a compression-based prefix tree where each root-to-leaf path serves as a training sample, reducing the complexity from O(NMK) to O(N). We construct a large-scale dataset containing 196K samples with only 5% of the computational resources required by previous methods. Empirical results demonstrate that PRMs trained on our dataset consistently outperform existing automated annotation approaches on both Best-of-N strategy and ProcessBench.