# SSPO: Self-traced Step-wise Preference Optimization for Process Supervision and Reasoning Compression

arXiv: https://arxiv.org/abs/2508.12604 · HTML: https://mlsanity.com/paper/2508.12604/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 21 of its 29 references that are in the map.
- First posted on arXiv 18 Aug 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, 21 of 21)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Self-Rewarding Language Models](https://mlsanity.com/paper/2401.10020/) (2024)
- [Training Language Models to Self-Correct via Reinforcement Learning](https://mlsanity.com/paper/2409.12917/) (2024)
- [rStar-Math: Small LLMs Can Master Math Reasoning with Self-Evolved Deep Thinking](https://mlsanity.com/paper/2501.04519/) (2025)
- [Step-DPO: Step-wise Preference Optimization for Long-chain Reasoning of LLMs](https://mlsanity.com/paper/2406.18629/) (2024)
- [REINFORCE++: Stabilizing Critic-Free Policy Optimization with Global Advantage Normalization](https://mlsanity.com/paper/2501.03262/) (2025)
- [A Survey on Test-Time Scaling in Large Language Models: What, How, Where, and How Well?](https://mlsanity.com/paper/2503.24235/) (2025)
- [VisualPRM: An Effective Process Reward Model for Multimodal Reasoning](https://mlsanity.com/paper/2503.10291/) (2025)
- [Between Underthinking and Overthinking: An Empirical Study of Reasoning Length and correctness in LLMs](https://mlsanity.com/paper/2505.00127/) (2025)
- [Self-Training Elicits Concise Reasoning in Large Language Models](https://mlsanity.com/paper/2502.20122/) (2025)
- [OverThink: Slowdown Attacks on Reasoning LLMs](https://mlsanity.com/paper/2502.02542/) (2025)
- [Critique-GRPO: Advancing LLM Reasoning with Natural Language and Numerical Feedback](https://mlsanity.com/paper/2506.03106/) (2025)
- [Fast-Slow Thinking GRPO for Large Vision-Language Model Reasoning](https://mlsanity.com/paper/2504.18458/) (2025)
- [Generalist Reward Models: Found Inside Large Language Models](https://mlsanity.com/paper/2506.23235/) (2025)
- [Med-PRM: Medical Reasoning Models with Stepwise, Guideline-verified Process Rewards](https://mlsanity.com/paper/2506.11474/) (2025)
- [Process-based Self-Rewarding Language Models](https://mlsanity.com/paper/2503.03746/) (2025)
- [Implicit Reward as the Bridge: A Unified View of SFT and DPO Connections](https://mlsanity.com/paper/2507.00018/) (2025)

## Built on by (most cited first, 2 of 2)

- [A Survey of Reinforcement Learning for Large Reasoning Models](https://mlsanity.com/paper/2509.08827/) (2025)
- [CARE-RFT: Confidence-Anchored Reinforcement Finetuning for Reliable Reasoning in Large Language Models](https://mlsanity.com/paper/2602.00085/) (2026)

## Abstract (arXiv)

Test-time scaling has proven effective in further enhancing the performance of pretrained Large Language Models (LLMs). However, mainstream post-training methods (i.e., reinforcement learning (RL) with chain-of-thought (CoT) reasoning) often incur substantial computational overhead due to auxiliary models and overthinking. In this paper, we empirically reveal that the incorrect answers partially stem from verbose reasoning processes lacking correct self-fix, where errors accumulate across multiple reasoning steps. To this end, we propose Self-traced Step-wise Preference Optimization (SSPO), a pluggable RL process supervision framework that enables fine-grained optimization of each reasoning step. Specifically, SSPO requires neither auxiliary models nor stepwise manual annotations. Instead, it leverages step-wise preference signals generated by the model itself to guide the optimization process for reasoning compression. Experiments demonstrate that the generated reasoning sequences from SSPO are both accurate and succinct, effectively mitigating overthinking behaviors without compromising model performance across diverse domains and languages.