Breaking the Reasoning Barrier A Survey on LLM Complex Reasoning through the Lens of Self-Evolution (2025)

Abstract: The release of OpenAI’s O1 and subsequent projects like DeepSeek R1 has significantly advanced research on complex reasoning in LLMs. This paper systematically analyzes existing reasoning studies from the perspective of self-evolution, structured into three components: data evolution, model evolution, and self-evolution. Data evolution explores methods to generate higher-quality reasoning training data. Model evolution focuses on training strategies to boost reasoning capabilities. Self-evolution research autonomous system evolution via iterating cycles of data and model evolution. We further discuss the scaling law of self-evolution and analyze representative O1-like works through this lens. By summarizing advanced methods and outlining future directions, this paper aims to drive advancements in LLMs’ reasoning abilities.

## introduction reasoning serves as the cornerstone in the domain of human cognition. the advent of openai's o1 @xcite represents a transformative milestone in the study of complex reasoning for large language models (llms), demonstrating the ability to generate intricate, human-like reasoning pathways @xcite . this breakthrough has ignited substantial interest across both industry and academia @xcite , driving efforts to replicate and extend its achievements. industry projects, like deepseek r1 @xcite (shorted as r1) and kimi-k1.5 @xcite , release opensource models and pioneer advanced methodologies like scaling reinforcement learning (rl). concurrently, academic research, exemplified by openr @xcite and o1-coder @xcite , delve into rl frameworks. studies ## data evolution as illustrated in figure 2 , this section describes how the reasoning system autonomously synthesizes higher-quality data. this process comprises two phases: task generation and cot generation, corresponding to task evolution and cot evolution. ## model evolution after collecting high-quality reasoning data, the next step is to evolve modules in the system, laying a strong foundation for further data evolution. we focus on training the reasoner, evaluator, and post-processor modules. before delving into specific model training work, we first introduce several representative rl algorithms in appendix b.1 as foundational knowledge. ## self-evolution in this section, we focus on self-evolution, which integrates data and model evolution in a cyclical process to enable continuous system advancement. we illustrate an intuitive explanation of how self-evolution works in figure 8 . however, selfevolution still poses specific implementation challenges during implementation, such as ensuring continuous improvement and coordinating modules co-evolution. we first introduce the convergence properties of self-evolution and propose a scaling law in appendix c. next, we survey self-evolution works from evolutionary strategies and patterns. finally, we reinterpret representative o1-like works from a self-evolution perspective in appendix d. ## challenges and future directions despite the remarkable performance of opensource works like r1 on complex reasoning tasks, there are still some challenges from the selfevolution perspective that require further investigation. we discuss existing challenges in appendix e and future directions in appendix f. ## conclusion this survey systematically reviews research on complex reasoning with llms from a higher view of self-evolution. we first explore data evolution and model evolution for complex reasoning, establishing the groundwork for self-evolution. next, we have investigated self-evolution from the evolutionary strategies and patterns. furthermore, we summarize o1-like open-source studies, demonstrating their alignment with our self-evolution framework. we hope this work inspires further advancements in llm-based complex reasoning.