CoT-Space: A Theoretical Framework for Internal Slow-Thinking via Reinforcement Learning
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914055509245952 |
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| author | Gan, Zeyu Yi, Hao Liu, Yong |
| author_facet | Gan, Zeyu Yi, Hao Liu, Yong |
| contents | Reinforcement Learning (RL) has become a pivotal approach for enhancing the reasoning capabilities of Large Language Models (LLMs). However, a significant theoretical gap persists, as traditional token-level RL frameworks fail to align with the reasoning-level nature of complex, multi-step thought processes like Chain-of-Thought (CoT). To address this challenge, we introduce CoT-Space, a novel theoretical framework that recasts LLM reasoning from a discrete token-prediction task to an optimization process within a continuous, reasoning-level semantic space. This shift in perspective serves as a conceptual bridge, revitalizing foundational principles from classical learning theory to analyze the unique dynamics of LLMs. By analyzing this process from both a noise perspective and a risk perspective, we demonstrate that the convergence to an optimal CoT length is a natural consequence of the fundamental trade-off between underfitting and overfitting. Furthermore, extensive experiments provide strong empirical validation for our theoretical findings. Our framework not only provides a coherent explanation for empirical phenomena such as overthinking but also offers a solid theoretical foundation to guide the future development of more effective and generalizable reasoning agents. We open-source our code at https://github.com/ZyGan1999/CoT-Space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_04027 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | CoT-Space: A Theoretical Framework for Internal Slow-Thinking via Reinforcement Learning Gan, Zeyu Yi, Hao Liu, Yong Artificial Intelligence Computation and Language Reinforcement Learning (RL) has become a pivotal approach for enhancing the reasoning capabilities of Large Language Models (LLMs). However, a significant theoretical gap persists, as traditional token-level RL frameworks fail to align with the reasoning-level nature of complex, multi-step thought processes like Chain-of-Thought (CoT). To address this challenge, we introduce CoT-Space, a novel theoretical framework that recasts LLM reasoning from a discrete token-prediction task to an optimization process within a continuous, reasoning-level semantic space. This shift in perspective serves as a conceptual bridge, revitalizing foundational principles from classical learning theory to analyze the unique dynamics of LLMs. By analyzing this process from both a noise perspective and a risk perspective, we demonstrate that the convergence to an optimal CoT length is a natural consequence of the fundamental trade-off between underfitting and overfitting. Furthermore, extensive experiments provide strong empirical validation for our theoretical findings. Our framework not only provides a coherent explanation for empirical phenomena such as overthinking but also offers a solid theoretical foundation to guide the future development of more effective and generalizable reasoning agents. We open-source our code at https://github.com/ZyGan1999/CoT-Space. |
| title | CoT-Space: A Theoretical Framework for Internal Slow-Thinking via Reinforcement Learning |
| topic | Artificial Intelligence Computation and Language |
| url | https://arxiv.org/abs/2509.04027 |