Mathematical Constraints of RL-Induced Reasoning: A Rebuttal to DeepSeek-R1
Abstract: Under review as submission to TMLR
Mathematical Constraints of RL-Induced Reasoning: A Rebuttal to DeepSeek-R1
Abstract
DeepSeek-R1 claims that reinforcement learning (RL) induces emergent reasoning capabilities in large language models (LLMs), suggesting a fundamental shift in AI development. However, our theoretical and computational analysis challenges this assertion.
Our mathematical framework (Section 2) demonstrates that RL alone cannot induce reasoning without a strong pretraining foundation, which remains the primary driver of reasoning capabilities. Due to high computational costs, poor sample efficiency, and reward sparsity, RL struggles to develop complex reasoning from scratch. Instead, it fine-tunes and reinforces existing pretraining knowledge rather than generating novel reasoning abilities.
Furthermore, DeepSeek-R1’s observed improvements align with well-established pretraining scaling laws, not independent RL-driven emergence. A detailed analysis of DeepSeek-R1’s RL algorithm (Section 3.3) reveals that its Group Relative Policy Optimization (GRPO) approach constrains RL updates within the limits of pretraining knowledge rather than driving reasoning innovation. Additionally, its rule-based reward system optimizes response formatting but does not introduce conceptual advancements in reasoning.
Given these findings, we emphasize the need for rigorous empirical testing to isolate RL’s role from pretraining effects. Until such evidence is presented, RL should be viewed primarily as a fine-tuning mechanism rather than a fundamental source of emergent reasoning in LLMs.
Submission Length: Regular submission (no more than 12 pages of main content)
Assigned Action Editor: ~Yu-Xiong_Wang1
Submission Number: 4136
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