Spectral-Driven Adaptive-Rank Optimizer for Large Language Model Reinforcement Learning with Verifiable Rewards
Reinforcement learning with verifiable rewards (RLVR) is reshaping how large language models (LLMs) acquire reasoning capabilities, yet the optimizers used remain largely inherited from teacher-forcing training. This raises a fundamental question: does RLVR induce a distinct optimization geometry that calls for a different optimizer? We investigate this question through the spectral structure of LLM gradients and find that gradient energy progressively concentrates into a shrinking effective subspace, which is characteristic of RLVR, as it is absent under supervised fine-tuning (SFT) and is largely removed when the verifiable reward is replaced by a random one. Moreover, the rank required...
| Authors | Zhipeng Chen, Wayne Xin Zhao, Ji-Rong Wen |
|---|---|
| Primary category | cs.CL |
| Published | 12 October 2026 |
| Last updated at source | 12 October 2026 |
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