Reasoning-Preserving Fine-Tuning of Post-RL LLMs with Null-Basis LoRA

Wenzhi Fang, Nicholas Tzou, Lazar Valkov, Srinivas Chappidi

Reinforcement learning (RL)-based post-training has become an effective approach for eliciting reasoning capabilities in large language models (LLMs). However, adapting post-RL models to new knowledge domains or behaviors through subsequent supervised fine-tuning (SFT) can severely overwrite these capabilities. Existing approaches mitigate such forgetting through experience replay, specialized initialization, or constrained optimization using gradient projection, but either provide limited preservation or incur substantial training overhead. Our analysis shows that reasoning activations concentrate in low-dimensional subspaces, leaving substantial null-space capacity for adaptation, and that the corresponding approximate null spaces can be reliably estimated from a modest number of examples. Motivated by these observations, we propose Null-Basis Low-Rank Adaptation (NB-LoRA), a parameter-efficient method for adapting post-RL LLMs while preserving their acquired reasoning ability. We formulate reasoning retention as a layer-wise hidden-state preservation constraint and construct a fixed approximate null basis from reasoning activations. LoRA updates are then reparameterized…