Fine-tuning large language models (LLMs) frequently induces catastrophic forgetting of prior capabilities. Recent work has shown that reinforcement learning (RL) retains prior capabilities more effectively than supervised fine-tuning (SFT), attributing this to policy-gradient updates remaining closer to the base policy \cite{shenfeld2025rl}. We extend this behavioral account to the mechanistic level and ask whether RL's advantage is mirrored by stronger preservation of internal computational circuits. We introduce differential circuit vulnerability, a head-level measure of how much a circuit degrades under fine-tuning, and use it to compare RL and SFT on Qwen2.5-3B-Instruct adapted to scientific question-answering. We find a clear mechanistic trade-off: SFT adapts more rapidly to the target task but produces substantially greater circuit disruption and forgetting of prior capabilities, whereas RL preserves a larger fraction of the base circuit at the cost of slower task adaptation. These findings suggest that circuit preservation may help explain why RL is more robust to catastrophic forgetting. We released our code here: https://github.com/rl-sft-circuit-research/differential-circuit-vulnerability.
Adapting language models (LMs) to new tasks via post-training carries the risk of degrading existing capabilities -- a phenomenon classically known as catastrophic forgetting. In this paper, toward identifying guidelines for mitigating this phenomenon, we systematically compare the forgetting patterns of two widely adopted post-training methods: supervised fine-tuning (SFT) and reinforcement learning (RL). Our experiments reveal a consistent trend across LM families (Llama, Qwen) and tasks (instruction following, general knowledge, and arithmetic reasoning): RL leads to less forgetting than SFT while achieving comparable or higher target task performance. To investigate the cause for this difference, we consider a simplified setting in which the LM is modeled as a mixture of two distributions, one corresponding to prior knowledge and the other to the target task. We identify that the mode-seeking nature of RL, which stems from its use of on-policy data, enables keeping prior knowledge intact when learning the target task. We then verify this insight by demonstrating that the use on-policy data underlies the robustness of RL to forgetting in practical settings, as opposed to other algorithmic choices such as the KL regularization or advantage estimation. Lastly, as a practical implication, our results highlight the potential of mitigating forgetting using approximately on-policy data, which can be substantially more efficient to obtain than fully on-policy data.
Supervised Fine-Tuning (SFT) followed by Reinforcement Learning (RL) has become a standard pipeline for Large Language Model (LLM) post-training. SFT is expected to provide a useful behavioral prior for RL to further enhance model capabilities. However, checkpoints with excessive SFT often show limited improvement during RL. We attribute this failure to the loss of model plasticity: the reduced ability of an SFT-initialized policy to be effectively reshaped by subsequent RL. To better understand this phenomenon, we conduct detailed analysis from multiple perspectives, including parameter changes, output spaces, and RL optimization dynamics. Our results show that models from excessive SFT tend to produce over-confident token distributions and exhibit sharp parameter landscapes, which make them harder to optimize in the RL stage. To enable a more robust SFT-to-RL handoff, we propose \texttt{Rejuvenation}, a simple yet effective method that restores plasticity while preserving useful SFT-acquired priors. Rejuvenation leverages base-anchored model fusion to reduce excessive SFT-induced drift with targeted neuron reset to mitigate model rigidity. Experimental results on both math reasoning tasks and agentic tasks demonstrate that our approach consistently improves RL performance on over-trained SFT models, while also enhancing generalization to out-of-distribution tasks.
Recent advances in large language models (LLMs) have demonstrated that reinforcement fine-tuning of pretrained base models can lead to significant gains in reasoning performance at inference time. In this work, we theoretically analyze why reinforcement fine-tuning induces better reasoning ability than purely supervised fine-tuning (SFT) methods. We model chain-of-thought (CoT) reasoning as a pathfinding problem on graphs and compare the popular method of reinforcement learning with verifiable rewards (RLVR) against traditional SFT. We prove that SFT, when trained on golden shortest paths without negative examples, fails to learn how to efficiently backtrack. In contrast, an RLVR-trained model can learn how to efficiently backtrack from dead ends using only outcome reward. This leads to an exponential separation in inference-time compute between the two methods, and demonstrates that RLVR leads the model to learn the location of difficult decisions in a reasoning chain, ultimately allowing for better allocation of inference-time compute. Finally, we show that the reasoning traces of an RLVR model can be distilled to train a base model to backtrack efficiently as well.