RL Is Neither a Panacea Nor a Mirage: Understanding Supervised vs. Reinforcement Learning Fine-Tuning for LLMs

Training large language models (LLMs) from scratch is increasingly impractical, making post-training methods such as supervised fine-tuning (SFT) and reinforcement-learning fine-tuning (RL-FT, e.g., PPO) central to modern practice. Using an out-of-distribution (OOD) variant of the 24-point card game and new spectrum-based diagnostics, we revisit how these two stages reshape model representation and OOD performance. Our key findings are- (1) RL-FT can restore much of the OOD performance loss from SFT (e.g., Llama-11B 8.97% to 15.38%, Qwen-7B 17.09% to 19.66%). But when SFT induces severe overfitting and a clear distribution shift, RL-FT cannot fully recover OOD performance. (2) Direction shifts of singular vectors matter more than singular value magnitudes. These shifts concentrate on directions linked to the largest and smallest singular values, leaving the bulk spectrum intact. (3) Low-rank and shallow recovery is effective: restoring singular vector directions for the top 20% of values or first 25% of layers recovers 70-80% of OOD performance. (4) Stronger SFT checkpoints enable better recovery by RL, while overfitted ones resist restoration. These results reconcile prior reports of RL superior OOD performance: RL primarily counteracts SFT-induced directional drift rather than finding new solutions. Our spectrum-aware analysis highlights inexpensive recovery knobs low-rank UV merging and shallow-layer resets that practitioners can use before costly RL fine-tuning.