Fulcrum: Predicting Layer Potential Before RL-Training

Reinforcement learning (RL) is a central paradigm for post-training large language models, yet it typically updates all parameters at substantial compute and memory cost. Prior research has shown that layers differ in their ability to reshape the final representation. Concentrating updates on high-potential layers may therefore achieve performance comparable to full-parameter training at lower cost with limited training resources. The challenge is to identify these layers before RL begins. To address this challenge, we propose Fulcrum, a pre-RL layer assessment and selection method. It measures a layer’s potential as the maximum gain of a change in its representation as it propagates through the downstream network. This gain is characterized by the spectral norm of the downstream Jacobian and efficiently estimated using power iteration based on vector–Jacobian products (VJPs). Fulcrum further converts the resulting discrete layer potential ranking into a contiguous high-potential interval for training. Identifying this interval takes approximately 10.9 seconds for an 8B model. In Group Relative Policy Optimization (GRPO) experiments with Qwen3-1.7B, 4B, and 8B, updating only 27.8%–35.7% of all layers matches full-parameter training across ten benchmarks. On Qwen3-8B, peak GPU memory use falls by 56.2%. Experiments with supervised fine-tuning (SFT) and LoRA fine-tuning of the SDXL U-Net further demonstrate Fulcrum’s applicability across training objectives, architectures, and update strategies.