Structure Over Scale: Rethinking Adaptation for Reinforcement Learning with Verifiable Rewards

The standard justification for Full Fine-Tuning (FFT) in Reinforcement Learning with Verifiable Rewards (RLVR) rests on a reasonable intuition: reasoning requires expressive weight updates that Low-Rank Adaptation (LoRA) cannot provide. We show this intuition identifies the wrong variable. Through a systematic rank sweep under GRPO, we document rank collapse—a discontinuous performance cliff where increasing LoRA rank beyond a threshold causes catastrophic, irrecoverable policy failure on moderate batch sizes, a phenomenon absent from the SFT literature. Spectral analysis reveals the mechanism: in a sparse binary reward landscape, unconstrained high-rank adapters allow the optimizer to satisfy rewards through degenerate solutions, bypassing coherent reasoning entirely. FFT exhibits the same pathology in milder form—achieving lower effective rank in its learned weight updates than structured adapters using less than 0.6% of the parameters. Expressivity is not the bottleneck; structure is. Structured adapters that constrain which high-rank solutions are reachable by gradient descent consistently outperform both LoRA and FFT, and do so more sharply as base-model pre-training scale increases—a pattern we term the Model Maturity Hypothesis, supported by behavioral replication across three architecturally independent models and by spectral signatures in frozen base weights that predict adaptation behavior before training begins. The operative question for RLVR is not whether to use LoRA or FFT, but what structure to impose over the update manifold.