ARCA: Adapter-Residual Credit Assignment When Token Signals Degenerate

Abstract

Token-level credit assignment for language-model reinforcement learning is usually formulated as if the policy were fully trainable, while practical LLM-RL pipelines often rely on parameter-efficient fine-tuning, especially LoRA. We argue that this separation hides a structural failure mode. Under LoRA, the policy is restricted to a low-rank neighborhood of the reference model, so the per-token output-distribution differences used by common intrinsic credit signals, surprisal, entropy reduction, and policy divergence, can become degenerate after within-trajectory normalization, either approaching uniform weights or concentrating on a small set of task-agnostic positions. We formalize this behavior and propose measuring it directly with concentration diagnostics such as weight Gini and effective-token ratio. We then introduce \emph{Adapter-Residual Credit Assignment} (ARCA), a lightweight alternative that derives token salience from the adapter's own hidden-state residual, $\|h^{\text{adapted}}_t - h^{\text{base}}_t\|_2$. ARCA asks where the adapter actually changes the model, rather than where the output distribution appears uncertain or shifted, and requires no learned reward model, value head, or tree construction. In a compact MATH/Qwen3-1.7B GRPO sweep, ARCA exhibits the predicted non-degenerate middle-regime credit distribution under matched rollout budgets and remains competitive with rank-matched baselines.