Reinforcement learning (RL) for retrieval-augmented language models enables policies to interleave generated reasoning with retrieved observations. However, in Search-R1-style PPO, training may become unstable after the model has already reached strong validation performance. This paper studies late-stage collapse as a training-stability problem in search-based RL. Four metrics are proposed to quantify validation drawdown (VDD), advantage-tail expansion (ATE), actor update stress (AUS), and observation-to-actor contamination in generalized advantage estimation (GAE), denoted as OAGC. The analysis further shows how observation tokens can influence actor updates through value targets, value-model learning, and GAE. To address this issue, Observation-aware Stabilization (OAS) combines observation residual decay, old-value anchoring, and boundary smoothing. On three benchmark datasets (NQ, TriviaQA, and HotpotQA), OAS improves Search-R1 PPO under multiple retrieval budgets. In the main Top-3 setting, our method improves the exact match (EM) measure from 31.8/49.6/18.7 to 37.6/56.8/23.9 and reduces OAGC from 0.331 to 0.088, with lower search-budget saturation and no increase in the no-search rate.

Linear attention offers a linear-time alternative to self-attention but often struggles to capture long-range patterns. We revisit linear attention through a prediction-correction lens and show that prevalent variants can be written as a combination of a historical prediction and a single-token correction, which creates an expressivity bottleneck. To address this bottleneck, we introduce Residual Linear Attention (RLA), a framework that equips linear attention with an explicit residual-fitting mechanism. RLA maintains an auxiliary recurrent state that learns to accumulate residual errors over time and correct the base prediction. We further instantiate a delta-rule version, Residual Delta Net (RDN), incorporating adaptive gating and residual clipping for enhanced correction control and stability. Our implementation leverages highly optimized linear attention kernels and preserves linear time and memory. Across language modeling and recall-intensive evaluations, RLA and RDN consistently outperform their respective baselines and other modern linear-attention methods, narrowing the gap to standard Transformers while retaining linear scaling.