We propose OASIS, an outlier- and sink-aware method that stabilizes dual-normalized attention-residual architectures through explicit null routing and token-to-depth null coupling. AttnResidual introduces an additional depth-wise normalization channel that improves inter-layer routing flexibility but can also amplify attention sinks, activation outliers, and low-bit quantization error. OASIS builds on explicit Softmax1-based null routes at both the token and depth levels and uses token-level null evidence to downweight depth branches exhibiting stronger null behavior. Theoretically, we characterize a conditional mechanism for sink-like attention concentration under dual normalization, offering insight into the low-bit sensitivity observed in AttnResidual. Experimentally, we compare OASIS against five baselines on three language-model backbones and multiple language-modeling, reasoning, and long-context benchmarks and observe consistent improvements in both attention sink mitigation and post-quantization performance. Notably, relative to Vanilla AttnResidual, OASIS reduces maximum infinity norm by 81.75% and average kurtosis by 95.90%, lowers W8A8 perplexity by 82.00%, and improves W4A4 GSM8K Pass@1 by 42.11% on average across LLaMA-3.2-1B, Qwen3-0.6B, and Phi-4. Code is available at: https://github.com/robinzixuan/OASIS.

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