这篇论文说清了为什么RMSNorm模型用排列对齐不够，必须考虑符号。实验数据很具体，SAE重建、情感引导效果对比鲜明，对做模型对齐和可解释性的人很有用。
该论文证明RMSNorm模型的残差流规范具有符号排列规范B_d，而LayerNorm只有排列规范S_d。使用符号边缘化匈牙利匹配解决了排列对齐的结构性缺陷。在TinyLlama上，B_d对齐的SAE重建误差NMSE为0.004，而S_d为1.08。Qwen情感引导效果在B_d下保留95.8%，S_d下仅17.2%。恢复的坐标可沿训练轨迹传输，1500步时跨运行坐标恢复率达91.1%，远超端点匹配的60.3%。
Modern LLM workflows move coordinate-indexed objects across checkpoints: steering vectors, sparse autoencoders, top-$k$ neuron sets, attribution lists, and merge alignments. This is only well posed after fixing the model's residual-stream gauge, which we show is architecture-dependent: LayerNorm residual charts have permutation gauge $S_d$ (up to a global sign flip), while RMSNorm charts with generic per-channel gain have signed-permutation gauge $B_d = S_d \ltimes \{\pm 1\}^d$. Permutation-only alignment is therefore symmetry-incomplete for RMSNorm models. We introduce sign-marginalized Hungarian matching and prove a sharp failure mode: with decorrelated coordinates, raw signed-correlation matching has a structural permutation-accuracy ceiling at the positive-sign fraction of the true gauge, which sign-marginalization removes. We then make coordinate-preserving transport, not function-level merging, the primary object: composing saved-checkpoint local $B_d$ gauges along same-base fine-tuning trajectories recovers 91.1% of cross-run coordinates at 1500 steps versus 60.3% for endpoint matching, and the gain is not explained by merely routing through the base. The recovered gauge transfers tools that permutation-only alignment breaks: TinyLlama SAE reconstruction has NMSE 0.004 under $B_d$ versus 1.08 under $S_d$; Qwen sentiment steering preserves 95.8% of its effect versus 17.2%; refusal steering reverses sign under $S_d$; coordinate-preserving merges behave the same way. The same covariance governs stateful training: signed transport of AdamW state preserves the resumed trajectory, while permutation-only state follows a different one from a functionally identical checkpoint. Finally, gauge-sweep audits show index-level interpretability claims are reproducible only relative to an explicit gauge.