More Edits, More Stable: Understanding the Lifelong Normalization in Sequential Model Editing

Lifelong Model Editing aims to continuously update evolving facts in Large Language Models while preserving unrelated knowledge and general capabilities, yet it remains plagued by catastrophic forgetting and model collapse. Empirically, we find that the few recent editors resilient over long horizons share the same core strategy: Lifelong Normalization (LN), which normalizes value gradients using running statistics. Removing LN causes immediate collapse, and we observe a counter-intuitive positive cumulative effect where early edits can facilitate later edits. This suggests that with LN, early edits can stabilize the model and promote the success of future edits. Yet the mechanism of LN remains a "black box", leaving its precise role in lifelong stability poorly understood. In this work, we provide the first theoretical account of LN in the lifelong regime. Our analysis reveals a self-reinforcing stability loop and proves that, when combined with ridge-regularized regression, LN yields updates with asymptotic orthogonality and bounded norms, directly mitigating forgetting and systemic collapse. Based on these insights, we derive StableEdit, which strengthens this stability loop via an explicit warm-up stage and full whitening, improving long-horizon stability at minimal overhead. Extensive experiments validate our theory and demonstrate competitive performance.