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

TL;DR

This paper provides a theoretical understanding of Lifelong Normalization in sequential model editing, revealing its role in stability and proposing improvements for long-term performance.

Contribution

It offers the first theoretical analysis of Lifelong Normalization, explaining its stabilizing effects and introducing StableEdit to enhance long-horizon stability.

Findings

Removing LN causes performance collapse.

Early edits can positively influence future edits.

StableEdit improves long-term stability with minimal overhead.

Abstract

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 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 performance collapse, and we observe a counter-intuitive positive cumulative effect where early edits can 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 parameter 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. Our code is available at https://github.com/MINE-USTC/StableEdit.