# Norm Growth and Stability Challenges in Localized Sequential Knowledge Editing

arXiv: https://arxiv.org/abs/2502.19416 · HTML: https://mlsanity.com/paper/2502.19416/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 28 references that are in the map.
- First posted on arXiv 26 Feb 2025.

## Builds on (most cited first, 18 of 18)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Mass-Editing Memory in a Transformer](https://mlsanity.com/paper/2210.07229/) (2022)
- [Neural Network Acceptability Judgments](https://mlsanity.com/paper/1805.12471/) (2018)
- [StarCoder: may the source be with you!](https://mlsanity.com/paper/2305.06161/) (2023)
- [Fast Model Editing at Scale](https://mlsanity.com/paper/2110.11309/) (2021)
- [Editing Large Language Models: Problems, Methods, and Opportunities](https://mlsanity.com/paper/2305.13172/) (2023)
- [LoRA Learns Less and Forgets Less](https://mlsanity.com/paper/2405.09673/) (2024)
- [Magicoder: Empowering Code Generation with OSS-Instruct](https://mlsanity.com/paper/2312.02120/) (2023)
- [PMET: Precise Model Editing in a Transformer](https://mlsanity.com/paper/2308.08742/) (2023)
- [Inspecting and Editing Knowledge Representations in Language Models](https://mlsanity.com/paper/2304.00740/) (2023)
- [MuTual: A Dataset for Multi-Turn Dialogue Reasoning](https://mlsanity.com/paper/2004.04494/) (2020)
- [A Unified Framework for Model Editing](https://mlsanity.com/paper/2403.14236/) (2024)
- [Rebuilding ROME : Resolving Model Collapse during Sequential Model Editing](https://mlsanity.com/paper/2403.07175/) (2024)
- [Effects of Parameter Norm Growth During Transformer Training: Inductive Bias from Gradient Descent](https://mlsanity.com/paper/2010.09697/) (2020)
- [Lifelong Knowledge Editing requires Better Regularization](https://mlsanity.com/paper/2502.01636/) (2025)

## Built on by (most cited first, 1 of 1)

- [When to Write and When to Suppress: Route-Specialized Dual Adapters for Memory-Assisted Knowledge Editing](https://mlsanity.com/paper/2606.14668/) (2026)

## Abstract (arXiv)

This study investigates the impact of localized updates to large language models (LLMs), specifically in the context of knowledge editing - a task aimed at incorporating or modifying specific facts without altering broader model capabilities. We first show that across different post-training interventions like continuous pre-training, full fine-tuning and LORA-based fine-tuning, the Frobenius norm of the updated matrices always increases. This increasing norm is especially detrimental for localized knowledge editing, where only a subset of matrices are updated in a model . We reveal a consistent phenomenon across various editing techniques, including fine-tuning, hypernetwork-based approaches, and locate-and-edit methods: the norm of the updated matrix invariably increases with successive updates. Such growth disrupts model balance, particularly when isolated matrices are updated while the rest of the model remains static, leading to potential instability and degradation of downstream performance. Upon deeper investigations of the intermediate activation vectors, we find that the norm of internal activations decreases and is accompanied by shifts in the subspaces occupied by these activations, which shows that these activation vectors now occupy completely different regions in the representation space compared to the unedited model. With our paper, we highlight the technical challenges with continuous and localized sequential knowledge editing and their implications for maintaining model stability and utility.