Norm Growth and Stability Challenges in Localized Sequential Knowledge Editing

2025-02-26

AI Summary

This work identifies a universal phenomenon in localized knowledge editing of large language models (LLMs): the persistent growth of the Frobenius norm of update matrices, which induces activation distribution shift, degradation of subspace structure in intermediate layers, and consequent model instability and downstream performance degradation. Method: We establish, for the first time, a causal link between localized parameter updates and model instability, proposing a diagnostic framework grounded in Frobenius norm analysis, activation statistics modeling, and quantification of subspace shift via PCA and centered kernel alignment (CKA). Contribution/Results: We empirically validate the monotonic norm growth and associated activation attenuation across diverse editing paradigms—including LoRA, hypernetworks, and locate-and-edit—demonstrating their shared vulnerability. Our framework provides theoretically grounded constraints and interpretable diagnostics for stable knowledge editing, advancing both understanding and practical reliability of LLM editing methods.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Natural Language Processing: Safety and Robustness
• Search and Optimization: Local Search

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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.

Problem

• Impact of localized updates on LLMs
• Frobenius norm increase in updated matrices
• Instability from norm growth in knowledge editing

Innovation

• Frobenius norm increases with updates
• Localized updates cause matrix instability
• Activation vectors shift subspaces post-editing