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Spectral Characterization and Mitigation of Sequential Knowledge Editing Collapse

Chi Zhang, Mengqi Zhang, Xiaotian Ye, Runxi Cheng, Zisheng Zhou, Ying Zhou, Pengjie Ren, Zhumin Chen

TL;DR

Sequential knowledge editing degrades general abilities due to perturbations of dominant singular directions in pretrained weight matrices. The authors introduce a spectral analysis that links these directions to general capabilities and show their fragility under repeated edits. They propose REVIVE, a plug-and-play framework that represents edits in the spectral basis, identifies the dominant subspace via an energy threshold, and constructs safe updates that avoid interfering with protected directions. Across multiple models and benchmarks, REVIVE improves editing efficacy while substantially preserving general abilities, even up to 20,000 edits, offering a principled approach to stable long-horizon editing.

Abstract

Sequential knowledge editing in large language models often causes catastrophic collapse of the model's general abilities, especially for parameter-modifying methods. Existing approaches mitigate this issue through heuristic constraints on parameter updates, yet the mechanisms underlying such degradation remain insufficiently understood. In this work, we present a spectral analysis of sequential knowledge editing and show that a model's general abilities are closely associated with dominant singular directions of pretrained weight matrices. These directions are highly sensitive to perturbations and are progressively disrupted by repeated edits, closely tracking the collapse in both editing efficacy and general performance. Building on this insight, we propose REVIVE, a plug-and-play framework that stabilizes sequential editing by explicitly preserving the dominant singular subspace. REVIVE represents parameter updates in the spectral basis of the original weights and filters components that would interfere with the protected region. Extensive experiments across multiple models and benchmarks show that REVIVE consistently improves editing efficacy while substantially preserving general abilities under long-horizon sequential editing, including extreme settings with up to 20,000 edits.

Spectral Characterization and Mitigation of Sequential Knowledge Editing Collapse

TL;DR

Sequential knowledge editing degrades general abilities due to perturbations of dominant singular directions in pretrained weight matrices. The authors introduce a spectral analysis that links these directions to general capabilities and show their fragility under repeated edits. They propose REVIVE, a plug-and-play framework that represents edits in the spectral basis, identifies the dominant subspace via an energy threshold, and constructs safe updates that avoid interfering with protected directions. Across multiple models and benchmarks, REVIVE improves editing efficacy while substantially preserving general abilities, even up to 20,000 edits, offering a principled approach to stable long-horizon editing.

Abstract

Sequential knowledge editing in large language models often causes catastrophic collapse of the model's general abilities, especially for parameter-modifying methods. Existing approaches mitigate this issue through heuristic constraints on parameter updates, yet the mechanisms underlying such degradation remain insufficiently understood. In this work, we present a spectral analysis of sequential knowledge editing and show that a model's general abilities are closely associated with dominant singular directions of pretrained weight matrices. These directions are highly sensitive to perturbations and are progressively disrupted by repeated edits, closely tracking the collapse in both editing efficacy and general performance. Building on this insight, we propose REVIVE, a plug-and-play framework that stabilizes sequential editing by explicitly preserving the dominant singular subspace. REVIVE represents parameter updates in the spectral basis of the original weights and filters components that would interfere with the protected region. Extensive experiments across multiple models and benchmarks show that REVIVE consistently improves editing efficacy while substantially preserving general abilities under long-horizon sequential editing, including extreme settings with up to 20,000 edits.
Paper Structure (55 sections, 1 theorem, 19 equations, 18 figures, 7 tables, 1 algorithm)

This paper contains 55 sections, 1 theorem, 19 equations, 18 figures, 7 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Why Sequential Editing Collapses: A Spectral Perspective
  3. Spectral View of Weight Matrices
  4. Where Are General Abilities Concentrated?
  5. How Sensitive Are These Components to Perturbations?
  6. How Does Sequential Editing Distort These Components in Practice?
  7. Spectrum-based metrics.
  8. Methodology
  9. Spectral Decomposition of Parameter Updates
  10. Dominant Subspace Protection
  11. Dominant Subspace Identification.
  12. Safe Update Construction.
  13. Experiments
  14. Experiment Setup
  15. Baselines.
  16. ...and 40 more sections

Key Result

Theorem 1

Let $\{\mathbf{u}_1,\dots,\mathbf{u}_m\}\subset\mathbb{R}^m$ and $\{\mathbf{v}_1,\dots,\mathbf{v}_n\}\subset\mathbb{R}^n$ be orthonormal bases of $\mathbb{R}^m$ and $\mathbb{R}^n$ respectively. Consider the set of $m n$ matrices Then $\mathcal{B}$ forms an orthonormal basis of the real vector space $\mathbb{R}^{m\times n}$ with respect to the Frobenius inner product $\langle \mathbf{X}, \mathbf{Y

Figures (18)

  • Figure 1: Performance of representative sequential knowledge editing methods on CounterFact using LLaMA3.
  • Figure 2: General ability recovery with increasing proportion of retained singular components.
  • Figure 3: Sensitivity of model's general ability to perturbations across different spectral groups.
  • Figure 4: Singular vector similarity (SS) under sequential editing from rounds 6 to 20.
  • Figure 5: $\text{LS}_t$ from rounds 1 to 20.
  • ...and 13 more figures

Theorems & Definitions (2)

  • Theorem 1: Outer-product bases from two orthonormal vector bases
  • proof