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Toward Ultra-Long-Horizon Sequential Model Editing

Mingda Liu, Zhenghan Zhu, Ze'an Miao, Katsuki Fujisawa

TL;DR

This work addresses the instability of ultra-long-horizon sequential model editing under the Locate-and-Edit framework, where repeated localized updates cause explosive growth in the edited weight norms and abrupt performance collapse. The authors provide a mechanistic analysis showing that the weight-norm evolves roughly as $E\|W_n\|^2 \approx R^n E\|W_0\|^2 + \alpha(R^n - 1)$ with $R>1$, and they prove that typical L\&E update rules can trigger this blow-up without explicit norm control. To counter this, they propose Norm-Anchor Scaling (NAS), a plug-in that rescales each edit’s target value $v^{new}$ to a fixed anchor norm $a$, yielding a stable dynamic $E\|W_n\|^2 \approx r^n E\|W_0\|^2 + \beta(1-r^n)$ with $0<r<1$. Empirically, NAS delays the collapse point by more than 4× on average and improves average editing performance by about 72% across multiple backbones (Llama3-8B, Qwen2.5-7B, GPT-J) and knowledge-editing streams (CounterFact, ZsRE), while preserving general capabilities and incurring negligible overhead. The results establish NAS as a robust, drop-in stabilization technique for lifelong knowledge updating in large language models.

Abstract

Model editing has emerged as a practical approach for mitigating factual errors and outdated knowledge in large language models (LLMs). Among existing methods, the Locate-and-Edit (L&E) paradigm is the dominant framework: it locates MLP parameters implicated in expressing a target fact, and then performs a localized update to rewrite that fact. However, long sequences of edits often trigger abrupt model collapse in L&E beyond a critical point. We empirically identify a strong correlation between collapse and explosive growth of edited MLP weight norms, and formally prove that commonly used L&E update rules can induce exponential norm growth across sequential edits in the absence of explicit norm control. To address this issue, we propose Norm-Anchor Scaling NAS, a plug-and-play norm-constrained strategy. Across extensive experiments, NAS delays the collapse point of representative L&E algorithms by more than 4 times and yields a 72.2% average relative gain in editing performance, requiring only a single additional line of code and incurring negligible computational overhead.

Toward Ultra-Long-Horizon Sequential Model Editing

TL;DR

This work addresses the instability of ultra-long-horizon sequential model editing under the Locate-and-Edit framework, where repeated localized updates cause explosive growth in the edited weight norms and abrupt performance collapse. The authors provide a mechanistic analysis showing that the weight-norm evolves roughly as with , and they prove that typical L\&E update rules can trigger this blow-up without explicit norm control. To counter this, they propose Norm-Anchor Scaling (NAS), a plug-in that rescales each edit’s target value to a fixed anchor norm , yielding a stable dynamic with . Empirically, NAS delays the collapse point by more than 4× on average and improves average editing performance by about 72% across multiple backbones (Llama3-8B, Qwen2.5-7B, GPT-J) and knowledge-editing streams (CounterFact, ZsRE), while preserving general capabilities and incurring negligible overhead. The results establish NAS as a robust, drop-in stabilization technique for lifelong knowledge updating in large language models.

Abstract

Model editing has emerged as a practical approach for mitigating factual errors and outdated knowledge in large language models (LLMs). Among existing methods, the Locate-and-Edit (L&E) paradigm is the dominant framework: it locates MLP parameters implicated in expressing a target fact, and then performs a localized update to rewrite that fact. However, long sequences of edits often trigger abrupt model collapse in L&E beyond a critical point. We empirically identify a strong correlation between collapse and explosive growth of edited MLP weight norms, and formally prove that commonly used L&E update rules can induce exponential norm growth across sequential edits in the absence of explicit norm control. To address this issue, we propose Norm-Anchor Scaling NAS, a plug-and-play norm-constrained strategy. Across extensive experiments, NAS delays the collapse point of representative L&E algorithms by more than 4 times and yields a 72.2% average relative gain in editing performance, requiring only a single additional line of code and incurring negligible computational overhead.
Paper Structure (92 sections, 4 theorems, 73 equations, 17 figures, 6 tables)

This paper contains 92 sections, 4 theorems, 73 equations, 17 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Knowledge Editing Setup
  4. Transformer FFN as Key--Value Memory
  5. Locate-and-Edit Paradigm
  6. Overall update objective.
  7. Closed-form rank-one update of $W$.
  8. Computing the target value $v^{\mathrm{new}}$.
  9. Sequential Editing
  10. Analysis and Method
  11. Computing $\|W_n\|^2$
  12. Exponential growth of $\| W_n\|^2$.
  13. Verification via curve fitting.
  14. Method
  15. Motivation.
  16. ...and 77 more sections

Key Result

lemma 3.1

The squared norm of the edited weight matrix satisfies

Figures (17)

  • Figure 1: Overview of ultra-long sequential knowledge editing performance on LLaMA3 under the Locate-and-Edit (L&E) paradigm, evaluated on the full CounterFact stream (20,877 edits) and ZsRE stream (19,082 edits). Metrics marked with an asterisk (*) correspond to ZsRE; all others are from CounterFact. See Section \ref{['sec:exp:rq1']} for the complete setup and detailed results.
  • Figure 2: Norm explosion accompanies sequential editing collapse. During sequential vanilla locate-and-edit, we track edit success (blue, left axis) and normalized weight growth $R_n \coloneqq \| W_n\|/\| W_0\|$ (orange, right axis) versus edit step $n$. For both Llama-3 and GPT-J, increasing $R_n$ coincides with deteriorating editing performance; Spearman $\rho$ is shown in each panel.
  • Figure 3: Log-linear growth of weight-norm ratio under sequential editing. We measure $\log R_n$ as a function of edit step $n$ ($R_n=\| W_n\|/\| W_0\|$) for Llama-3 and GPT-J. Linear fits (dashed) achieve high $R^2$, supporting an approximately exponential increase of $\| W_0 \|$ with the number of edits.
  • Figure 4: Hidden representation drift under sequential L&E updates. We probe the target-module representations on 1,000 held-out factual prompts for pre-edited (blue), vanilla (green), and vanilla+NAS (orange) after 100 and 500 edits, and visualize them in a shared 2D PCA space (PCA fit on pre-edited). Cross markers indicate state-wise means; ellipses denote 95% confidence regions. We report $\Delta(\textit{pre}\!\to\!\cdot)=\|\mu_{\cdot}-\mu_{\textit{pre}}\|_2$ (centroid distance in the original hidden space).
  • Figure 5: RQ2: GLUE performance (F1) during sequential editing. NAS preserves base-task performance substantially longer than baselines. Insets zoom into the early-edit region (0--4k); inset x-ticks are shown at 2k and 4k for readability.
  • ...and 12 more figures

Theorems & Definitions (6)

  • lemma 3.1
  • Proposition 3.2
  • Corollary 3.3
  • Definition 2.1: Frobenius norm
  • Definition 2.2: Frobenius inner product
  • lemma 2.3: Useful identities