Perturbation-Restrained Sequential Model Editing
Authors: Jun-Yu Ma
Hong Wang
Hao-Xiang Xu
Zhen-Hua Ling
Jia-Chen Gu
Venue: ICLR 2025 Poster (2025)
Keywords: Sequential Model Editing
Matrix Perturbation
General Abilities
Large Language Models
Primary area: transfer learning, meta learning, and lifelong learning
TL;DR: We investigate what is the bottleneck of the general abilities during sequential editing and how to how to break through it.

Abstract: Model editing is an emerging field that focuses on updating the knowledge embedded within large language models (LLMs) without extensive retraining. However, current model editing methods significantly compromise the general abilities of LLMs as the number of edits increases, and this trade-off poses a substantial challenge to the continual learning of LLMs. In this paper, we first theoretically analyze that the factor affecting the general abilities in sequential model editing lies in the condition number of the edited matrix. The condition number of a matrix represents its numerical sensitivity, and therefore can be used to indicate the extent to which the original knowledge associations stored in LLMs are perturbed after editing. Subsequently, statistical findings demonstrate that the value of this factor becomes larger as the number of edits increases, thereby exacerbating the deterioration of general abilities. To this end, a framework termed Perturbation Restraint on Upper bouNd for Editing (PRUNE) is proposed, which applies the condition number restraints in sequential editing. These restraints can lower the upper bound on perturbation to edited models, thus preserving the general abilities.
Systematically, we conduct experiments employing three editing methods on three LLMs across four downstream tasks.
The results show that PRUNE can preserve general abilities while maintaining the editing performance effectively in sequential model editing. The code are available at https://github.com/mjy1111/PRUNE.

Published as a conference paper at ICLR 2025
PERTURBATION-RESTRANED SEQUENTIAL MODEL EDITING
Jun- Yu Ma 12 Hong Wang', Haanniang Xu Zhen-Hua Ling" 1,, Jia-Chen Gu
1 University of Science and Technology of China
2 National Engineering Research Center of Speech and Language Information Processing
University of California, Los Angeles
(m wanghong1 70c, nh2001 620 Y @mail. wasst..edu.cm
zh zhlingeustc. edu.e en, gujc@uc a.edu
ABSTRACT
Model editing is emerging field that focuses on updating the knowledge embedded within large language models (LLMs) without extensive retraining. However, current model editing methods significantly compromise the general abilities of LLMs as the number of edits increases, and this trade-off poses a substantial challenge to the continual learning of LLMs. In this paper, we first theoretically analyze that the factor affecting the general abilities in sequential model editing lies in the condition number of the edited matrix. The condition number of matrix represents its numerical sensitivity, and therefore can be used to indicate the extent to which the original knowledge associations stored in LLMs are perturbed after editing. Subsequently, statistical findings demonstrate that the value of this factor becomes larger as the number of edits increases, thereby exacerbating the deterioration of general abilities. To this end, framework termed Perturbation Restraint on Upper bouNd for Editing (PRUNE) is proposed. which applies the condition number restraints in sequential editing. These restraints lower the upper bound on perturbation to edited models, thus preserving the general abilities. Systematically, we conduct experiments employing three editing methods on three LLMs across four downstream tasks. The results show that PRUNE can preserve general abilities while maintaining the editing performance effectively in sequential model editing. The code are available at https//github.com//ijj 11//RUNE
INTRODUCTION
Despite the remarkable capabilities of large language models (LLMs), they encounter challenges such as false or outdated knowledge, and the risk of producing toxic content (Zhang et al., 2023; Peng et al., 2023; Ji et al., 2023; Huang et al., 2023). Given the high cost of retraining LLMs to address these issues, there has been surge in focus on model editing (Dai et al., 2022; Meng et al., 2022; Mitchell et al., b022a;b; Meng et al., 2023; Zhang et al., 2024; Hu et al., 2024; Ma et al., 2024; Jiang et al., 2025; Fang et al., 2025), which aims at updating the knowledge of LLMs cost-effectively. Existing editing methods can be roughly classified into either parameter-modiffing methods (Mitchell et al., 2022a; Meng et al., 2023) that directly modify small subset of model parameters, or parameter- preserving methods (Mitchell et al., 2022b; Yu et al., 2024) that integrate additional modules without altering the model parameters. In this paper, we study the parameter-modifyine editing methods.
Sequential model editing involves making successive edits to the same model over time to continuously update knowledge, as illustrated in Figure 1(a). Recent studies (Gu al., 2024; Gupta et al.. 2024b; Lin et al., 2024; Gupta et al., 2024a) indicate that parameter- modiifiinn editing methods significantly compromise the general abilities of LLMs as the number of edits increases, such as summarization, question answering, and natural language inference. However, these studies neither provide a theoretical analysis of the bottleneck of the general abilities of the edited models, nor propose a solution to preserve these abilities in sequential editing. These affect the scalability of model editing and pose a substantial challenge to the continual learning of LLMs.
"Corresoonding author.

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Edit
Edit
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Performance after restrained editing
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(b) Condition number of matrices
(c) General downstream task performance
(d) Editing performance
Figure (a) Illustration of sequential model editing. (b) The condition number of edited matrix rapidly increases the number of edits increases. (c) Comparison of general downstream task performance before editing, after regular editing. and after restrained editing by PRUNE. (d) Comparison of editing performance after regular editing and after restrained editing by PRUNE. fw. fw. and fw, denote the models that are unedited, regularly edited n times, and restrainedly edited by PRUNE respectively. W is denoted
matrix to be edited.
In light of the above issues, we first theoretically analyze through matrix perturbation theory (Vaccaro, 1994; Wedin, 1972) to elucidate a crucial factor affecting the general abilities during sequential editing: the condition number (Smith, 1967: Dedieu, 1997; Sun, 2000) of the edited matrix. The condition number of a matrix represents its numerical sensitivity and therefore can used to indicate the extent which the original knowledge associations stored in LLMs perturbed after editing. As shown in Figure 1(b), statistical findings demonstrate that the condition number of the edited matrix substantially increases the number of edits increases, thereby exacerbating the perturbation of original knowledge and the deterioration of general abilities. Therefore, we assume that the bottleneck of the general abilities during sequential editing lies in the escalating value of the condition number.
Towards continual and scalable model editing, we propose Perturbation Restraint on Upper bouNd for Editing (PRUNE) based the above analysis, which applies the condition number restraints in sequential editing to preserve general abilities and maintain new editing knowledge simultaneously. Specifically, the condition number of the edited matrix is restrained by reducing the large singular values (Albano et al., 1988; Wall et al., 2003) of the edit update matrix. Consequently, the upper bound on perturbation to the edited matrix is lowered, thus reducing the perturbation the original knowledge associations and preserving the general abilities of the edited model, as shown in Figure (cc). Additionally, we observe that these larger singular values often encapsulate redundant editing overfitting information, regularizing them will not affect the newly editing knowledge, as shown in Figure (d). In this way, the new editing knowledge is embedded into LLMs without affecting their original general abilities. Overall, the proposed editing framework requires only minimal computing resources, and is adaptable to be coupled with multiple existing editing methods.
To validate the effectiveness of the proposed PRUNE, our study comprehensively evaluates the edited LLMs for both general abilities and editing performance in sequential editing scenarios. Extensive research involves three popular editing methods, including MEND (Mitchell al., 2022a), ROME (Meng et al., 2022), and MEMIT (Meng et al., 2023), which are analyzed based on three LLMs including GPT-2 XL (1.5B) (Radford et al., 2019), LLaMA-2 (7B) (Touvron et al., 2023), and LLaMA-3 (8B). Four downstream tasks including reasoning (Cobbe et al., 2021), summarization (Gliwa et al., 2019), open-domain QA (Kwiatkowski language inference (Dagan et al., 2005) are employed to demonstrate the impact of editing on the general abilities of L.LMs. Experimental results demonstrate that the proposed PRUNE can preserve considerable general abilities and maintain almost all editing performance in sequential editing.
al., 2019), and natural
In essence, our research offers three contributions: (1) This study theoretically analyzes that the escalating value of the condition number of the edited matrix is the bottleneck of sequential model editing. (2) The PRUNE based on the analysis is proposed to preserve the general abilities of the edited model while retaining the editing knowledge. (3) Experimental results including both editing and downstream task performance across three editing methods on three LLMs demonstrate the effectiveness of PRUNE.
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2 RELATED WORK
Model Editing Methods From the perspective of whether the model parameters are modified, existing editing methods can be divided into purameter-modifingg (Mitchell et al., 2022a; Meng et al., 2022; 2023; Dai et al., 2022) and puremeler-preservingg methods (Mitchell et al., 2022b; Hartvigsen et al., 2023: Yu et al., 2024). This paper focuses on the former. Previous works have investigated the role of MLP layers in Transformer, showing that MLP layers store knowledge, which can be located in specific neurons and edited (Geva et al., 2021; Da et al., 2021; Geva et al., 2022). KE (Cao et al., 2021) and MEND (Mitchell et al., 2022a) train hypernetwork to get gradient changes to update model parameters (Mitchell et al., 2022a). Besides, Meng et al. (2022) and Meng et al. (2023) used Locate-Then-Edii strategy, which first located multi-layer perceptron (MLP) storing factual knowledge, and then edited such knowledge by injecting new key-value pair in the MLP module. Parameter- preseervng methods do not modify model weights but store the editing facts with an external memory. For example, Mitchell et al. (2022b) stored edits in a base model and learned to reason over them to adjust its predictions as needed.
Model Editing Evaluation Some works investigate the paradigm for model editing evalua- tion (Zhong et al., 2023; Cohen et al., 2024; Ma et al., 2023; Li et al.; Hase al., 2023; Wu et al., 2023; Gandikota et al., 2023; Ma et al., 2024). Cohen et al. (2024) introduced the ripple effects of model editing. suggesting that editing a particular fact implies that many other facts need to be updated. Ma et al. (2023) constructed a new benchmark to assess the edited model bidirectionally. Besides, Li al. explored two significant areas of concern: Knowledge Conflict and Knowledge Distortion. These early studies mainly evaluate edited models per edit rather than sequentially, and they focus narrowly on basic factual triples. Recently, some works assess the impact of editing methods on the general abilities of LLMs in sequential editing scenarios. These studies (Gu et al., 2024; Gupta et al., 2024b; Lin et al., 2024; Yang et al., 2024; Gupta et al., 2024a;c) have conducted comprehensive experiments, showing the purameter-modifyyee methods significantly degrade the model performance on downstream tasks.
It plays a crucial role in the field of artificial intelligence (Al) by providing a systematic framework to understand the impact of small changes or perturbations in various Al algorithms and models. Some studies (Harder et al., 2020; Qin et al., 2022; Singh et al., 2024) delve into the interpretability of L.MMs, revealing how minor alterations in input features or model parameters influence the model's 'ss predictions. This understanding helps uncover significant feature connections within the model architecture. Morcover, it has been instrumental in assessing and enhancing the robustness of models (Chen et al., 2023; 2024). Furthermore, Bird et al. (2020) and Dettmers et al. (2023) have employed it for sensitivity analysis to identify critical factors affecting algorithm performance. It also contributes the development of efficient optimization techniques (Li et al., 2020; Jiang et al., 2024), improving convergence rates and stability of optimization algorithms.
Matrix Perturbation Theory
Compared with previous works (Meng et al., 2022; 2023; Yao et al., 2023; Gu et al., 2024; Gupta et al., 2024b; Lin et al.. 2024) that are the most relevant, main difference should be highlighted. They neither theoretically investigate the reasons for general ability degradation, nor propose effective methods to maintain these abilities during sequential editing. In contrast, our study makes the first attempt to theoretically explore the bottleneck of general abilities in sequential editing and proposes the PRUNE framework to preserve these abilities for continual model editing.
ANALYSIS ON BOTTLENECK OF SEQUENTIAL MODEL EDITING
3.1 PRELIMINARY
Model Editing This task involves modifying the memorized knowledge contained in LMs. Various kinds of complex learned beliefs such as logical, spatial, or numerical knowledge are expected to be edited. In this paper, following previous work (Meng et al., 2022: Zhong et al., 2023; Meng et al., 2023; Zhang et al., 2024), we study editing factual knowledge in the form of (subject s, relation r. object 0), e.g.. (s United States, r = President of. o = Donald Trump). An LM is expected to recall memory representing given a natural language prompt p(s. r) such as "The President of the United States is" Editing a fact is to incorporate new knowledge triple (s, r, o*) in place of the current. one (s, r, o). An edit is represented as o8, for brevity. Given set of editing facts
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E f= E2, ...} and an original model feg. sequential model editing operationalizes each edit after the last edit', i.e., K (f en) = -fo., where fe,, denotes the model after n edits.
Singular Value Decomposition SVD (Albano et al., 1988) a fundamental and effective matrix factorization technique for analyzing matrix structures. Formally, an SVD of a matrix W E IRx is given by W UEVI, where U = [w), U2,..., Up] E Rpxp, V = [V1,22, ..,,..,, Uyl E R and Σ E R u, and 22 are the column vectors of U and V. and constitute basis of I" and I' respectively. E is a diagonal matrix whose diagonal entries are given by the singular values of W in descending order. Additionally, the SVD of W could also be formulated
orthonormal
as: W = -im1 min(()-) "u where o; is singular value, and 01 2 02 2 2 Jmin(p.q) 2 0. In the scenario of this paper, W is full-rank matrix, min(p.g) > 0.
3.2 MATRIX PERTURBATION THEORY ANALYSIS
Previous works (Geva et al., 2021; Meng et al., 2022; Gupta et al., 2023; Wang et al., 2024) have analyzed and located that the MLP modules in Transformer (Vaswani al., 2017) store various kinds of knowledge (Pearl, 2001; Vig et al., 2020). The MLP module of the 1-th Transformer layer consists of two projection layers, where the first and second layers are denoted as W7 and W proj respectively. W proj is considered as linear associative memory which stores knowledge in the form of key-value pairs (kg, v2),, and is usually regarded as the editing area (Meng et al., 2022; 2023). In this paper, W proj denoted as W for brevity. W is assumed to store many key-value pairs P [k, v;) I 2, ...} which satisfies Wk; Us where k; E R2 and U; E R2, Assuming E - N in sequential model editing, an edit update matrix AW; is calculated for the edit e, and added to W, which can be formulated as: WN = W + Σ j= A with AW, calculated from fø,-1"
N
Problem Modeling To explore the reasons for the general ability degradation of edited models, we begin by noting that most of the key-value pairs of P correspond to facts unrelated to editing. For the sake of analysis, only the matrix W of a single layer assumed to be modified. We intuitively hypothesize that for the facts that are irrelevant to the editing fact, the cumulative modifications applied during sequential model editing may lead to significant mismatches in the associations between the original key-value pairs P. Specifically, consider key-value pair (k., e;) E P. After applying an edit ej that generates AW, and adding it to W, if the extracted value 8/ remains unchanged, the corresponding key k; needs to be adjusted with an adjustment denoted as AK. Mathematically, this can be represented as² WN(k; + Σÿ= AK!) U; after N edits. However, during the editing process, it's challenging guarantee such adjustments completely, leading inaccuracies in the knowledge extracted from the edited model. To delve deeper, let's analyze how the key k; changes (i.e., Σ 1=1 AK() when its corresponding value U; remains unchanged after N edits.
j=
Perturbation Analysis of Single Edit According to matrix perturbation theory (Luo & Tseng, 1994; Vaccaro, 1994; Wedin, 1972), the edit update matrix AW from an edit can be regarded as perturbation for W, so we first analyze the situation where W E Rpxx is appended with perturbation AW. Define W is the generalized inverse (Stewart & Sun, 1990) of W, * represents 2-norm, and W = W + AW.
Theorem 3.1 Consider Wk there exists Ak such that i k + Ak satisfies Wh Let k Wto and k- = Wt. v. and AW is an acute perturbation of W. Then:
|| AkIl
kll |&||
AE [W]
(RAB12) [
A (1)
A
V22
2
11 (''9(()+
[W]
where ΛEН. AEi and 2 are directly related AW. V2(F) is monotonically increasing function of ||F|]| and g(v) is a function about v. A [W]|[[W Il. where W is square and related to the reduced form of W. Each term on the right-hand side involves R, which means that the upper
'This paper studies editing single fact time and leaves the exploration of batch editing future work.
2 "A W, RP*0, and we observed p < in LLMs, so there will be Ak? that satisfies this formula. Wee obtained some A W, and found |AW < [[W]], which satisfies the definition of perturbation.
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MEND
Condil Number
Cand tinn Number
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Figure 2: The condition number, maximum singular value and minimum singular value of the edited matrix in sequential editing. Three editing methods including ROME, MEND, and MEMIT are used to edit LLaMA-2 (7B) on the COUNTERFACT (Meng et al., 2022) dataset. For editing methods that modify the parameters of multiple MLP layers, one of them randomly selected for illustration. W and W., denote the unedited and edited matrices respectively.
bound on the perturbation of the vector & is constrained by Å. Readers can refer to Appendix A.3 for the details and proof of this theorem. However, calculating [Wn'l involves the reduced form W. which incurs unnecessary additional overhead. Therefore, consider the following theorem and give an alternative estimation.
Theorem 3.2 Let || Wi and suppose that y = 1- A|
> 0. Then:
[W]
|
| <
7
Amaz is daiin According Theorem 3.2, |W $ |W [ so h S Here =
the condition number of W, where max and min are the maximum and minimum singular values of W. respectively. Combining Theorem 3.1, know that the larger is, the greater the upper bound on the perturbation of the vector Readers can refer to Appendix A for the full theoretical analysis.
3.3 TREND OF THE CONDITION NUMBER DURING SEQUENTIAL EDITING
As mentioned above, we have analyzed that the condition number of the edited matrix can be used to indicate the upper bound on the perturbation of the key-value pair associations by single edit. In order to explore the impact of sequential model editing on these associations, the change trend of the condition number of the edited matrix during sequential editing is illustrated in Figure 2.
Surprisingly, we observed that regardless of the editing methods employed, condition number of the edited matrix exhibited rapid increase as the number of edits increased, particularly after large number of edits. According to Theorem 3.1, the adjustment norm A l| corresponding to the n-th edit tends increase as the number of edits n increases. Therefore, can draw two conclusions: (I) As more edits are performed, the upper bound of the perturbation caused by new single edit to the key-val key-value pair associations increases. (2) During the sequential model editing process, the cumulative perturbation of these edits will become larger and larger. These factors further disrupt the stored original knowledge and exacerbate the deterioration of general abilities. As the second conclusion is easy to understand, here is an example for the first point. From the first subfigure of Figure 2, we can observe that the condition number of the W200 matrix after the 200th edit significantly higher than that of the unedited matrix W. Therefore, the perturbation of the model caused by the 201s edit is likely to be much greater than the perturbation of the model caused by the 1st edit.
4 PRUNE: PERTURBATION RESTRAINT ON UPPER BOUND FOR EDITING
Motivation According to the analysis Section the bottleneck of the general abilities during sequential editing lies in the escalating value of the condition number. Assuming set of edits {e:} and their corresponding edit update matrices (AW;) J. the information contained in these edit update matrices coordinates with each other to certain extent since the parametrie knowledge of LLMs is distributional rather than independent. This editing overfitting reflected SVD, where the largest singular value of the edited matrix Wx becomes significantly large after the addition of these edit
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update matrices. To illustrate this, consider extreme example: suppose make N edits, where each edit changes the answer to the question "Who is the president of the United States?" to "Biden". Each edit update matrix is denoted as AW1, and its maximum singular value is ó Smaz. Then the sum of the edit update matrices is N A W1, and its maximum singular value is N Nomar. which is amplified by N times. Therefore, our goal is to reduce the editing overfitting in edited matrix WN as much as possible while also retaining valuable editing information. In this section, a framework termed Perturbation Restraint on Upper bouNd for Editing (PRUNE) is proposed, which applies the condition number restraints to preserve general abilities and maintain new editing knowledge.
Principle Given an edited matrix with N edits, WN W + +E AW,, as shown Figure 2, its maximum singular value is constantly increasing, while the minimum singular value is basically unchanged as the number of edits N increases. This directly leads to the increasing condition number of the edited matrix. Therefore, our motivation is to restrain the large singular value the edited matrix to lower the upper bound the perturbation. we directly perform SVD operation on WN and reduce
Table I: The maximum singular values of Σ AW, with three edting meth- ods. Other settings are the same as those illustrated in Figure
Edits (N)
ROME
MEMIT MEND
10
7.25
7.46
14.08
50
11.38
15.63
75.53
its singular values, the original W will be inevitably
100
15.62
23.39
127.89
destroyed. Consequently, an analysis of the singular values
200
57.61
935
191.04
of Σe= AW, is conducted, and the results in Table present that its maximum singular value becomes very large when N is large. Since the singular values of W are relatively small, we can assume that the large maximum singular value of Σ AW, is the main reason why the maximum singular value of WN is large, our method therefore aims to restrain the large singular values of ΣØ=1 AWG.
Design Firstly, SVD is operated the original W and Dj=1=
AW, respectively
min(p.g)
N
min(p.g)
W Σ o
AAw,
Σ o,
(3)
J=1
i=1
This paper considers W to be the main part, and any singular value in Σド AW, should be ensured not obviously exceed the maximum singular value of W. Subsequently, any singular value o, of ΣN AW, is greater than the maximum singular value of W, will be restrained with a function F, otherwise it remains unchanged, which could be formulated as:
F(os): if à. > max as),
T, - Oi: if o S max
(4)
F(G.) loga (o:) loga (max (a:)) ) + max(a:)-
In the main paper, we use the log function in F to restrain oū Here a is hyperparameter control the degree of restraints, readers can refer to Appendix B.3 for its details for experiments. Besides, we also provide the definition and results of linear function in Appendix C.3. Finally, we obtain the restrained edited matrix W to replace Wx:
min(p.g]
W N = W
Σ o, 1=1
In this way, the condition number of the edited matrix is reduced (see Appendix C.4) and the upper bound on perturbation significantly restrained. is worth noting that the PRUNE proposed here only used once in Section 5, but can actually be used multiple times in the editing process to better maintain the general ability. We provide a comparison of the two strategies in Appendix C.6.
EXPERIMENTS
In this section, both the downstream task performance and editing performance of three editing methods on three LLMs were evaluated in sequential model editing. The proposed PRUNE was plug-and-play which can be coupled with these editing methods.

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5.1 BASE LLMs AND EDITING METHODS
Experiments were conducted on three LLMs including GPT-2 XL (1.5B) (Radford et al., 2019), LLaMA-2 (7B) (Touvron al., 2023) and LLaMA-3 (8B)'. Three popular editing methods were selected as the baselines including MEND (Mitchell et al., 2022a), ROME (Meng et al., 2022), and MEMIT (Meng al., 2023). Appendix B.1 shows the details of these editing methods.
5.2 EDITING DATASETS AND EVALUATION METRICS
To make a more comprehensive evaluation, we used two types of knowledge for editing: factual knowledge and conceptual knowledge. (1) For factual knowledge, two popular model editing datasets Zero-Shot Relation Extraction (ZsRE) (Levy et al., 2017) and COUNTERFACT (Meng et al., 2022) were adopted in our experiments. These two datasets are QA datasets. key distinction between COUNTERFACT and ZsRE datasets is that ZsRE contains true facts, while COUNTERFACT contains counterfactual examples where the new target has lower probability when compared the original answer (Gupta et al., 2024b). (2) For conceptual knowledge, the ConceptEdit dataset (Wang al., 2024) was adopted. Due to the limitations of computing resources and pages, most of the experiments in this paper were conducted on factual datasets, with the results presented in Sections 5.4 and 5.5. Meanwhile, Section 5.6 provided some results on conceptual datasets. Readers can refer to Appendix B.2 for examples of each dataset.
To assess the editing performance of editing methods, following previous works (Cao et al., 2021; Mitchell et al.. 2022a: Meng et al.. 2022; 2023; Ma al., 2024), three fundamental metrics were employed: efficacy, generalization and locality. Given an original model fe,, an edited model fe. with times sequential editing. Define as the indicator function. Each edit e₃ (8i, Te, Oz, of) has an editing prompt Pt paraphrase prompts P.C. and locality prompts P.f.
Efficacy validates whether the edited models could recall editing fact under editing prompt p;. The assessment is based on Efficacy Score (ES) representing as: [E argmaxx Pf., (ol (o]pt)= of]]
Generalization verifies whether the edited models could recall the editing fact under the paraphrase prompts D. via Generalization Score (GS): E, [ppppol argmax, Pfo, (olp) =
Locality verifies whether the output of the edited models for inputs out of editing scope remains unchanged under the locality prompts P.L via Locality Score (LS):
E, pep: [rgmaax Pf.., (olp:) = oj]]], where oj the original answer of pt-
Different from previous studies that assess the edited models after each individual edit (Gupta et al., 2024b; Yao et al., 2023), this paper evaluated whether the final edited models after completing all edits still recall all preceding edits, which is more challenging and common in real-workle
5.3 DOWNSTREAM TASKS, DATASETS AND METRICS
To explore the side effects of sequential model editing on the general abilities of LLMs, four representative tasks with corresponding datasets were adopted for assessment following previous work (Gu al., 2024; Gupta al., 2024b; Lin al., 2024: Zhang et al., 2024), including:
Reasoning on the GSMSK (Cobbe et al., 2021), and the results were measured by solve rate.
Summarization on the SAMSum (Gliwa et al., 2019), and the results were measured by the average of ROUGE-1, ROUGE-2 and ROUGE-L following Lin (2004).
Open-domain QA on the Natural Question (Kwiatkowski al., 2019), and the results were measured by exact match (EM) with the reference answer after minor normalization as in Chen et al. (2017) and Lee et al. (2019).
Natural language inference (NLI) on the RTE (Dagan et al., 2005), and the results were measured by accuracy of two-way classification.
For each dataset, some examples were randomly sampled for evaluation. Details of prompts for each task were shown in Appendix B.4.
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Reasoring
Summarizatiion
Opendomain-GA
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Summarization FRUNE
Opendomain-QA PRUNE
NL PRUME
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1.AMA-22 (7B)ROME
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LLAMA-2 2LAMA-2((H)-MEED (78)-MEND
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Ple Parformmtaro (50)
Performaccee (16)
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Figure 3: The downstream task performance (%) of models edited by three editing methods with LLaMA-2 (7B) on the ZsRE dataset. The dashed lines refer to the results of the unrestrained editing methods. The solid lines refer to the results of the editing methods coupled with the proposed PRUNE framework. Statistical significance tests were performed demonstrate that the improvement in PRUNE compared to baseline was statistically significant (t-test with p-value <0.05).
5.4 GENERAL ABILITIES RESULTS ON FACTUAL KNOWLEDGE
Figure 3 illustrates the downstream task performance of editing methods with LLaMA-2 (7B) on the ZsRE dataset. Due page limitation, results of other LLMs and factual datasets were put in Appendix C.I. These results were analyzed from the following perspectives.
Current editing methods significantly compromised general abilities. As depicted by the dashed lines of Figure 3, both the ROME and MEMIT methods initially maintained relatively stable performance in downstream tasks when the number of edits was small (< 50). However, as the number of edits surpassed 100, noticeable decline in performance was observed across all tasks for both methods. Additionally, the MEND method exhibited significant performance degradation after just 20 sequential edits, indicating its inadequacy as sequential model editing method. Furthermore, when comparing LLMs of different sizes, general trend emerged: larger models suffered more pronounced compromises in their general abilities when subjected to the same number of edits. For instance, with 300 edits, MEMIT'S performance on GPT2-XL remained largely unchanged, whereas it dwindled to nearly 0 on LLaMA-2 and LLaMA-3.
The performance decline was gradual initially but accelerated with increasing edit count. This trend aligned with the fluctuation observed in the size of the condition number, as depicted in Figure 2. When the number edits was small, the condition number was small, and each new edit introduced relatively minor perturbations to the model. However, the number of edits increased, the condition number underwent a substantial increase. Consequently, each subsequent edit exerted a significant perturbation the model, leading pronounced impairment of its general abilities. These results substantiated the analysis presented in Section 3.3.
The proposed PRUNE preserve considerable general abilities. As shown by the solid lines of Figure 3, when MEMIT was coupled with PRUNE and subjected to 100 edits, its downstream tasks performance remained close that of the unedited model. However, for the unrestrained MEMIT, downstream task performance had plummeted to nearly 0 by this point. This consistent trend was also observed with ROME and MEND. Nevertheless, for models edited using the unrestrained MEND method, performance degradation was stark after just 10 edits. Even with the addition of PRUNE, preservation could only be extended up to 20 edits. This suggests that while PRUNE effectively preserves general abilities, it does have an upper limit determined by the unrestrained editing method.
5.5 EDITING PERFORMANCE RESULTS ON FACTUAL KNOWLEDGE
Figure 4 shows three metrics used for measuring the editing performance with LLaMA-2 (7B) on the ZsRE dataset. Other results were put in Appendix C.2. Three conclusions can be drawn.
Previous editing facts were forgotten the number of edits increased. As shown by the dashed lines of Figure 4, the decline in efficacy and generalization suggests that in sequential editing scenarios, post-edited models gradually forget knowledge acquired from previous edits after few iterations.
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1. 1---2 (7B)-ROME
100
2 MEMIT
100
L.aMA-2 (7B-MEND
Porfemance (h))
Porformace (71)
Porfommne
60-
50-
Conersttation
Localty
Localty MINC
100
150 Number Edis
200
Number od Edits
Number Edits
Figure 4: The editing performance (%) of editing methods with LLaMA-2 (7B) on the ZsRE dataset. The dashed lines refer to the results of the unrestrained editing methods. The solid lines refer the results of the editing methods coupled with the proposed PRUNE. Statistical significance tests were performed to demonstrate that the improvement in PRUNE compared to baseline was statistically significant (t-test with p-value <0.05).
Comparing these editing methods, we also observed a notable drop in efficacy and generalization after hundreds of edits with ROME and MEMIT, whereas these values decreased significantly after only 15 edits with MEND. This indicates that in sequential editing scenarios, the MEND method struggled successfully integrate new knowledge into LLMs after several edits.
Unrelated facts were perturbed as the number of edits increased. The locality metric served as an indicator of perturbation for unrelated facts. It became evident that for each editing method, the locality decreased significantly. Additionally, an observation emerged: when the locality of the edited model was low, the performance of downstream tasks was also low. This observation underscores that perturbations of irrelevant knowledge compromise the general abilities of the edited model.
PRUNE can effectively maintain the editing performance. This is shown by the solid lines of Figure 4 and could be analyzed from two aspects. On the one hand, when the number of edits was small, the editing performance of each editing method coupled with PRUNE was about the same as the unrestrained method. On the other hand, it significantly mitigated the forgetting of editing facts and the perturbation of irrelevant facts when the number of edits was large during the sequential editing. Specifically, when the number of edits reached 100, the editing performance of MEMIT was very low. But when coupled with PRUNE, its performance remained relatively stable. These observations further validate motivation in Section 4, demonstrating that the information in the edit update matrices is coordinated, and that performing too many edits can easily result in overfitting. Therefore, applying certain degree of restraint edit perturbations can help preserve the model's general abilities while maintaining the editing knowledge.
5.6 EDITING WITH CONCEPTUAL KNOWLEDGE
Section 5.4 and 5.5 analyzed the results on factual knowledge. This section conducted some experiments with ROME conceptual knowledge using the ConceptEdit dataset (Wang al., 2024) to make a more comprehensive evaluation. For editing performance, in addition to the three basic metries, this dataset also designed new metric "Instance Change" to measure whether the instances under the concept changed accordingly when the definition of the concept was changed.
As shown in Table 6, the performance trends of editing and downstream tasks were similar those observed with the factual datasets. But there are several key differences: (1) When the number of edits was the same, the editing performance of conceptual knowledge was lower than that of factual knowledge. (2) Both editing performance and general abilities deteriorated more quickly than factual knowledge. For example, even if the number of edits was 100, the editing performance and downstream task performance of ROME were very low, while it was still relatively high when editing factual knowledge. (3) The low "Instance Change" indicated that when the definition of a concept was altered, the instances contained in the original concept were still recognized by the model as belonging to that concept. This shows that this editing method primarily modifies the definition without successfully altering the relationship between concepts and instances, which is not reasonable. These findings indicate that conceptual knowledge is more abstract and more difficult to edit than factual knowledge, highlighting the need to explore editing methods for different types of knowledge.

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Table 2: Evaluation results (%) of L (7B) edited by ROME on the ConceptEdit dataset.
Mode
General Abilities
Editing Performance
Method
Edits
Reasoning
Summa
Open-QA
NLI
Efficacy
General
Locality
Instance
20
75.13
11
6.50
24.7
49.15
52.58
35.68
25
50
0.7
12
ROME
100
12.29
4.7
0.77
0
28.25
30.18
5.68
10
200
8.65
5.31
-8.99
20
89.38
14.34
23.17
63.54
75.66
58.35
71.7
25
50
25.29
50.52
45.55
73.16
ROME+PRUNE
100
90.78
13.75
21.46
53.17
46.22
42.26
64.06
20
200
46.15
34.95
46.65
32
5.7 ANALYSIS ON THE FORGETTING OF EDITING FACTS
Section conducted analysis to elucidate the reasons behind the degradation general abilities with an increasing number of edits. Subsequent experiments quantitatively demonstrated the effectiveness of PRUNE. Here, we delve into qualitative analysis to explain why editing facts are forgotten and how PRUNE can mitigate this forgetting.
LLaMA-2(7B)-ROM
30
Veureer
Veatin
20
Veran
10-
Initially, given set of editing facts & fe1,,e,.... c2....). .) where 3 |-|= 200. ROME was employed for analysis, and the original matrix defined as W. During sequential editing, ROME computed key-value pairs (kg, vf) of the last subject token generate AW, for each edit e, incorporate new facts, satisfying the equation: W3 kř = D... However, when evaluating editing performance, the edited model obtained from the last edit was utilized, thus computing values": W200 kj = ir.. After adopting PRUNE to ROME, this equation became W 200 k = v. We hypothesized that if 05 was similar to uf. the editing fact e, could be maintained.
-10
=v5.
11
30
Figure 5: 2-dimensional PCA visual- ization of first 100 values. The model was edited by ROME with LLaMA-2.
Denote Varrent {of). VEditing = {6f]. and Vprune {T Specifically, these corresponding values of the first 100 edits were used, as they are more prone to be forgotten than the last 100. Principal Component Analysis (PCA) (Gewers et al., 2022) was employed to visualize these values. The first two principal components of each value were calculated and illustrated, as they can represent most of its features (Zheng et al.). As shown in Figure 5, on the one hand, the discrepancy between the principal components of Vourrent and VEditing was markedly large. This indicates that after 200 edits to the model, the values corresponding to the first 100 facts stored in the edited matrix are severely corrupted, leading significant forgetfulness. On the other hand, after adopting PRUNE, the discrepancy between the principal components of VCurrent and Vrrune was small. This demonstrates that PRUNE effectively maintains the values and mitigates the forgetting of editing facts.
CONCLUSION AND LIMITATION
In this paper, a theoretical analysis is firstly conducted to elucidate that the bottleneck of the general abilities during sequential editing lies in the escalating value of the condition number. Subsequently, a plug-and-play framework called PRUNE is proposed to apply restraints to preserve general abilities and maintain new editing knowledge simultaneously. Comprehensive experiments on various editing methods and LLMs demonstrate the effectiveness of this method. We aspire that our analysis and method will catalyze future research on continual model editing.
Limitation Firstly, this paper focuses on editing single fact at a time in sequential model editing, but some works study updating hundreds of facts simultaneously batch editing. Therefore, investigating batch-sequentia editing could enhance the scalability of model editing. Secondly, it is necessary to explore the performance of larger-size models and more editing methods on more downstream tasks.
SSince ROME only modifies matrix, the kj remains the across these edited models.
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ACKNOWLEDGMENTS
We would like express gratitude the anonymous reviewers for kind comments. This work is funded by the National Science and Technology Major Project (No. 20232D0121103),
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APPENDIX
A THEORETICAL ANALYSIS BASED ON PERTURBATION THEORY
Here, we provide detailed analysis and proof of Section 3.2. We begin by introducing some definitions and then present several preliminary lemmas and theorems. These lemmas and theorems finally used to prove Theorem 3, which is most relevant to our problem discussed in Section 3.2.
A. DEFINITION
We discuss the problem Ar = b, where Å a perturbation A given by -= A E. We assume remains unchanged and 7 represents the corresponding change, satisfying Aü = b. Here Cm
b C
is noteworthy that in the following derivation, A denotes the conjugate transpose of A, At represents the generalized inverse of A. and || represents 2-norm (Stewart & Sun, 1990).
To simplify the problem, we apply a rotation. Specifically, R(V]) R(A"), ), and let U (U1 U2) be unitary matrix with R(U1) R(A), where R refers to the rank. Then
= (Vi V2) be a unitary matrix with
UU UH AV U AVi
(A. 9).
U AV AV
(7)
U
where An is square and nonsingular. If we set
U EV UV EV EV2
Eu
E12
UHEV
(8)
E21
E2
then
T AV
(An + En Ez1
E12 Ez
An
E12 E22
(9)
Ez1
We will call these transformed, partitioned matrices the reduced form of the problem. Many statements about the original problem have revealing analogues in the reduced form.
In this form, is replaced by 4 x and b is replaced by " If a and b are partitioned in the forms
b1
x
x2
b2
(10)
where Tı, b2 CT, then
01 Añi bj
(11)
and
32 = 0.
(12)
Moreover, the norm of the residual vector
r= b - Ar
(13)
given by
||||| ||b2|
(14)
Here, we define the symbol ry:
|||||] |x|||
(15)
||||
and for any F Ckxr (k 2 r) the symbol vi (F), for the spectral norm:
F
V2(F)
(16)
(1 + 1//21/12"
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A.2 PRELIMINARY LEMMAS & THEOREMS
After introducing some definitions, we give some preliminary lemmas and theorems, which are used prove Theorem
Lemma Let
<(A) |||||||-||||
be the condition number of A. Ā nonsingular, then
| - A- (<A)
||8 |||]
(17)
||-11|
addition
||a|]] <(A) < 1,
|All
then À is perforce nonsingular and
||A-||
| v - <(A)
(18)
|All
Moreover
A
A-1
[
A
(19)
AA-1
((A)
E
Lemma In the reduced form the matrices A and Á are acute if and only if An is nonsingular and In this case, we set
E22 = E E12.
(20)
F21 = Eni and F12 = Aji E12,
then
A -= (
An (I Fi2)
F21
and
At -1 F12)
A
(21)
F21
Lemma The matrix
F
satisfies
(t)
<1
(22)
and
(() - 0) 0) (F())).
(23)
Theorem Let Á be acute perturbation of A, and let
= ||||]] A ||.
(24)
Then
Atll
Em
(RE12
|RE21
R
+ V2
V2
(25)
||A||]
A
[[
[[I
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Proof. Let
121 = (1)
112 = (I 0),
(26)
I
J21
J12 = (I F12).
(27)
P21
Át J|24 12 hence
Át - At = 12) + J2 - 1 - AT))
(28)
From Lemma
we have the following bound:
En ||
1 - AT s |A4 R
(29)
|
By Lemma
[J
A2) 12 >
12ll = =IA I (212))
(30)
= ||
F12)
(31)
11F
$ ||
(32)
|||||
and likewise
[RE21
(RE21
11 2il s || V2
S
(33)
|||||
|AI
Theorem In Theorem 1, let
||||||
(34)
and suppose that
A |1| || < 1,
(35)
so that
E1
0.
(36)
|||||
Then
||AT||
|| -
(37)
and
|| - -A
xi|EEn| ||
K=E21
(KE12
+ 1/2
- V2
(38)
||AT||
7 |||
Proof. From the equation Ät = 1122 A Jrh we have
|| | S || |I ( s ||
(39)
By Lemma 1,
| S |
|AT
(40)
which establishes equation 37, Also & < R. and the inequality equation 38 follows from equation 25.
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A.3 CORE THEOREM
Finally, we give the core theorem used in main paper. Some symbols and definitions have been claimed in Appendix A. and A.2.
Theorem 3 Let
Atb and E Atb, where À A E, and E is an acute perturbation of A.
Then
x
E11
1
E12
|
+ 2/2
+ A?
(41)
|A|
|||]
|A
|6,
|||
Proof. By Lemma write
I - x = ( - A + (J12 - 12) b1 + 12 i ( 12)6
(42)
Then
( 1 $ A E11 ||
|,0||
(43)
|||||
and
RRE12
1[ 100--1)44 42)4 b1ll s U22
||=||-
(44)
||
Now
Ji ( - == J Aī ( Fa) 1)b1 + A (I + Fff F (45)
To bound the first term in equation 45, note that
(1 ( F2)
= -
F221 F F21
Hence
[112 F2) r)b1
5 || [2))+++ [21b
$ || ||1 b1ll
S || |||| ||2 |2:||
A: E21 ll2
2
||x||
(46)
||-4||
For the second term in equation 45 we have
An (I + Fil F21) F S || 11 E21 [2]
1b2
| 12 F2
||==||||4||
E21
[bell
S <n n22
||=|||-
(47)
|||||
b1
The bound equation 41 follows on combining equation 42- equuataioon 47.
Readers can refer to this work (Stewart & Sun, 1990) for more details of perturbation analysis.
Returning to our problem, consider WK k = v. where (k, v) E P. Let W = W + AW, where AW is the corresponding perturbation matrix. Assuming remains constant, there exists Ak such that
k k Ak satisfies Wk v. And we have k W and k Wie. Applying Theorem 3,
obtain
Ak|l
||k-
7ell
|AFUIl
(KAPI) + R?2 |122l (, ||/2|| |l || + | ((FFl))
I): (48)
+ T22
|| where AET AE12 AEZ1. and AW are directly related, and each term the right-hand side
|&]|
||A||
|[||
|[]]
involves R. This means that the relative perturbation of the vector constrained by &. According ||]]]][[|||| is the condition number of W. This indicates that is
to Theorem 2, A < y,
K, where
robust indicator of the impact of AW the vector k.
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B EXPERIMENTAL SETUP
B. BASELINE EDITING METHOОSS
Three popular model editing methods were selected as baselines including:
MEND (Mitchell et al., 2022a)": : it learned hypernetwork to produce weight updates by decomposing the fine-tuning gradients into rank- form.
ROME (Meng et al., 2022)²: it first localized the factual knowledge at a specific layer in the transformer MLP modules, and then updated the knowledge by directly writing new key-value pairs in the MLP module.
MEMIT (Meng et al., 2023);: it extended ROME to edit a large set of facts and updated set of MLP layers to update knowledge.
The ability of these methods were assessed based on EasyEdit (Wang et al., 2023), an easy-to-use knowledge editing framework which integrates the released codes and hyperparameters from previous methods.
B.2 EDITING DATASETS AND EVALCATION METRICS
Table shows the examples of two factual datasets (ZsRE) (Levy et al., 2017) and COUNTER- FACT (Meng et al., 2022). Figure shows an example of ConceptEdit dataset, which is cited from Wang al. (2024). More details can refer the original paper of these datasets.
Table 3: The editing datasets of both ZsRE and COUNTERFACT.
Datasets
Editing prompt
ZsRE COUNTERFACT
Which was the record label for New Faces, New Sounds? In America, the official language is
An Example of ConceptEdit Dataset
Concept
publisher
Phrased prompt
When we refer publisher, we are talking about
Descriptor
The definition publisher
Localit sentence
The definition curling league group sports that compete against each other
y (Intra module)
group of sports tears individual athietes that very tail building
Instences
FFamitsu Bunko', "BitComposer" ....]
Descriptor y (Inter module)
Instance prompt
Whether Famitsu Bunka belongs to category publisher?
Figure 6: An example of ConceptEdit dataset
Besides, following previous works (Meng et al., 2022; Mitchell et al., 2022a; Meng et al., 2023), the editing performance metrics for the ZsRE and COUNTERFACE datasets efficacy, generalization and locality, but there are some computational differences. In the main paper, the metrics of editing performance are used for the ZsRE dataset.
For the COUNTERFACT dataset, here are the details:
Efficacy validates whether the edited models could recall the editing fact under editing prompt p:.
The assessment is based on Efficacy Score (ES) representing as: E. Ps,, (oī pp)) > Pje, (o<[p:)]]
where 1 is the indicator function.
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"http:://githbb.co
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Generalization verifies whether the edited models could recall the editing fact under the paraphrase prompts P. via Generalization Score (GS): E, peppo [1[ (oī p) > Pro,, (o, [p]]
Locality verifies whether the output of the edited models for inputs out of editing scope remains unchanged under the locality prompts Pf via Locality Score (LS): E, Epepp [1 P/o, (or pt) >
PJo, (oī pP)]]], where of was the original answer of pt.
B.3 HYPERPARAMETERS OF PRUNE
When conducting experiments, for different editing methods, LLMs and editing datasets, the hyperparameter a function F of PRUNE is different. Table shows the details of this hyperparameter. is the base of the natural logarithm.
Table 4: The hyperparameters for PRUNE.
Datasets
Models
ROME
MEMIT
MEND
GPT-2 XI.
1.2
1.2
1.2
COUNTERFACT
LLaMA-2
1.2
e
1.2
LLaMA-3
1.5
ZsRE
LLaMA-2
1.2
e
B.4 TASK PROMPTS
The prompts for each downstream task illustrated in Table 5.
Table 5: The prompts to LLMs for evaluating their zero-shot performance these general tasks.
Reasoning:
Q: (QUESTION) A: Let's think step by step. (HINT) Therefore, the answer (arabic numerals)
is:
NLI:
[SENTENCE1] } entails the (SENTENCE2). True or False? answer:
Open-domain QA: Refer to the passage below and answer the following question. Passage: (DOCUMENT) Question: [QUESTION]
Summarization:
(DIALOGUE) TL:DR:
B.5 EXPERIMENTS COMPUTE RESOURCES
We used NVIDIA A800 80GB GPU for experiments. For LLaMA-2 (7B) and LLaMA-3 (8B), occupies about 40+GB memory and costs about 3 hours for each editing method 200 edits and then to test downstream tasks For GPT-2 XL (1.5B), it needs 10+GB and costs about 1.5 hours for each editing method 200 edits and then test downstream tasks.
C EXPERIMENTAL RESULTS
C.1 RESULTS OF GENERAL ABILITIES
Figure 7, 8 and 9 show the downstream task performance of edited models with GPT-2 XL. LLaMA-2 (7B) and LLaMA-3 (8B) on COUNTERFACT dataset. Due to limitations of computing resources. experiments were conducted using only LLaMA-2 (7B) on the ZsRE dataset. We will supplement experiments with other L.LMs in the future.
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Reasoring Reasoning_ PRUNNE
Summarization
Opendomain-OA
NLI
Summarizttion
Opendomain QA,
NUL PRUME
XL-ROME
XL-MEMIT
Performaee (8Q
Perfoemance (%Q
30
200
250
300
300
300
705
1005
1205
1506
2000
100
of Ediit
Number
Number
Figure 7: The downstream task performance (%) of models edited by three editing methods with GPT-2 XL the COUNTERFACT dataset.
Reasoning
Opendomain--OA
Reasoning_PRUNE PRUNE
Summarttaton_FRRUR
Opendomain QALPRUNE
NLL PRUNE
1LaMA ROME
ILMMA (78-MEND
Perfetinne (%)
PerGomanco (N)
60
%0
TerformomorrC
60
20
100
200 Number Edils
2003
400
500
50
80
100
150
200
10
20
10
Nember
Number of
Figure 8: The downstream task performance (%) of models edited by three editing methods with 2LaMA-2 (7B) on the COUNTERFACT dataset.
LLaMA-3 (8B)-ROME
LLaMA-3 MEMIT
100
100
Performance (%)
Performance
Difckcy
Generalzation
Localiy
pificcy PAUMEE
Eencionizzion PRUME
Locally, HHURE
40
50
100
150
200
250
300
20
50
80
100
150
200
N Number of Edits
Number of Edits
Figure 9: The downstream task performance (%) of models edited by two editing methods with LLaMA-3 (8B) on the COUNTERFACT dataset. Since the code framework EasyEdit used in this paper does not currently support MEND editing LLaMA-3, there are results of MEND here.
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C.2 RESULTS OF EDITING PERFORMANCE
Figure 10, 11 and 12 shows the editing performance of edited models with GPT-2 XL, LLaMA-2 (7B) and LLaMA-3 (8B) on COUNTERFACT dataset.
100
GPT-2 XI-ROME
100
GPT-2 MEMIT
100
MEN-D
Terfommance (4Q
Pecformacee (14)
80
Tefommncc
60
DTiccy
Gererelcation
STOOK PRI1E
Octeralaating PUUCE
FRUNE
40
100
150
200
250
3143
100
300
500
700
1000
1300
1500
2000
30
20
30
50
Number Edits
Number lidits
Number Edits
Figure 10: The editing performance (%) of three editing methods with GPT-2 XL on COUNTERFACT.
L.MA-2 200 COME
1LMA-1 MEMIM
100
2LMMA-2.7R-MENN
100
100
Peformanc
50
Gevertaatan
60
Locally
Geveddation 2LRR
Localt Peunt
100
300
2507
Nunber of Edits
Number of Edits
Number of Ealite
Figure 11: COUNTERFACT dataset.
The editing performance (%) of three editing methods with LLaMA-2 (7B) on the
LLaM--1 ROM-
LLaMA-1 (SMMA--(SR--MEMM (SBI-MEMIT
100
100
Performance (1
50
Paforssunce (%))
40
60
60
01iroy FRUE
patis
40
40
50
100
150
300
250
300
30
50
80
150
150
200
Number of Edits
Number of Edit
Figure 12: The editing performance (%) of three editing methods with LLaMA-3 (8B) COUNTERFACT dataset.
C.3 RESULTS OF ANOTHER FUNCTION FOR PRUNE
In the main paper, log function is used in F in PRUNE to restrain d; Here we use the linear function, which could be represented as: F(a,) = * o. + 8-1 * maz Here 3 > 1 was hyperparameter and was set as 2 in this section. Figure 13 and 14 respectively show some downstream task performance and editing performance with linear function on FACT dataset.
Compared with Figure 7 and 10, we observed that although the lincar function in PRUNE played a role preserving general abilities and maintaining editing performance, its effectiveness was noticeably inferior to that of the log function when the number of edits was large.
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Reasoning Reasoning, PRUNE
Sumiorzzttion
Operdomain QA
NLI
Summar salior PRUNE
Opendomain GA, PRUME
NIL PRUME
G2T-2 XL-ROME
GPT MEMT
GPT22 XL MLMEN
Perormmenae (59)
40
Perfomanne
Peeformance
100
150
200
250
300
500
300 700
1000
1200
1500 2005
20
100
Figure 13: The downstream task performance (%) of models edited by three editing methods with GPT-2 XL on the COUNTERFACT dataset. Here the linear function was used in PRUNE.
XIROME
XL-MND
101
Porfemaane (16)
Performanee (15)
Peroemanes
60
Catenairatin
Lanalry
Coneralatioo entoon 70.M2
Localry TL.E
100
150
700 1000
2000
Number Bddl
Number Eddts
Number od Edits
Figure 14: The editing performance (%) of editing methods with GPT-2 XL on the COUNTERFACT dataset. Here the linear function was used in PRUNE.
C.4 CONDITION NUMBER WITH PRUNE
Figure 15 shows after coupling with PRUNE, the condition number MEMIT is significantly restrained.
MEMIT
Condition Number
500
Condition Numbar PRUNE
Condition Number
400
300
200
100
W20
Ws0
W1o0
W150
W1s0
Figure 15: The condition number of MEMIT with LLaMA-2 (7B) on the COUNTERFACT dataset.
".PRUNE" refers the condition number of MEMIT coupled with the proposed PRUNE.
C.5 THE CORRELATION BETWEEN CONDITION NUMBER AND GENERAL. ABILITIES
Figure 16 simultancously shows the condition number and general abilities of three editing methods without PRUNE in the sequential editing process. From these experiments, we observed that dramatic increase the condition number often accompanied by rapid decline in general abilities.
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Reasoning
Summarizatio
- Opendemain-OAA
++
NU
Condition Number
L (78)-ROME
LLaMA-2 (78)-MEMIT
LLaMA-2 (78)-MEN)
100
400
100
100-
250
200
100
200
Downdhram tark
80
100
20
30
100
200
300
100
120
1.0
20
50
Nummer Edits
Nuumber
Figure 16: The condition number and downstream task performance of three editing methods with LLaMA-2 (7B) the COUNTERFACT dataset. Since MEMIT and MEND have multiple parameters to be edited, we randomly selected one of them to calculate the condition number.
C.6 ENHANCED PRUNE
We find applying multiple operation of PRUNE for longer-term performances will perform better than only once. The results of applying PRUNE once have been shown in paper. Here, make a comparison. For convenience, we list some results of using ROME to edit GPT 2-XL on the CounterFact dataset.
Table 6: comparison of applying once operation of PRUNE and applying multiple multiple operation.
Mode
General Abiltties
Editing Performance
Method
Edits
Reasoning
Summa
Open-QA
NLI
Efticacy
General
Locality
100
30.12
12.12
22.63
49.83
74,10
ROME+PRUNE (once)
500
27.26
10.78
17.86
45.34
56.80
46.05
72.32
ROME~PRUNE (multiple)
30.17
48.83
76.1
500
32.68
11,52
22.99
51.17
84.6
78.7
75.1
D BROADER IMPACTS
This work offers significant advancements in the field of model editing for LLMs. By addressing the challenge of preserving general abilities while performing sequential edits, PRUNE facilitates continual learning and adaptability in LLMs. This can lead several positive impacts, such as:
Enhanced Adaptability. It enables LLMs to update their knowledge base quickly and accurately without extensive retraining. This adaptability is crucial in dynamic environments where up-to- date information is vital, such as real-time translation services, personalized learning systems, and interactive virtual assistants.
Resource Efficiency. By mitigating the need for full retraining, PRUNE significantly reduces computational resources and energy consumption. This aligns with sustainable Al and makes it more feasible to deploy I.LMs in resource-constrained settings.
Improved Performance in Specialized Tasks. PRUNE's ability to perform targeted edits without compromising overall model performance enhance LLMs effectiveness in specialized domains, such as medical diagnostics, legal analysis, and technical support, where precise and updated knowledge is essential.
While this work offers many benefits, there are potential negative societal impacts that must be considered:
The capability to edit LLMs efficiently could be exploited to inject harmful or biased information into models, thereby spreading disinformation propaganda. This risk is particularly concerning in applications involving social media and news dissemination where LLMs might generate amplify misleading content.
Misuse for Malicious Purposes.
Fairness. Unintended biases could be introduced during the editing process, potentially exacerbating existing biases in LLMs. This could lead unfair treatment misrepresentation of specific
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Published as a conference paper at ICLR 2025
groups, especially if the editing is not conducted with proper oversight and consideration of ethical implications.
Privacy Concerns. The ability update models quickly might also pose privacy risks, models could be edited to include sensitive or personal information. Ensuring that editing processes do not compromise individual privacy is critical, particularly in applications involving personal data.
To mitigate these potential negative impacts, several strategies could be implemented:
Gated Release and Monitoring. Limiting access to the framework through gated releases and monitoring its usage can help prevent misuse.
Bias and Fairness Audits. Conducting regular audits to assess and address biases in the model editing process can help ensure that edits do not unfairly impact any specific group. Developing guidelines for ethical editing practices is also essential.
Privacy Protection Measures. Establishing clear protocols for handling sensitive data during the editing process can help protect privacy. Anonymization and eneryption techniques should be employed to safeguard personal information.
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Reviews:
[{"review_id": "mn3boIRnNz", "reviewer": "Reviewer_oQtG", "summary": "This paper analyzes how the condition number of the edited matrix affects the models' sensitivity to perturbations and proposes a framework called PRUNE to impose constraints that lower this sensitivity. Experiments demonstrate that PRUNE effectively preserves the general abilities of LLMs while maintaining strong editing performance across various tasks.", "questions": "Please see the Weaknesses section above.", "limitations": "", "rating": 8, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "* Sequential editing is indeed a crucial research issue in knowledge editing, and this paper examines it from a relatively comprehensive perspective while proposing an excellent solution.\n\n* The literature review is thorough.\n\n* The evaluation scope is extensive, based on three representative LLMs, including GPT-2 XL, LLaMA-2, and LLaMA-3. It also includes four representative downstream tasks—reasoning, summarization, open-domain question answering, and natural language inference—to broadly demonstrate the impact of model editing on the general abilities of LLMs.\n\n* The performance of the method proposed is good, effectively mitigating the decline in model general abilities caused by sequential edits across multiple metrics.", "weaknesses": "1. It would be helpful to report the results on the \"Probability\" metric, which is described in both [1] and [2]. I would like to know if applying the proposed framework to impose constraints on sequential editing affects the generalization and ripple effects of the edits themselves.\n\n2. It would be more comprehensive if we could see some results on larger-scale models, such as at least those with 13B parameters or more.\n\n3. Methods like MEMIT support batch editing, so it would be worthwhile to experiment on whether PRUNE can still maintain good model general ability in such batch editing scenarios.\n\n---\n**References**\n\n[1] Evaluating the Ripple Effects of Knowledge Editing in Language Models\n\n[2] Editing Large Language Models: Problems, Methods, and Opportunities", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "1v0FNOSrEA", "reviewer": "Reviewer_FxE7", "summary": "This paper investigates the capability of large language models (LLMs) to preserve their general knowledge after sequential editing through a plug-and-play framework named PRUNE. The authors suggest that the condition number of the edited matrix significantly influences the general abilities of the edited models. They propose a method which involves SVD decomposition to ensure that the updated matrix maintains the singular values of the original matrix, thereby preventing substantial perturbations. The paper evaluates the effectiveness of this method across three popular editing methods and three large language models", "questions": "See weaknesses.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. Knowledge editing is an important topic, and addressing sequential editing is a challenging yet meaningful direction.\n2. This paper is well motivated and the design of PRUNE clearly explained.\n3. This paper proposes a plug-and-play method, which demonstrates significant improvements in sequential editing across various models.", "weaknesses": "1.  Some important details need further clarification. For example, in the editing setup, the key $k$ in the key-value pair $(k, v)$ typically does not change, and usually only $W$ and $v$ are modified. It is unclear why the paper focuses on analyzing the changes in $k_i$ instead of $v$ or $W$.\n2.   The PRUNE method imposes constraints on parameters (as described in Equations (3), (4), and (5)), which might potentially reduce the model’s ability to retain other capabilities or preserve historical knowledge. However, the paper lacks sufficient analysis and investigation of the potential negative impacts on the efficacy of the most recent knowledge edits. A more detailed discussion in this regard would improve the overall quality of the analysis.\n3.   A comparison with other sequential editing methods should be included in the related work section. Moreover, additional discussion is needed on works aiming at preserving the general capability of an edited model.\n4.  The model requires utilizing historical $\\Delta W$ in each editing operation, meaning that historical information must be reused. This could potentially lead to an increase in computational resources.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "bUrtc8btAs", "reviewer": "Reviewer_1Sg3", "summary": "The research tackles the issues that arise due to weight shifts in sequential model editing when using weight-modifying approaches. The authors present a new approach, PRUNE, which aims to stabilize editing by maintaining control over these shifts. Importantly, the paper proposes an upper bound on weight modifications, beyond which the model's original capabilities degrade, resulting in reduced performance and an inability to retain edits. This bound serves as a theoretical safeguard, ensuring that model modifications remain within an optimal range for consistent, reliable performance.", "questions": "The PCA visualization discrepancy is not entirely clear maybe a slightly modified visualization would clarify what is being referred to. \n\nThe baseline capabilities of Llama on general abilities in Table 2 are missing.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "The paper introduces a theoretically derived upper bound for weight modification. By defining this threshold, the authors provide a quantitative limit which when exceeded, triggers degradation in the model’s original functions and leads to edit forgetting. This contribution deepens understanding of the trade-offs involved in weight modification and offers a practical guideline for preserving model performance.\n\nThe authors demonstrate that PRUNE effectively mitigates the negative impacts of sequential edits. PRUNE shows considerable performance improvement by stabilizing the model against shifts in weight values, which may otherwise lead to inconsistencies or loss of prior knowledge.", "weaknesses": "The study focuses solely on the Llama-2 (7B) model, with a relatively small set of samples for evaluation which is a concern as editing in large numbers might exacerbate the impact of the shift that needs to be controlled. To broaden the scope, the authors could consider using a smaller model from the GPT series or a single editing approach, allowing for an expanded sample size under computational constraints. This could strengthen the study by providing more robust evidence for PRUNE’s effectiveness across different architectures. (major)\n\nWhile PRUNE is effective, some edits may still be lost in the process, particularly when just applying the operation. A deeper analysis of this limitation could provide valuable insights. (minor)", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "95zyIqCWiz", "reviewer": "Reviewer_KEXb", "summary": "Knowledge editing methods when applied sequentially lead to significant model degradation. In this paper, the authors identify the reasons behind the loss of model's general abilities in the form of increasing singular value of edit-matrix as a function of the number of edits, and propose methods to control that.", "questions": "1. In section 3.2, where the authors perform matrix perturbation analysis, it is not clear to me how that is relevant. The main objection I have is that if an MLP layer in a model is edited, everything until that layer remains the same. This means that \"keys\", which are by definition input to the edited matrix, remain identical before and after editing. Then I'm not sure what is the meaning of ∆k here, since the value of k never changes when an edit is made. \n\n2. In line 241, the spectral norm definition is used, whereas line 203 says that ||*|| represents 2-norm. \n\n3. The hypothetical situation described in line 271-275 is not clear to me. Does the situation involve making N sequential edits about the same fact? If that's the case, then each edit matrix will not be equal to ∆W_1 as the value of ∆W_1 depends on the base matrix, which would be been changed. Although I understand that this is not important in the larger scheme of things, I think it is not correct. I am happy to provide more explanation. \n\n4. In Table 4, we can see that the singular value of the edited matrix increases way more dramatically for MEMIT compared to other methods. Why is that the case? Also it makes me question that the singular values are the only underlying cause for model degradation, as if that was the case, since MEMIT has the largest singular value blow up, it would be the least stable and see maximum model degradation. But that is not the case, in fact MEMIT is the most stable of the three. What is the author's take on this?\n\n5. In equation 4 and 5, I would like some more intuition and explanation of the choice of restraining function. It is not obvious to me why the log function suggested by them works. I think this part of the paper has the least detail whereas I would have preferred a lot more detail here. For example, I would like to see more ablations on the different actions that can be performed on the larger singular values of the ∆W_N matrix. \n\n6. From an intuitive understanding, this paper tries to attenuate the largest singular values of the edit matrix. But the largest singular values are the most important part of a matrix, providing the direction of largest variance and loosely speaking is the direction along which the most significant action is done by the matrix. How is attenuating the most significant action of a matrix not resulting in a lot of issues? Why is it okay to attenuate the largest singular values of a matrix? I think this is a much deeper question and warrants investigation. \n\n7. The experiments shown in Figure 3 and 4 involve too few sequential edits. This method will be a lot more believable if the authors presented results for atleast 1000 edits, but preferably even more. \n\nMy final comment to the authors is that while this paper presents an interesting empirical contribution and figure 5 makes a very good empirical case for usefulness, I have a hard time understanding why the approach proposed by the authors works (questions 4-6). I do not find the explanations or motivations given in the paper appropriate so far. I am looking forward to hearing the author's comments during the discussion phase and am very happy to update my scores based on it if the authors are able to sufficiently clarify these questions.", "limitations": "", "rating": 5, "confidence": 5, "soundness": 1, "presentation": 3, "contribution": 2, "strengths": "1. The authors provide an interesting analysis of the potential reasons behind the loss of general ability of a model as it is edited sequentially. \n2. The proposed methods is plug and play and can be applied on top of all existing parameter modifying model editing methods.", "weaknesses": "Many choices and decisions made in the paper seem unmotivated or not explained properly. I defer to the questions sections where clarifications are requested. I am happy to revise my review post the discussion period once the questions have been answered.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)