Rethinking LLM Unlearning Objectives: A Gradient Perspective and Go Beyond
Authors: Qizhou Wang
Jin Peng Zhou
Zhanke Zhou
Saebyeol Shin
Bo Han
Kilian Q Weinberger
Venue: ICLR 2025 Poster (2025)
Keywords: LLM Unlearning
Primary area: alignment, fairness, safety, privacy, and societal considerations

Abstract: Large language models (LLMs) should undergo rigorous audits to identify potential risks, such as copyright and privacy infringements. Once these risks emerge, timely updates are crucial to remove undesirable responses, ensuring legal and safe model usage. It has spurred recent research into LLM unlearning, focusing on erasing targeted undesirable knowledge without compromising the integrity of other, non-targeted responses. Existing studies have introduced various unlearning objectives to pursue LLM unlearning without necessitating complete retraining. However, each of these objectives has unique properties, and no unified framework is currently available to comprehend them thoroughly. To fill the gap, we propose the metric of the G-effect, quantifying the impacts of unlearning objectives on model performance from a gradient lens. A significant advantage of our metric is its broad ability to detail the unlearning impacts from various aspects across instances, updating steps, and LLM layers. Accordingly, the G-effect offers new insights into identifying drawbacks of existing unlearning objectives, further motivating us to explore a series of candidate solutions for their mitigation and improvements. Finally, we outline promising directions that merit further studies, aiming at contributing to the community to advance this critical field.

Published as a conference paper at ICLR 2025
RETHINKING LLM UNLEARNING OBJECTIVES: A GRADIENT PERSPECTIVE AND Go BEYOND
Qizhou Wang' Jin Peng Zhou? Zhanke Zhou' Bo Han Kilian Q. Weinberger
Saebyeol Shin?
TMMR Group, Department of Computer Science, Hong Kong Baptist University 2 Department of Computer Science, Cornell University
ABSTRACT
Large language models (LLMs) should undergo rigorous audits to identify poten- tial risks, such as copyright and privacy infringements. Once these risks emerge, timely updates are crucial to remove undesirable responses, ensuring legal and safe model usage. It has spurred recent research into LLM unlearning, focusing erasing targeted undesirable knowledge without compromising the integrity of other, non-targeted responses. Existing studies have introduced various unlearning objectives to pursue LLM unlearning without necessitating complete retraining. However, each of these objectives has unique properties, and no unified frame- work is currently available comprehend them thoroughly. To fill the gap, we propose a toolkit of the gradient effect (G-effect), quantifying the impacts of un- learning objectives advantage is its broad ability to detail the unlearning impacts from various as- pects across instances, updating steps, and LLM layers. Accordingly, the G-effect offers new insights into identifying drawbacks of existing unlearning objectives, further motivating us to explore a series of new solutions for their mitigation and improvements. Finally, we outline promising directions that merit further studies, aiming at contributing to the community to advance this important field. The code is publicly available at: https: / github.. cwm/ oolr group/G-ou--- GeGG--ffffctt
model performance from a gradient perspective. A notable
INTRODUCTION
Large language models (L..Ms) (Brown et al., 2020; Touvron et al., 2023b; Achiam et al., 2023) rep- resent the cutting edge of machine learning for the field of language understanding. These models architectures (Vaswani et al., 2017) with bil-
typically leverage multi-head attention decoder-basee lions of learnable parameters and are autoregressively trained (Zhao et al., 2023) over web-sourced datasets encompassing trillions of tokens. Such extensive scaling enables LLMs to handle broad spectrum of complex linguistic tasks, demonstrating remarkable proficiency in understanding and generating languages across a board range of practical applications.
The scaling of LLMs, on the other side, also brings notable drawbacks alongside its benefits. A pri- mary concern is their high tendency to memorize data, which can reproduce sensitive information encountered during web-sourced training, such copyright and privacy-related content (Yao et al., 2023a). These issues are particularly concerning due to the potential misuse of LLMs for illegal activities (Li al., 2024), also posing challenges to protect individual rights to be forgot- ten (Zhang et al., 2023). Mitigating these undesirable behaviors in LLMS is non-trivial, involving regularly auditing LLMs to recognize sensitive content and subsequently adjusting the associated, parameterized knowledge. In previous works, supervised fine-tuning (De Cao et al., 2021) and align- ment methods (Ouyang et al., 2022) have been explored to overwrite I.LMs against such undesirable model behaviors. However, these well explored directions face practical deficiencies -thy can be costly (Yao et al., 2023b), require high-quality crafted preference datasets (Chowdhury et al., 2024), and exhibit concerns regarding robustness (Patil et al., 2023; Qi et al., 2023; Wang et al., 2024).
Work done during a remote visiting at Cornell University. Correspondence Bo Han (bhanml (ww@@//oom.....oooooc hkhu.edu.hk).

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LLM unlearning (Yao al., 2023b) has emerged as promising alternative, with direct goal of removing parameterized knowledge targeted to be unleamed, meanwhile preserving the model integrity for all other, con-targeted data (Wang et al., 2025). Highlighted by Yao et al. (2023b), LLM unlearning is cost-effective over aforementioned more demanding methods, thus attracting emerging research attention these days (Liu al., 2024). A representative baseline of LLM unlearning is gradient ascent (GA) (Maini et al., 2024), adjusting LLMs to increase the prediction losses for targeted data thereby removing parameterized knowledge, GA offers a potentially viable path to implement LLM unlearning; however, it is severely susceptible to excessive unlearning (Zhang et al., 2024), where the effectiveness in removing undesirable data comes at the high cost of compromising the overall model integrity. It motivates series of subsequent works that improve upon GA, such as negative preference optimization (NPO) (Zhang et al., 2024), preference optimization (PO) (Maini et al., 2024), and representation misdirection for unlearning (RMU) (Li et al., 2024).
Given the increasing number of unlearning objectives, we need to discern good objectives from those less promising ones. A step further, it is also interesting to pinpoint beneficial components within existing methods, isolating those that are useless or potentially harmful. Sadly, to our knowledge, general toolkit for in in-depth analysis of various unlearning methods is still lacking. To bridge this gap, we propose the concept of the gradient effect (G-effect), which approximates the performance change associated with particular unlearning objectives via the dot product of their gradients, ef., Definition 1. The G-effect provides more than mere performance evaluations-it enables detailed examinations of various unlearning methods for their impacts with respect to data points, updating steps, and layers, cf., Section 4. We outline below for some of the general observations we achieved.
Unlearning affects shallow layers more. Shallow layers are more affected than deeper layers, showing that general knowledge encoded in shallow layers undergoes substantial alterations.
Unlearning compromises retention. Although conceptually existing (cf., Section 3), current unlearning objectives all fail to retain the overall performance when conducting unlearning.
Excessive unlearning is harmful. An excessive extent of unlearning has severe impacts such that the deterioration in common model responses can outweigh improvements in unlearning.
Risk weighting is powerful. Prioritizing certain points is justified to be effective for unlearning. However, there still exists a large space to further refine risk weighting mechanisms.
Regularization is important. Regularization terms continue to play crucial role in maintain- ing overall model integrity, with the KL (Maini et al., 2024) emerging as a promising choice.
We benchmark both existing and new methods explored throughout analysis the well- established TOFU fictitious unlearning datasets (Maini et al., 2024). Our experiments identify several new state-of-the-ards that merit further attention. Additionally, based on our analysis, highlight promising research directions that warrant exploration to further advance the field.
2
LLM UNLEARNING
We focus on auto-regressive LLMs parameterized by O, which recursively estimate the probability distributions over the next tokens, denoted as p( |s; 0). LLMs are, in general, trained on large- scale, web-sourced corpora following the distribution D. with the negative log-likelihood (NLL) loss function of log p(s; s; 0), where p(s; 0) 11
|a| p(s* ( 0) with s' the i-th token and < the
prefix up to s'. While LLMs are capable of handling a broad spectrum of language generation tasks, the use of training corpora sourced from the open world raises the risk that our LLMS will learn from sensitive data, precipitating a series of legal and ethical concerns (Liu et al., 2023).
LLM Unlearning. These issues necessitate the need for post-training mechanism that enables LLMs to eradicate any parameterized knowledge that is undesirable. This requirement motivates the recent research on LLM unlearning (Yao et al., 2023b; Maini et al., 2024), of which the main goals are in two folds (a) ensuring the removal of data / knowledge targeted to be unlearned and (b) retaining the integrity of model responses for non-targeted data. Formally, we consider the data distribution D,, that should be unlearned and define the risk metric R to assess model performance. Then, our goal is to adjust the original L.LM parameters O, to get the unlearned ones O,, such that:
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Removal. The performance the unlearning dataset Du should significantly deteriorate, i.e., R(Du: 0.) > R(Du: Bo), revealing effective unlearning on data targeted to be erased. Retention. The performance on other data, i.e., Dr (D. should be maintained or enhanced, i.e., R(Di)Du; 0.) I R(D, DDu (o), ensuring model responses on common data are not damaged.
Here, we consider practical objective of erasing targeted knowledge as much possible (Liu et al., 2024), i.e., full removal, slightly diverging from the classical definition of machine unlearn- ing (Bourtoule et al., 2021) that seeks make models behave if they were trained without the targeted data, i.e., influence removal. The pursuit of full removal simplifies our subsequent discus- sions, and as we will see later in Section 5, the outcomes of these two goals are typically aligned.
This paper delves into exploring various objective functions that implement LLM unlearning, topic that requires our fundamental interest. As an example, GA (Yao al., 2023b) directly increases the NLL loss for targeted data, of which the objective is articulated as ming Ex,,DD, log p(..i 0). GA represents one of the pioneering methods for LLM unlearning, paving a feasible road to implement unlearning in practice. However, it often exhibits the propensity excessive unlearning (Zhang et al., 2024; Wang et al., 2025)-the efficacy in eliminating undesirable knowledge comes at a high cost to compromise the model integrity. It motivates series of subsequent works (Zhang et al., 2024; Maini et al., 2024; Li et al., 2024), which will be discussed later in Section 4.
3 G-EFFECT
Before delving into specific methods, we need proper criteria for assessing whether an objective is suitable for unlearming or not. Recalling our earlier discussion on the main goals of unlearning, we can quantify the performance change before and after unlearning to evaluate their effects, i.e., R(D,; 0.) R(Dui 0.) for removal and R(D, DD: 0..) RDD, (Du; 0o) for retention. Sadly, merely comparing performance provides limited insights into understanding the underlying mecha- nisms (cf., Section 4). Therefore. suggest a more insightful scheme that can facilitate the analysis of various unlearning methods from a gradient perspective, named the gradient effect (G-effect).
Generally speaking, the G-effect compares the gradients of the unlearning objective Lu and the risk metrie R. If the gradients of f. align in similar directions to R, model updating based on Lu is capable to enhance model performance measured by R. an obvious alternative of R(D; 0.) R(D; 0.) to measure the performance change. The degree of such similarity between gradients can be quantified using their dot products (Lopez-Paz & Ranzato, 2017): A positive dot product indicates that L. is capable to improve R, whereas a negative dot product suggests potential harm to R. Please refer Appendix A for formal derivation. It motivates the G-effect as follows.
Definition (G-effect). The G-effect e!!) for an unlearning objective Lu at the 1-th step of model updating is given by VD (TTDD:OOTVVVO (D,, (()). We further define the un- learning G-effect (t) VoR(D,; ((0) VoLa 0(0) and the retaining G-effect (t) RoR(D, DDu; T (D 0(0)
reflect the respective goals of removal and retention.
(eD(D(Du
The G-effect measures the impacts of unlearning ob- jectives on either targeted or non-targeted data when implementing gradient updates. Overall, to fulfill the unlearning goals outlined in Section 2, we aim for no- tably negative values of ( pursue a sufficient re- moval of targeted knowledge and non-negative values
< 0 0
2
of ez (4) maintain the model integrity for non-targeted data. Figure 1 further depicts these two essential gra- dient conditions to ensure effective unlearning:
Figure Gradient Directions and Un- learning Behaviors. We show directions for VoR 0.) and VDR(D) 0.) and regions ensuring (t) < 0 (red) and e( 0 (blue). Their intersection (black dashed) fulfills the unlearning goals.
Removal, The red region indicates ( < 0, en- suring Lu to eliminate targeted knowledge.
Retention, The blue region represents ( 2 0, ensuring C., to retain the overall model integrity.
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What Can We Learn from the G-effect? In Figure 1, the intersection, delineated by black dashed lines, is the region that meets the primary goals of unlearning effeective removal of targeted knowl- edge while retaining the integrity of non-targeted data. This area highlights the conceptual possibil- ities of achieving perfect unlearning objective, under the mild conjecture that (DR 0.) will differ from VoR(DD)D Du; 0.) more less. Also, the dependency dynamics of unlearning, and the gradients helps us to explore the impacts of particular layers or data points involved during unlearning. It will facilitate our understanding of existing unlearning mechanisms, which will be detailed below. Please refer to Appendix A for more discussions.
& enables to examine the
4 ANALYSIS FOR UNLEARNING OBJECTIVES
In this section, we employ the G-effect to assess a range of unlearning objectives that are well- recognized, aiming to understand their mech- anisms as well as identify their advantages and deficiencies. Due to the high costs in fully com- puting the G-effect, we focus on experiments based on 5% TOFU fictitious unlearning (Maini et al., 2024) with Llama-2-7B (Touvron et al., 2023a) (cf. Appendix B). Later in Section 5, we will demonstrate that the conclusions can be generalized to many other unlearning scenarios. All the methods will run for 5 epochs, totaling about 60 steps. Moreover, as indicated in Fig- ure 2, we will report the unlearning (red) and retaining (blue) G-effect, as well as their detailed values for particular layers within Llama-2-77 2B (dashed lines for the stacks of layers and dash- lines for input/output layers). We default to consider the NLL as the risk metric R.
unlearn embed
shallow
middle deep
retain embed
shallow
middle
deep
Im
Figure 2:
Figure Legends We present the un- learning (unlearn) and the retaining (retain) G- effect, and also their values for specific layers, in- cluding input embedding layer (embed), layers 1- 1 (shallow), layers 12-22 (middle), layers 23-33 (deep), and output unemhedding layer (Im).
4.1 GRADIENT ASCENT (GA)
As discussed in Section 2, GA represents one of the most basic unlearning objectives (Yao et al., 2023c), which simply decreases the log-likelihood log p(s.; 0) for the unlearning data.
The G-effect across Unlearning Steps. We illustrate the G-effect of GA in Figure 3(a). As we can see, the unlearning G-effect reflects the high capability of GA in erasing parameterized knowledge for targeted data, with its values rapidly declining from about to -3.5 x 10 However, this excessive extent of unlearning incurs large cost to the integrity for non-targeted data, evidenced by the trajectory of negative values in the retaining G-effect that mirror the scales and trends of the unlearnnn G-effect. Overall, such scenario suggests that the improvements in unlearning are accompanied by similar, or even greater, deterioration on non-targeted data.
Note that relatively near-zero values of the G-effect in the later updating stages do not imply that the model can relearn the knowledge. In general, the G-effect exhibits cumulative behaviors, where the presence of extremely negative G-effect, particularly between steps 20 to 40, has already indicated a large deterioration on model performance. Smaller values of the G-effect in the later stages only suggest that the subsequent damage to model integrity less severe, mainly due to the GA objective reaching its empirical convergence stage. Refer to Figure 9(b) in Appendix C.1 for more analysis.
The G-effect across Layers. We also observe that the G-effect values are notably greater in the shallow layers than those in the middle and deep layers, which can be more clearly shown in Fig- ure 3(b). It indicates that the general knowledge, which parameterized within shallow layers, is notably distorted, while such side impacts are less severe for middle and deep layers with context- specific knowledge (Geva et al., 2020; Belrose et al., 2023). It is also worth noting that we isolate the input embedding layer (embed) from other shallow layers (shallow), where we observe that the input embedding layer has relatively negligible impacts on both removal and retention, highlighting the distinct influences of the GA unlearning procedure low layers. Furthermore, the middle and top layers exhibit much smaller G-effect values than that for shallow layers. However, the G-effect for the last layer, i.e., the output unembedding layer (LMM,
the input embedding layer and other shal-
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Figure 3: The G-effect for GA and WGA. We depict the G-effect for GA (a) and its values in the range between about -3.5 x 10t and 0 in (b). We further depict the G-effect for WGA, which improves upon GA following equation 2, (c). The legends are summarized in Figure 2. The horizontal axis denotes the unlearning step and the vertical axis denotes the values of the G-effect.
is notably large and do not converge to near zero. This behavior suggests that such a linear model performs some scaling operations to further reduce the GA objective that is lower unbounded.
Unlearning Mechanisms. We hope to further explore the unlearning behaviors behind GA, par- ticularly focusing on its wrong tendency towards exhibit extremely negative values of the retaining G-effect. Specifically, the gradients of (us(Dus O) with respect to 0, i.e., V CoC (D; 0), are
E Bn DD
(1)
p( S
inverse confidence
where the inverse confidence term tends to allocate more attention to those tokens that have been notably unlearned, along with the decrease of the likelihood p(s 0) throughout GA.
In this case, even minor negative values of each V VoR(D;;) V s ;) 0) can result in the cor- responding (D 0) p(s 5 0)-00---- -V Vep( Is 0) be extreme. This trend will lead the extreme negative values of the unlearning G-effect, consistent with prior findings for the excessive unlearning of GA (Wang et al., 2025). Therefore, this inverse confidence mechanism predomi- nantly responsible for excessive unlearning. One can counteract the impacts of the inverse confi- dence by weighting the log-likelihood for each token via its own confidence, i.e.,
Es,- D.. Σ w W.. log Dogp(suls
with ""."" = s5 0) the confidence weights for the i-th token and a the hyper- hyper-paramee parameter of inverse temperature. We refer to this approach as the weighted GA (WGA). An example of its G-effect in mitigating excessive unlearning is illustrated in Figure 3(c). Remarkably, that the negative impact on common data is considerably less severe compared to the improvements observed on targeted data. Its underlying mechanism is not mystic, functioning early stopping to curb the unlearning extent. Particularly, when the unlearning extent is well-controlled, even the original GA can outweigh the improvements of unlearning obvious scenario that is further elaborated in Figure 10 of Appendix C.I. Overall, the findings em- phasize that excessive unlearning profoundly compromises the overall model integrity, necessitating careful controls. For more detailed discussions about WGA, please refer to Appendix D.I.
observe
the deterioration integrity, a less
4.2 NEGATIVE PREFERENCE OPTIMIZATION (NPO)
NPO is motivated by direct preference optimization (DPO), an alignment method (Rafailov et al., 2024), which originally utilizes paired corpora comprising preferred versus dis-preferred data. NPO segregates the dis-preferred part from DPO, heuristically employing it as the unlearning objective, of which the formulation can be written as
B En, D. log (1 p(sui
p( sn; 0.)
where 3 is the inverse temperature. NPO has shown notable enhancements over GA in preserving the model integrity, which is recognized as the current state-of-the-art within the community.
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Figure 5: The NPO Weighting Mechanisms. We depict the curves average NPO weights in (a) and the relationship of NPO weights with PG-effect in (b). Distributions of PG-effect for different value ranges of whPo are depicted, considering the checkpoints at 5, 10, and 15-th steps jointly. Moreover, darker shades within distribution contours signify the groups of wp with overall larger weights. We further depict the G-effect for an improved version of NPO, named TNPO, in (c). The horizontal axes denote the unlearning step for (a) and (c), and the unlearning G-effect for (b). The vertical axes denote the NPO weights for (a), the retaining G-effect for (b), and the G-effect for (c).
The G-effect across Unlearning Steps. We show the G-effect of NPO in Figure 4. We observe that its values converge much faster than GA, aligning with previous observations (Zhang et al., 2024). Moreover, the magnitudes of G-effect for NPO are notably smaller than those observed with GA. In terms of the unlearning G-effect, it indicates that the unlearning strength of NPO is weaker; however, for the retaining G-effect, it suggests that NPO better preserves the model integrity. More importantly, magnitudes of retaining G-effect outweigh those of unlearning when / 1 or 2, signifying that the negative impacts on model integrity are less pronounced than the beneficial effects of unlearning, rendering NPO promising method to mitigate excessive unlearning.
The G-effect across Layers and 3. Similar to GA, deeper layers exhibit weaker G-effect. How- ever, both the input embedding and output linear layers display negligible values, which are dif- ferent from the behaviors seen with GA. For both middle and deep layers, their retaining G-effect relatively small. Furthermore, across different values of the inverse temperature, we observe that larger 3 makes the G-effect converge faster and their magnitudes become smaller. This phenomenon generally arises because smaller / causes the NPO formulation more closely resemble that of GA (Zhang et al., 2024), of which the power in controlling the extent of unlearning is weaken. The relationship between GA and NPO is further elucidated below equation
Unlearning Mechanisms. We now aim to understand the factors that contribute to the efficacy of NPO. To begin with, we write the gradients NPO with respect to the following
E Eg *n
Aonoo Vo log p(s.; 0),
(4)
with uno p(a.:0)) -ppPpp...,0 83 Notably, compared with GA in equation 1, we find that NPO exhibits similar gradient formulation, albeit with a reweighting scheme wPpo Therefore, wapo in-depth focus.
2)
primarily contributes the advantages of NPO over GA, thus requiring
We illustrate the curves of wipo Figure 5(a), observing a rapid decrease of wTpo from 1 to The decreases-indicativee formulation of wppe reveals that, the NPO risk decreases indicative of the drop in the confidence p(s,; -tethe the weight wip' reduces consequently. This weighting behavior seems quite resemble to WGA. Then, the question arises whether wapo encompasses some intriguing mechanisms beyond

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early stopping as in WGA. To further elucidate the G-effect of NPO, expand it as follows:
Ba w VoR(DD; (0) Vo p(s; )0)).
(5)
PG-efflect
which details the G-effect on individual data points, represented as the product of the NPO weighting term why and the point-wise G-effect (refer to PG-effeect of GA. Accordingly, we plot the joint distributions for the PG-effect of GA with respect to unlearning (i.e., D = D.) and retention (i.e., D = D. (,) Figure 5(b). These distributions are categorized into five groups based on the associated different value ranges of wPpo As we can see, the distributions of PG-effects vary notably across different ranges of w"... Generally speaking, wa where the retaining PG-effect is near-zero. it is a preferred scenario as w can prioritize data points that have small negative impacts on model integrity. However, the side effect is to emphasize those data points with less contributions to unlearning, thus compromising the unlearning strengths. We conclude that NPO weighting can prioritize certain points that have small negative impacts on non-targeted data, thereby enhancing the overall model integrity after unlearning.
tends to allocate larger weights to points
One Step Further. We also notice some shortcomings for the NPO weighting mechanism. First, there are many failure cases where some data points with near-zero retaining PG-effect while large unlearning PG-effect is inappropriately assigned with small weights. Also, the distribution of PG- effect with whr in the range between 0.4 to 0.6 demonstrates a wrong trend in assigning large weights to those data points that have large negative impacts on model integrity, i.e., notably negative retaining PG-effect. Ideally, we hope the weighting mechanism can prioritize points that not only have near-zero retaining G-effect and also exhibit large negative unlearning G-effect, a capability that the current NPO weighting does not possess.
It is worth noting that our above analysis does not disqualify wapo as a meaningful mechanism. In- deed, when uapo applied token-wise, which allows for more granular control over the unlearning process, the unlearning procedures are notably more effective. Formally, consider the objective
E B DD D.
Empo log sms
p( (1
2p(a 1e 0)
p( 00)* +p(s' 15 o. generalizes the weighting mechanism of NPO for tokens. We refer to equation 6 as token-wise NPO (TNPO) and show its G-effect in Figure 5(c). Therein, we observe that the unlearning G-effect exhibits sufficiently large negative values while the retaining G-effect is overall close-to-zero. It underscores the efficacy of w. tokens during unlearning, thus achieving unlearning efficacy. Please refer to Appendix D.2 for more discussions about TNPO, as well as its further improved version named WTNPO.
where wa..
tnpo in properly prioritizing certain
4.3 MORE OBJECTIVES
We also examine two other unlearning objectives that do not fall into the variants of GA.
Preference Optimization (PO) (Maini et al., 2024) overwrites LLMss with new outcomes instead of crasing old ones. Given some prefix ς² and the new suffix 5po. the PO unlearning objective is given by
Gelfect
Es.-D. - logopspoll <);
stop 20
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step 50
is particular suitable for LLMS fine-tuned for ques- tion answering, where 55 is the original question and Spo is the new answer. We show its G-effect in Figure 6. Unfortunately, we note that the PO may not be suitable for LLM unlearning: Its validity in erasing targeted knowledge is limited to the early phases model updating. Then, PO may even in- advertently facilitate the knowledge relearning.
-10
Figure 6: The G-effect for PO. The legends for the G-effect are in Figure 2. The hor- izontal axis denotes the unlearning step and the vertical axis is the values of the G-effect.
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Figure 7: The G-effect for RMU. The legends for the G-effect are summarized in Figure The horizontal axis denotes the unlearning step and the vertical axis indicates the values of the G-effect.
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Figure 8: The G-effect for Regularization. The legends for G-effect are Figure 2. The horizon- tal axis denotes the unlearning step and the vertical axis indicates the values of the G-effect.
Representation Misdirection for Unlearning (RMU) (Li et al., 2024) implements unlearning by perturbing model representation. Denote the embedding features by ((8; 0), RMU is articulated as
B Ben Du
1 st -c.4 ul
(8)
E=
where u is a random vector with elements sampled uniformly from [0, 1) and is scaling hyper- parameter. We adopt outputs for 11-th, 22-th, and 33-th (before unembedding) layers o0s; 0), and their G-effect is summarized in Figure 7. We notice that its performance is very sensitive to different choices of (ss; 0), where middle (22-th) layers seem to be better choice than shallow (1 (1)- and deep (33-th) layers. In Appendix C.3, we further show that RMU is also sensitive to varying e, where wrong configuration may be even completely contrary to the goal of unlearning.
Moreover, we observe that the improvements on unlearning come at similar costs in terms of im- pairing the general utility, a phenomenon reminiscent of the challenges faced with the vanilla GA. can also be considered as a scenario of excessive unlearning, where the magnitudes of parameter up- dates are too large, thus failing to preserve essential knowledge for common data. Given its current limitations, more explorations are needed to advance unlearning through embedding perturbation.
4.4 REGULARIZATION
Although we have identified several promising objectives, the retaining G-effect overall remains negative. It indicates that there are still adverse effects the common model integrity. We also want to note that, while some of the magnitudes are steadily small, e.g., for the retaining G-effect of TNPO in Figure 5(c), their accumulation across steps will still have notable impact. A wide- accepted strategy to improve retention is by regularization, involving a set of additional common data to maintain the original model responses. In this section, we explore representative regu- larization terms, named gradient difference (GD) ( (Yao et al., 2023b), KL divergence (KL) (Maini et al., 2024), and representation retention (RR) (Li et al., 2024) (cf., Appendix E). We choose NPO as the unlearning objective, computing the G-effect for various regularization terms. The results are summarized in Figure Overall, our observations indicate that RR does not serve for effective reg- ularization due to its unstable G-effect behaviors. In contrast, both GD and KL effectively facilitate knowledge retention. However, the strength of the G-effect associated with KL surpasses that of GD, leading to suggest KI. default choice of regularization for retention.
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5 EVALUATIONS
In this section, we further benchmark aforementioned unlearning objectives on the TOFU unlearning datasets (Maini et al., 2024), focusing the removal of fictitious author profiles from LLMs fine- tuned on them. Comprising a series of poestion-answer pairs about author profiles, the TOFU dataset is further separated into targeted and non-targeted parts, thereby providing an intuitive platform to effectively evaluate the impact of various unlearning methods.
We test two popular LLMs: Phi- 1.5 (Li et al., 2023) and Llama-2-7B (Touvron et al., 2023b), un- der three ratios-1% 1%, 5%, and 10%-off targeted data. For hyper-parameter tuning, we follow the unlearning with control (UWC) framework (Wang et al., 2025), which surpasses the challenges of trade-offs between removal and retention. Please refer to Appendix for additional details on the experimental setups and Appendix G for hyper-parameter configurations.
Configurations. We default to apply the following settings: the AdamW optimizer (Loshchilov & Hutter, 2017), a batch size of 16, maximal gradient norm of 1, and the (un)learning rate of 2 for Phi-1.5 and 1e for Llama-2-7b with linear warm-up for the first epoch. Each method is executed over a total of 5 epochs. Moreover, the model-specific hyper-parameters after fine-tuning are as follows: For the 1 1% and 5% setups, we set a = 5 for WGA; 3 = 0.5 for NPO; 3 4 for TNPO; a = 1.5 and 3 5 for WTNPO. For the 10% setup, we set a = for WGA; B = 0.5 for NPO; 1.5 and B 7 for WTNPO. For RMU, we set the 9-th layer with e 4 for Phi-1.5 and the 21 layer with c = 2 for Llama-2-7B. Moreover, our experiments are conducted on GPUs and Intel(R) Xeon(R) Gold 6248R CPUs. The systems utilize Transformers version 4.42.4 and CUDA version 12.1.
3 3= 5 for TNPO;
computation nodes equipped with NVIDIA-AI00-
Evaluation Metrics. We adopt the suggest evaluation metrics from (Maini et al., 2024), specifically forget quality (FQ) for unlearning and model utility (MU) for retention. FQ evaluates model perfor- mance by jointly examining output quality, confidence, and truth ratio, fully reflecting the common model integrity. MU produces p-values to assess the change of model outputs between the gold standard model, which is trained from scratch without targeted data, and the unlearned model. We utilize the log-scale for these p-value to make the results more readable. We aim for high values in both FQ and MU. We further report the ES scores (Wang al., 2025), which more directly quantify the extent of knowledge parameterized within models, potentially making them more effective met- rics than FQ and MU. The ES scores can be calculated for either targeted data or non-targeted data, thereby reflecting model performance of removal and retention, respectively. Notably, the ES scores are available in two variants: ES-exact, which used for original data to reflect direct parametriza- tion, and ES-perturb, which applies to their rephrasing to reflect generalization. Overall, the ES scores should be high for retention and low for removal.
The results are summarized in Table 1, where we use KL regularization to stabilize the unlearning procedures. Among previous methods, PO is identified as the least attractive choice, which may even inadvertently maintain data that ought be unlearned, corroborating tions from the G-effect analysis. Conversely, GA is most effective in removing targeted data but at the expense of compromising model integrity. Both NPO and RMU offer a better balance between data removal and retention, with NPO overall outperforming RMU (except for 10% unlearning with Llama-2-7B). This can be attributed to the more stable G-effect of NPO over that of RMU.
Analysis.
observa-
For our newly explored methods, WGA remarkably overcomes the drawbacks of GA, particularly in mitigating excessive unlearning, meanwhile maintaining its strong capability for the removal of targeted data. Additionally, both TNPO and WTNPO improve upon NPO by not only enhancing unlearning performance but also excelling in retaining common performance. WTNPO typically outperforms TNPO as it further mitigates the potential issues of excessive unlearning observed in TNPO. Overall, when comparing methods across different unlearning setups and models, WGA and WTNPO stand out as the most effective, underscoring the crucial role of loss weighting in the un- learning process for LLMs. However, we recommend the default use of WGA, as it requires tuning only one hyper-parameter and generally perform well, recognized as effective for LLM unlearning.
is worth noting that most of the above analyses are based on our results measured by ES. When it comes to MU and FQ, our refined methods can still outperform it previous counterparts in most cases, suggesting that the goals of full removal and influence removal are generally aligned. How- ever, there is also an abnormal case of 5% unlearning with Llama-2-7B, where the MU scores of

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Table 1: Comparison between Unlearning Objectives on TOFU with KL regularization sta- bilize unlearning, 4 t indicate smaller / larger values are preferable. The log scale is used for FQ to improve readability. The top two results are in bold font for each unlearning setup.
LIM
Phi-1.5
Llama-2-78
sctup
method
retain
ES
unlearn
retain
ES ES-peturb
unlcam
MUT
FQT
retain
ES-oxact
unlearn
rotain T
ES-penturb
unlcam
MU
PQ2
unlearning
0.4433
0.5969
0.5232
-7,5930
(AA
0.1101
D30890
0.3799
-0.5471
0.425%
IJU570
0.5778
21,5471
PO
0.3667
0.8472
0.1622
0.3688
0.5112
-.2474
0.7508
0.8399
0,4724
0.5259
0.6245
-5.8051
WGA
0.3629
0.03444
0.1857
0
0,5191
-0.5471
0.6701
0,0818
0.3814
0.0001
0.6541
-0,0547
1%
XPO
0.2727
0.0916
0.1125
0.7233
0.4845
-29162
0.4757
0.1215
0.3890
0.0905
0.6243
-1.3251
TNPO
0.3351
0.0665
0.1239
0.4991
-00847
0.5168
0.0337
0.4304
0.6495
-0,0847
WINPO
0.4117
0.1969
0.5126
4.3667
0.6701
0.0807
0.3734
0.0001
0.6453
400847
RMU
0.2397
0.0850
0.1539
0.0567
0.4349
0.5471
0.2397
0,0850
0.1539
0.0567
0.5298
-1.5254
before unlearning
0.4433
0,5619
0,2115
0.2354
0,5232
.2965514
0.8277
0.7735
0,5302
0.4126
0,6345
33.13330
GA
010000
0,0000
0J0000
00000
-11.4900
00000
1,0000
D0220
0,0000
(.000
-12,4290
PO 0.2646
0.7966
0.1629
0.4925
0.5118
-265006
0.5572
0.8437
0.3682
0,4933
0.646
-28.8776
0,2980
0.1199
0.1645
0.1999
0.5108
-1.306
0,4709
0.0053
0.3982
0,0080
0/6438
-1,3271
5%
NPO
0.0876
0.1267
0.0876
0.0099
0.3841
-7.7503
0.1747
0.0764
0.1233
0.0802
0.5285
-9,9500
TNPO
0.1695
0.0126
0.0805
0,038
0.4673
-2. 18687
0.5817
0.0160
0.3495
0.099
0.6848
-52.1350
WINPO
0.2185
0.0179
0.1281
0.0188
0,5084
-3:2299
0.4595
0
0,3989
0.0000
0,6410
-21
RMU
0,2162
0.0000
0.1299
0.0000
0.2744
-1.9514
0.1262
0.0000
0.1299
0.0000
0.5801
22144299
before unlearning
0,4799
39.0042
0,5277
0.8307
-44,594
GA
010000
0,00000
0J0000
030000
D1000
0,0000
PO
0.3222
0.7321
0.1406
062667
0.507S
-38 2556
0.5572
0.8437
0.3777
04305
0.6240
-3977004
WGA
0,3466
0,0000
0,1651
0,0000
0,5183
-9.0336
0.6642
0,0287
0.4289
0.0123
0.6235
.24.8591
10%
NPO 0.0859
0.0955
0.0716
0.0710
0.3878
-10.5721
0.1296
0.1388
0,1085
0,1410
0.5055
-12.1912
TNPO
0.2085
0.0163
0.0991
0.5009
-7.6651
0.4531
0.0192
0.0168
0.6381
-13,4785
WINPO
0.2969
0.1862
0.0105
-7.0070
0.4997
0.0278
0.3246
0.0174
0.6236
-6.6801
RMU
0.0317
0.0541
0,0357
0.0632
0.3163
-7.0070
0,2580
0,0194
0.2017
0.0174
0,5930
-16.2771
our proposed methods remain high, while the FQ for NPO notably surpasses methods. Given that our methods better preserve retention, we believe they offer more practical applicability than NPO. Nonetheless, the disagreement between ES and FQ metrics still deserves our further attention. necessitating deeper explorations into the reliability of these metrics and determining which goals. either full removal influence removal, are better suitable for LLM unlearning.
6 CONCLUSIONS
LLM unlearning aims to eliminate unwanted knowledge while preserving the overall model in- tegrity. This paper particularly focuses on understanding the mechanisms behind various unlearning objectives, based on our proposed evaluation tool named the G-effect. Our findings suggest that GA- based unlearning objectives remain to be promising, but we need to mitigate the risk of excessive unlearning and the potential harm on model integrity. We further introduce advanced unlearning objectives, such as WGA and TNPO, that set new state-of state-of-thh--rte within the community.
Drawbacks of the G-effect. As shown in Appendix A, to motivate the G-effect, we assume that singular values of the matrix A have low variance. However, it may neglect important model prop- erties with unlearning smoothness. Refining the G-effect to better incorporate A could make the evaluation scheme more accurate and insightful. However, its computation requires estimating the Hessian matrix, tedious process that needs approximation (Singh & Alistarh, 2020). Also, using NLL as the risk metric to define R may not be the optimal choice, given that model likelihood can be misleading to characterize the knowledge parametrization (Duan et al., 2024).
Promising Directions. Although we achieve several powerful unlearning objectives. their practical implementations still require regularization for retention; otherwise. the common model integrity will be compromised. Thus, further enhancements in unlearning objectives are anticipated, such as devising improved weighting mechanisms (Ren et al., 2018) and exploring robust representation methods. Moreover, on the optimization side, techniques like sub-model updating (Yao et al., 2024) and layer-adapted updating (Schaul et al., 2013) can be promising to further advance the research area. On the data-oriented side, unlearning methods that incorporate filtering or prompting to foster improved G-effect behaviors also be intriguing, while currently not covered. On the evaluation side, it is also intriguing to explore the G-effect using advanced metrics, such as risk aversion (Yang et al., 2023) and effective robustness (Taori et al., 2020), to better quantify the impacts of unlearning.
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ETHIC STATEMENT AND REPRODUCIBILITY
Unlearning mechanisms are crucial for LLMs, as they facilitate the removal of sensitive data that may lead to copyright and privacy violations, significantly boosting the overall confidentiality of models. By identifying and eradicating privacy risks, we fulfill the ethical obligation to respect in- dividual privacy. Adapting LLMs to prevent the replication sensitive information further aligns with the principles of responsible data use. In essence, the process of unlearning in LLMs enhances socictal well-being by improving both the safety and legal compliance of these technologies. Ad- ditionally, benefit the research community by introducing designed to measures the comprehensive impacts of unlearning objectives on LLMs. This tool fa- cilitates detailed analysis of existing unlearning objectives and offers the potential to evaluate the efficacy of broad range of new methods. The deployment of such toolkit contributes to open in- quiry and could encourage collaboration and further studies in this pivotal area. For reproducibility, we have detailed the configurations, hyper-papne parameter setups, and hardware specifications. The code publicly available at: https: //gi///ii /ttpbub.tbb/gt//gg//gg thub. com/ tml r gww.ggrooooeeeeeeeeeeee
analytical tool, the G-effect,
ACKNOWLEDGMENTS
JPZ is supported by grant from the Natural Sciences and Engincering Research Council of Canada (NSERC) (667916). The authors also would like express their sincere gratitude to the anonymous reviewers and the area chairs for their thorough review and constructive feedback. Their insight- ful comments and valuable suggestions have significantly enhanced the quality and clarity of this manuscript. We deeply appreciate their time and effort in helping us improve our work.
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A A FORMAL MOTIVATION FOR THE G-EFFECT
Overview. To formalize our key concept of the G-effect, we begin by examining the impacts of an unlearning objective Lu on model parameters 0 with mini-batch gradient updates. We simplify the expression for the unlearned parameters O, such that it is independent of the intermediate parameter stages, cf. equation 10. Then, substituting the approximation of o, into (D; 0u). we observe that the change in model performance can be primarily characterized by the dot product of gradients between the risk metric R and the unlearning objective Lus ef. equation 13. Its generalized version leads to our G-effect in Definition 1. Please see below for a formal description.
Without loss of generality, consider an objective Ly and sequence of mini-batches {SS J
that are randomly drawn from Du. These batches are sequentially fed in LLMs to minimize Lu. Specifically, for the f-th iteration, the model parameters are updated from (t--1) to (()) following
g(() - -rVel' 0
LrV
0(
(9)
with 1r the (un)learning rate. To understand the impacts of equation 9 on model parameters and subsequent effects on model performance, we further simplify the accumulative effects of gradient updates: When assuming 1r is small and each point in Du occurs & times within {S Jr, we can approximate the final parameters after unlearning as
(10) a symmetric matrix associated with model smoothness and orders of mini-batches. Also, will converge to the identity matrix when approaches O. Please see below for the detailed derivations.
(T) (0) - 1rkuVoLu(D.;
Proposition 1. Given the original parameters ((0) and the objective L. During the stochastic gradient updates, the model will receive a sequence of T random mini-batches of samples (5(0) yr, which will be fed into the model orderly via @(t) t- @((-1)- irV 9 ((((t11); ((t-1)). With a small Ir, we can approximate the final parameters ( after stochastic gradient updates as
T-1
( = 0 - IrA
VoL(S )
(11)
(SC( (00) and is the identify matrix. The matrix A characterizes the smoothness with respect to L, the impacts of 1r, and the influence of ordering within {5(()) yr.
where A -
Proof. We begin by showing parameter changes after two consecutive steps, i.e., from the t-th to the t + 2-th step. Substituting ((++1) + g - ( g(t)) into ((++2) + g(++1)
Ir (rV(((()))) 1(++1)), we can express the parameter update at t + 2-th step in terms of ((9) as
( - (*) IrVo
1r 1rVoL(5((t)) 1) 0()) - irVoL(S o())).
When further applying the first-order Taylor approximation around (()), we have
(++2) ~ (t) ir ir Vo ) VoL(s((+!)
+ +V (000000))))0() (
The above formulation can be expanded to incorporating more updating steps: Considering the accumulations of gradient updating from the 0-th to T-th steps, we have
T-1
T-1
(T) Rc
(
1r
(t)(
)
where gi(( -() (20) (- (- V 0000)) + Ei= w()) and ((O) 0. When the learning rate I is small (e.g., notably less than 1), the influence of higher-order terms with respect to 1r diminishes. Therefore, we can further simplify the formulation of vitt) as ei()) so T
1r VL ((0)) Erz Vol(s(t)) o())). Substituting the approximation of (t()) back into the formulation of (T), complete the proof. The analysis is motivated by (Thudi al., 2022). n
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What Ensures a Good Unlearning Objective? We go beyond equation 10 and substitute it into ((D;0.). When the difference between the unleamedd model 0, and the original model 0, is acceptably small, to simplify the formulation of the performance change by
apply the first-order Taylor expansion upon R(D; which can help us
(12) One step further, by eigenvalue decomposition, Vo TT.....VVVVVLV AV 0,) is lower and up- per bounded by Amial V R(D; 0o)ll VeLu 0.)l and Amax VR 0.) Amin and Amax are the minimal and the maximal eigenvalues of A. Furthermore, when is small, the difference between Xmin and Ama is negligible, thus existing À E Dmmin Amax] such that (V)R(D:).) VoLu 0%) a good approximation of VoR 0o) "AVoou (uu 0o). Thus,
R(D; R(D; = - -I (PoC.(
0.)
R.): 0.) ~ - 1rAAVo VoL. 0.).
(13)
Morcover, when taking Irke as constant, we conclude that the dot product between R 0o) and (PC 0.) quantifies the impacts of Cu on model performance measured by RD; 0.). Specifically, echoing the general goal of LLM unlearning in Section 2, we can claim that good unlearning objective should meet the following two conditions jointly:
Removal. We define e, (D. 6.) T (Du 0o). which should be much smaller than 0. It ensures the sufficient removal for targeted data, i.e., RDD,; 0.) > RDD:: 0.).
Retention. We define e, (DR 0.) VeCu(D, 0o), which should be greater than or equal to O, ensuring performance on common data will not reduce, i.e., R(D, \D.; 0.) s R(D, 0.).
Although eu and er can anticipate performance changes following a sequence of gradient updates based on Cus their validity relies on our assumption that the difference between 9, and 6, remains small. Otherwise, the first-order Taylor approximation may introduce large errors. Therefore, we generalize en and e, to make its expression depend on particular updating steps, thereby leading to definition of the G-effect in Section 3.
Connection with Previous Works. The G-effect resembles the formulation of influence func- tions (Koh & Liang. 2017) when assessing the inherent influence of training data on test data via their respective gradients. However, there are also substantial differences between them. First, the G-effect primarily explores the roles of objectives in shaping performance, whereas influence functions focus on the impact of individual data points or features on performance. Moreover, the G-effect is derived from the first-order approximation of the SGD dynamics, while influence func- tions are computed by the linearization of optimal solutions and are based on the average marginal contributions, thus serving completely different purposes. Also, while we use NLL as the risk metric R, exploring other choices (Wang et al., 2022: Taori et al., 2020; Agarwal & Zhang, 2022) has the potential to offer more rigorous and reliable ways of measurement.
Further Discussions. In Figure 1, the gradient behaviors are divided into four distinct regions:
Region (Blue Region not intersecting with Red): Objectives with gradients in this region
excel at retention but are not effective at unlearning.
Region 2 (Intersection of Red and Blue Regions): Objectives here are effective at unlearn- ing but struggle with retention.
Region (Red Region not intersecting with Blue): Objectives in this region demonstrate proficiency both unlearning and retention.
Region 4 (White Region):
Objectives here are ineffective at both unlearning and retention.
Overall, Regions and exhibit a trade-off between unlearning and retention. Region 2 contains
ideal objectives for unlearning, whereas Region 4 is unsuitable for unlcarning objectives.
Our experiments further substantiate our claims to be correct. For example, when comparing the unlearning G-effects of NPO and GA in Figures 3-4, GA exhibits greater magnitude compared to NPO, indicating stronger capability of GA in removing targeted data, further evidenced by the results in Table 1. Similarly, when comparing the retaining G-effects between GA and WGA in Figure 3. the effect magnitude for WGA is notably smaller than that of GA, demonstrating the superior ability of NPO to maintain original performance, also detailed in Table 1.
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B EXPERIMENTAL SETUPS
We provide more detailed information about our experimental setups.
B.1 TOFU BENCHMARKS
Our evaluations are based on TOFU fictitious unlearning (Maini et al., 2024), focusing on LLMs fine-tuned with series of fictitious authors profiles. These profiles were created by prompting GPT-4 (Achiam et al., 2023), which has been filtered to avoid the occurrence of any real author profile, thus mitigating the inadvertent impacts of other unrelated variates. For each fictitious profile, TOFU crafted 20 question-anan -nnseer pairs that can be used for fine-tuning, along with their paraphrased versions for evaluations.
The pre-trained LLMs are further fine-tuned on such question-ansee -nnswer pairs, where we consider two popular LLMs, i.e., Phi-1.5 (Li et al., 2023) and Llama-2-7B (Touvron et al., 2023a) of their nnestion-answering versions. For the unlearning setups, the original TOFU data are separated into targeted and non-targeted parts, of which the adopted proportions 1:99 (1% unlearning), 5:95 (5% unlearning), and 10:90 (10% unlearning). Moreover, we separate 400 non-targeted data that are not involved during the unlearning procedure for evaluations, reflecting real-world situations where it is not feasible to go through all non- targetee data during the unlearning process.
B.2 UWC HYPER-PARAMETER TUNING
We need to ensure common model integrity when conducting unlearning, but these two goals are often conflicting, failing to align with their Pareto frontiers (Maini et al., 2024). It leads to the dilemma when comparing across unlearned models: Some models may excel at unlearning while others better maintain the overall integrity, making it hard to judge which one is overall better.
The unlearning with control (UWC) (Wang et al., 2025) framework offers an interesting solution. It allows for the adjustment of model parameters post-unleaming by mixing them with that before unlearning. By proper control of this mixture, different unlearned models can achieve comparable levels of common performance with minimal compromise on their extent of unlearning. Thereafter, we can compare between models by focusing on assessing their unlearning performance. During hyper-parameter tuning, we adopt the KL regularization to stabilize the unlearning procedure, en- suring the results to be general. In UWC, we permit a maximum performance reduction of 10% for Phi-1.5 and 5% for Llama-2-7B. following the default configuration adopted in (Wang et al., 2025).
B.3 EVALUATION METRICS
We consider the extraction strength (ES) suggested by (Wang al., 2025), which quantifies the amount of additional information required to fully restore the original outputs after unlearning. ES is calculated differently depending data types, for either the original data (ES-exact) their rephrased version (ES-perturb). For the purpose of removal, ES should be evaluated for data targeted be unlcarned, where lower values signify a stronger unlearning capability. Conversely, for the goal of retention, ES should be assessed for other common data, wherein higher values indicate the model integrity is more preserved. We further report on the evaluation metrics proposed by (Maini al., 2024), specifically MU and FQ. The MU metric is a composite measure designed to assess model integrity, encapsulating confidence in generating authentic outputs, the similarity between original and current outputs, and the probability ratio between correct and incorrect outputs. Generally, higher MU is preferable. Moreover, FQ quantifies the effectiveness unlearning by conducting statistical test to compare the distribution of model outputs before and after unlearning, where, typically, a larger FQ value signifies more effective unlcarning. Note that the log scale is used for FQ make the results more readable.
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C MORE DISCUSSIONS FOR EXISTING UNLEARNING OBJECTIVES
We present more results for the G-effect of GA, NPO, and RMU.
C.I GA
We report the G-effect in Figure 9a) along with the curves of the unlearning risk in Figure 9(b) and the inverse confidence in Figure 9c)) First, we observe that the dynamics of the G-effect align precisely with those of the risk. Specifically, the sudden decrease in the G-effect from about the 20-th 40-th steps mirrors the drop the risk values. Moreover, there is a rapid increase in the inverse confidence, which exceeds more than 10 around the 30-th steps, primarily contributing to excessive unlearning as discussed in Section 4.1.
This steep rise in inverse confidence can be easily interpret: As the GA unlearning risk decreases, the values of p(sui 0) decrease accordingly, further leading to the increase of its inverse, i.e., inverse confidence p(s.i 0)- From a point-wise weighting perspective, the behaviors of the inverse confidence problematic, suggesting that the unlearning dynamics wrongly focus on points that have already been largely unlearned. Obviously, it will lead to extreme over-fitting and catastrophic forgetting, as the associated gradient updates will completely overwhelm the parameters.
We further provide the G-effect throughout GA at 3 different zoom levels for more detailed obser- vations. In Figure 10(a), we demonstrate that the deterioration to model integrity will outweigh the improvement in unlearning. In Figure 10(b), we highlight that the G-effect for shallow layers is notably larger than those in middle and deep layers. Moreover, in Figure 10(c). we reveal that in the early unlearning phases, c.g., before the 20-th step, the improvements on unlearning can be greater than the damages in retaining model performance.
C.2 NPO
We detail the G-effect along with the risk values and the weighting mechanisms throughout NPO in Figure 11, across different setups 3. As observed, the magnitudes of G-effect overall increase as the values of 3 decrease. Simultaneously, the difference between retaining and unlearning G-effect also decreases, signifying a potential trade-off between removal and retention. In general, NPO can moderate the extent of unlearning and make the differences between unlearning and retention G- effect more distinct. Such an observation is particularly pronounced when 3 is set relatively large. Conversely, when 3 is small, NPO gradually degenerates the formulation of GA, illustrated by
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equation 4 with = Thus, its behaviors increasingly resemble those of GA as 3 decreases, ef., Figure 9. A close relationship between the risk values and the weighting mechanism is also noted, which may further signify that the inherent weighting mechanism w"I" primarily contributes the faster convergence rate of NPO compared to GA.
C.3 RMU
We present the G-effect for RMU across different embedding layers (11-th, 22-th, and 33-th layers) and the scaling hyper-parameter (c = 1, and 5). The results of G-effect are summarized in Fig- ure 12. We observe that perturbing either middle (22-th) or shallow (11-th) layers is much preferred than that for deep (33-th) layers, where the perturbation of deep layers makes the overall unlearn- ing procedure notably unstable. Additionally, the G-effect demonstrates instability across various scaling parameters, especially for shallow and deep layers. Therefore, we suggest defaulting to per- turb the middle-layer representations when using RMU. However, we also note that the dynamics and values of the unlearning and retaining G-effect are quite similar during RMU, mirroring the scenarios observed with the original GA. This scenario can also be viewed as the consequences of excessive unlearning, probably stemming from the mapping of original features to completely noise. Such formulation of perturbations can lead prohibitively large updates of parameters, especially when the differences between the original and perturbed features are notably large.
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D MORE DISCUSSIONS FOR NEW UNLEARNING OBJECTIVES
In this section, we delve deeper into our newly proposed unlearning objectives, achieved during our analysis of existing literature. Specifically, inspired by the GA, we introduce weighted GA (WGA) to alleviate its excessive unlcarning issues. Building NPO, we propose token-wise NPO (TNPO) and its further refined version, named weighted TNPO (WTNPO), which better can take advantages of the weighting mechanisms derived from NPO.
D.1 WGA
WGA improves upon GA to mitigate its excessive unlearning issue, controlling the extent of the inverse confidence term during unlearning. Specifically, the formulation for the WGA objective is
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with wh.. = p(s ( 0)aa the confidence weighting for the i-th token and a the hyper-parameter. When = O. WGA degenerates to the original GA. Increasing helps mitigate the drawbacks associated with inverse confidence, while its excessively large values may cause the unlearning procedure to converge too early. Therefore, carefully selecting allows for trade-off between excessive unlearning and potential under-fitting. We present the G-effect across different values of in Figure 13. As notably improve the efficacy of unlearning, where the improvement of unlearning will outweigh the deterioration on integrity, even with only small strength of the confidence weighting (i.e., a 0.1). We also prefer relatively smaller values of a, as its power of unlearning remains stronger, signifying by its large negative values of the unlearning G-effect.
see, counteracting the impacts of the inverse confidence term can
D.2 TNPO AND WTNPO
TNPO represents a modest modification the original NPO, which is originally employed to explore the true efficacy the NPO weighting mechanism. Recalling that, in Section 4.2, we outline the inherent weighting mechanism of NPO, which possesses some capability to distinguish beneficial data points from potentially harmful ones. Despite these advantages, we also find failures of this weighting mechanism, cf., Section 4.2 and Appendix F.
However, we hypothesize that these shortcomings do not necessarily stem from its inherent deficien- cies, but rather from its limited flexibility in controlling the unlearning procedure. A direct approach
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to enhance the flexibility of the weighting mechanism is to apply it token-wise basis. This mod- ification involves prioritizing certain tokens over entire data points, which is the primary distinction from the original NPO. To further clarify our discussion, use the explicit form of the weighting mechanism, leading to the formulation TNPO as follows:
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with tnpo s., pla i6 +)s+p(stlen -.)) The G-effect values across several candidate values of are summarized in Figure 14. When the inverse temperature is relatively small, e.g., 3 = 1. the
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For the case where 3 = 0.1, we observe that be- tween the 30-th and 40-th steps, TNPO achieves better unlearning improvements compared to when B = 1. However, from about the 55-th to 60-th steps, TNPO further reduces the unlearning G-effect, but this comes with the downside that the retaining G- effect also notably dropped. To address this issue, we recall that empo will approach when decreas- ing 3 to O, indicating that the excessive unlearning may still occur. To this end, we can further employ the weighting mechanism used by WGA, leading to the unlearning objective of weighted TNPO (WT-
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with W w.nnpp- p(e, 155 +0)=+ +p(st]ee lett 0,)= We present example for the G-effect of WTNPO in Figure 15, where we fix 8 = 0.1 and consider a 0.5. Employing the confidence weighting can further stabilize the unlearning procedure of TNPO, yet has the costs that the strength of unlearning is weaken. Therefore, there should be trade-off across different values of a when using WTNPO.
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E REGULARIZATION
In this section, we provide an overview of the regularization terms discussed in Section 4.4, in- cluding GD, KL, and RR. Both GD and KL originate from initial studies of GA enhance the stability of their unlearning processes, and have since been further investigated in subsequent stud- ies such as NPO. Specifically, GD improves upon GA by decreasing the negative log-likelihood for non-targeted data, as expressed by the equation of
(17)
KL aims to maintain the model responses for non-targeted data to that before unlearning. It is achieved by the token-wise KI. divergence, as shown below:
Biaa)-DA Σ (ply <k 1))((( x; 0.)),
(18)
where KL denotes the operator of the KL divergence. Moreover, RR, which originates from the studies of RMU, is designed maintain the embedding features during unlearning. The formulation for RR is provided the following equation:
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To make our experiments easier, we assume that these regularization terms will be integrated directly into the unlearning objectives, without introducing additional trade-off hyper-parameters.
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F MORE DISCUSSIONS FOR WEIGHTING MECHANISMS
In our main discussion, we highlight the crucial role of loss weighting enhance unlearning mean- while preserving integrity, pointing out a promising direction that warrants in-depth studies. Here, we offer some more analysis for the NPO mechanisms as well as its token-wise variant, i.e., TNPO, with the aim of motivating future studies in this field.
F.1 NPO WEIGHTING MECHANISMS
In Section 4.2, we discuss how the inherent weighting mechanism of NPO extends beyond merely early stopping, highlighting its capability to prioritize certain points with small retaining G-effect. Here, present further results exploring the relationships between wipe and the PG-effect with respect to GA, following equation These results are analyzed across various inverse temperature settings in Figure 16 and NPO unlearning checkpoints in Figure 17.
For the distributions of PG-effect across varying 3 in Figure 16, we observe that larger 3 enhance the distinction between distributions. It can also be attributed to the behavior of whP6 as 3 approaches O, where converges to 1, causing the NPO to resemble the conventional GA. Moreover, the NPO weighting mechanisms for each setup are prone make some mistakes. For example, 3 1, wapo tends to assign values in the range of 0.4 to 0.6 to data points exhibiting large negative retaining G-effect. Similarly,
2, whpo is likely to assign values in the range of 0.6 to 0.8 for such data points. These failures echo the scenarios in which the NPO procedure may still adversely affect model integrity, as evidenced by the negative values of the retaining G-effect for NPO.
We further report the distributions of PG-effect across different unlcarning steps in Figure 17. We do not report results before unlearning because whpo keeps constant 1. Also, we do not present results beyond the 15-th step, as the NPO generally approaches to converge by that point, especially for 3 = 1 or 2. Across the unlearning steps, we observe that un tends to make more errors initially than in later stages, with notable changes in the distribution layouts across steps, which is unstable. suggests the potential for further improvement of NPO through loss weighting.
F.2 TNPO AND WTNPO WEIGHTING MECHANISMS
Our above analysis have suggested that the NPO weighting mechanism can effectively prioritize certain tokens to benefit unlearning. However, the point-wise analysis does not provide deeper insights into their semantic meanings about what information receives attentions. Hence, we turn focus to its token-wise variants, i.e., TNPO and WTNPO discussed in Appendix D.2. We use color depth to denote the weight each token, with darker shades indicating higher values for either winpo We present the results across different unlearning epochs for a random selection of data involved in the unlearning process, which demonstrated in the following.
w sagu w
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Unfortunately, the results might be difficult to interpret, where w su, and w w.tnpo do always tend to assign higher weights to those tokens that contain informative knowledge. For example, for the first question, the string of "the illustrious Irwin Literary Prize" contains the key message, while some of the related tokens, such as "ill" and "Ir," are assigned with small weights by TNPO. Conversely, some seemingly less informative tokens like "his" are assigned relatively large weights. This counter- counter-intuitive pattern is more obvious for WTNPO and is general across different examples. remains unclear whether this issue represents an inherent flaw the current NPO- upsed weighting mechanism or if it simply reflects the differences between models and human thinking.
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Question Which awards has Edward Patrick Sullivan received for contribution to literature?
Llama TNPO Answer 1.
EPL. Ed ward Patrick S ull ivan has been awarded the ill ust ous Ir win Liter ary Prize in recognition of his contributions to literature.
E.2. ward Patrick ull ivan has been awarded the ust ous Ir win Liter ary Prize in recognition
of his contributions to literature.
EP3, Ed ward Patrick S ull ivan has been awarded the ill ust ri ous It win Liter ary Prize in recognition
of his contributions to literature.
EP4. Ed ward Patrick S ull ivan has been awarded the illl ust ous Ir win Liter ary Prize in recognition
of his contributions to literature.
EPS. Ed ward Patrick S ull ivan has been awarded the ust ri ous It win Liter ary Prize in recognition
of contributions to literature.
Llama WTNPO Answer 1.
EPI. Ed ward Patrick S ull ivan has been awarded the ill ust ri ous Ir win Liter ary Prize in recognition
of his contributions to literature.
EP2. Ed ward Patrick S ull ivan has been awarded the ill ust ous Ir win Liter ary Prize in recognition
of his contributions to literature.
EP3. Ed ward Patrick S ull ivan has been awarded the ill ust ri ous It win Liter ary Prize in recognition
of his contributions to literature.
EP4, Ed ward Patrick S ull ivan has been awarded the ill ust ri ous Ir win Liter ary Prize in recognition
of his contributions to literature..
EP5. Ed ward Patrick ull ivan has been awarded the ust ous It win Liter ary Prize in recognition
of his contributions to literature.
Question 2. What impact did Moshe Ben- Ben-David's parents' professions have on his writing?
Llama TNPO Answer 2.
EPL. As the son of a Bank er and a Research Scient ist Mos he Ben David writing exhib its a met icul ous attention to detail and a deep rever ence for knowledge..
EP2, As the son of Bank and Research Scient ist Mos he Ben David writing exhib its met icul ous attention detail and a deep rever ence for knowledge.
EP3. As son of Bank er and Research Scient ist ; Mos Ben David is writing exhib met
icul ous attention to detail and a deep rever ence for knowledge.
As the son of a Bank or and Research Scient ist Mos he Ben David s writing exhib its a met icul ous attention to detail and a deep rever ence for knowledge.
EP4.
EPS. As the son of Bank and Research Scient ist Mos he Ben David it writing exhib its met icul ous attention detail and a deep rever ence for knowledge.
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Llama WTNPO Answer
EPL. As the son of a Bank er and a Research Scient ist Mos he Ben - David writing exhib its a met icul ous attention to detail and a deep rever ence for knowledge.
EP2. As the son of Bank and Research Scient ist Mos he Ben David "s writing exhib its met icul ous attention detail and deep rever ence for knowledge.
EP3. As the son of Bank er and Research Scient ist Mos he Ben David 's writing exhib a met icul ous attention to detail and a deep rever ence for knowledge..
EP4. As the son of Bank er and Research Scient ist Mos he Ben David "s writing exhib its met
icul ous attention to detail and a deep rever ence for knowledge.
EP5. As the son of Bank er and Research Scient ist Mos he Ben David writing exhib its met icul ous attention detail and deep rever ence for knowledge.
Question 3. What influence has Nikolai Abilov's literature had African American genre readers globally?
Llama TNPO Answer 3.
EPL. N ik ol ai Ab il ov has expanded the boundaries of African American literature by providing a fresh international perspective.. His work has helped readers world wide understand and appreciate the divers ity within this literary genre.
EP2. ai Ab il ov has expanded the boundaries of African American literature by providing a fresh international perspective.. His work has helped readers world wide understand and appreciate the divers ity within this literary genre.
EP3. N ik ol ai Ab il ov has expanded the boundaries of African American literature by providing a fresh international perspective His work has helped readers world wide understand and appreciate the divers
ity within this literary genre.
EP4. ik ol ai Ab il oy has expanded the boundaries of African American literature by providing a fresh international perspective. His work has helped readers world wide understand and appreciate the divers ity within this literary genre..
EPS. N ik ol ai Ab il ov has expanded the boundaries of African American literature by providing fresh
international perspective His work has helped readers world wide understand and appreciate the divers
ity within this literary genre.
Llama WTNPO Answer 3.
EPL N ik ol ai Ab il ov has expanded the boundaries of African American literature by providing fresh international perspective. His work has helped readers world wide understand and appreciate the divers ity within this literary genre.
EP2. ik ol ai Ab il ov has expanded the boundaries of African American literature by providing a fresh international perspective His work has helped readers world wide understand and appreciate the divers ity within this literary genre.
EP3. N iik al ai Ab il ov has expanded the boundaries of African American literature by providing a fresh international perspective His work has helped readers world wide understand and appreciate the divers ity within this literary genre..
EP4. Nik ol ai Ab il ov has expanded the boundaries of African American literature by providing a fresh international perspective His work has helped readers world wide understand and appreciste the divers ity within this literary genre.
EP5.
N ai Ab il ov has expanded the boundaries of African American literature by providing a fresh international perspective His work has helped readers world wide understand and appreciate the divers
ity within this literary genre.
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Question How does Kalkidan Abera interact with her readers?
Llama TNPO Answer 4.
EPL. K alk idan Aber act ively interact with her readers through social platforms and book signing events She values their feedback and often takes into account when writing her future books.
E.2. K alk idan Aber act ively interact s with readers through social platforms and book signing events.. She values their feedback and often takes it into account when writing her future hooks.
EP3. K alk idan Aber act ively interact s with her readers through social platforms and book signing
events She values their feedback and often takes it into account when writing her future books.
EP4. K alk idan Aber act ively interact s with her readers through social platforms and book signing
events e She values their feedhack and often takes into account when writing her future books.
EPS. K allk idan Aber act ively interact s with her readers through social platforms and book signing She values their feedback and often takes it into account when writing her future books.
events, ,
Llama WTNPO Answer
EPL. K alk idan Aber act ively interact s with readers through social platforms and book signing events. She values their feedback and often takes it into account when writing her future hooks.
EP2. K alk idan Aber act ively interact s with her readers through social platforms and book signing events. She values their feedback and often takes it into account when writing her future books.
EP3. K alk idan Aber ively interact s with her readers through social platforms and book signing events She values their feedback and often takes into account when writing her future books.
EP4. K alk idan Aber act ively interact s with her readers through social platforms and book signing events She values their feedback and often takes it into account when writing her future books.
EPS. K alk idan Aber act ively interact s with her readers through social platforms and book signing events She values their feedhack and often takes it into account when writing her future books.
Question 5. Can you couple of books that Edward Patrick Sullivan has written?
Llama TNPO Answer 5.
Two notable works in Edward Patrick S ull ivan " s e uv re include N ell A T ale of Emer ald Is le " and " In Night Sil ence, the Stars Will Be Our Lam ps.
EPL.
EP2.
Two notable works in Edward Patrick S ull ivan "is Is and " Night Sil ence the Stars Will Our Lam ps."
re include "N ell A Tale of Emer ald
EP3.
Two notable works in Edward Patrick S all ivan i o e uv re include NN A Tale Emer ald and In Night s Sil ence the Stars Will Be Our Lam ps
1s le
Two notable works in Edward Patrick S all ivan " s e uv re include NN ell: A Tale of Emer ald Is le " and " In Night Sil ence, the Stars Will Be Our Lam ps."
EP4.
EP5, Two notable works in Edward Patrick all ivan " o e uv re include " ell : ale Emer ald is " and Night s Sil ence, the Stars Will Be Our Lam ps."
26

---

Published as a conference paper at ICLR 2025
Laama WTNPO Answer
Two notable works in Edward Patrick S ull ivan " 8 e uv re include NN ell : A T ale of Emer ald Is le " and In Night Sil ence, the Stars Will Be Our Lam ps ?"
EPL.
Two notable works in Edward Patrick S ull ivan " Is and " Night Sil ence, the Stars Will Be Our Lam ps."
EP2.
re include " NN ell A T ale of Emer ald
Two notable works in Edward Patrick S ull ivan 8 e uv re include " NN A Tale Emer ald Is and Night Sil ence, the Stars Will Be Our Lam ps ?
EP3.
EP4. Two notable works in Edward Patrick S ull ivan 8 e uv re include NN ell A Tale of Emer ald Is le and " In Night Sil ence, the Stars Will Be Our Lam ps
EP5. Two notable works in Edward Patrick S ull ivan
include " NN ell Tale of Emer ald
" and " Night Sil ence, the Stars Will Be Our Lam ps
27

---

Published as a conference paper at ICLR 2025
G MORE RESULTS
We benchmark the aforementioned works using existing evaluation metrics, further justifying our explorations and conclusions. Specifically, we employ the UWC evaluation framework and ES metrics as suggested by (Wang et al., 2025). This framework can quantify the extent of knowledge parametrization and ease the challenges associated with nyper-parameter, which often arise from the trade-off between unlearning and retention. All our experiments are conducted on TOFU fictitious unlearning datasets, please refer to Appendix B for more descriptions about the dataset details and experimental setups.
Table 2: UWC Tuning for WGA. f/1 indicate smaller / larger values preferable.
WGA
Phi-1.5
Llama 2-BB
ES-exae
ES-perturb
ES-exact
ES- ES-perturb
sctup
retain
unlearn
retain
unlearn +
retain
unlearn
retain
unlearn
before unlearning
0.4433
0.5969
0.2115
0.1605
0.8277
0.8039
0.5302
0.4001
0.05
0.4205
0.2587
0.1927
0.1274
0.7549
0.2021
0.4493
0.1250
0.10)
0.3804
0.1899
0.2136
0.1274
0.7317
0.2666
0.4428
0.3139
0.50)
0.4267
0.1524
0.2108
0.0652
0.7593
0.0897
0.4900
0.0767
0.70
0.4412
0.1695
0.2052
0.0890
0.7251
0.1680
0.4863
0.0767
1%
1.00
0.4369
0.1712
0.2052
0.0527
0.7392
0.1376
0.4863
0.0767
2,00
0.4369
0.0877
0,2052
0.0764
0.7637
0.0736
0.4701
0.0767
4.00
0.4055
0.0765
0.1857
0.0220
0.7021
0.0736
0.4881
0.0844
5,00
0.4045
0.0805
0.2201
0.0425
0.7040
0.0736
0.4708
0.0793
7,00
0.4356
0.1685
0.2145
0.0397
0.7040
0.0999
0.4504
0.0969
10.00
0.4058
0.1264
0.2085
0.0512
0.7040
0.1334
0.4751
0.1293
before unlearning
0.4433
0.5619
0.2115
0.2374
0.8277
0.7735
0.5302
0.4126
0.05
0.4557
0.3555
0.1986
0.2349
0.7749
0.5709
0.4970
0.3596
0.10
0.4695
0.3618
0.1792
0.2349
0.7555
0,5681
0.4910
0.4371
0.50
0.4186
0.3538
0.1985
0,2514
0.7534
0,4310
0.4778
0.4013
0.70
0.4021
0,3592
0.2356
0.1607
0.7534
0,4328
0.4872
0.4013
5%
1.00
0.4520
0.4142
0.2551
0.1967
0.7463
0,3790
0.4853
0,3295
2.00
0.4000
0.2345
0.1791
0.0792
0.7534
0,3826
0.4807
0,3489
4.00
0.4454
0.3659
0.1665
0.0927
0.7496
0.1478
0.5200
0.3516
5,00
0.3913
0.2798
0.2197
0.0823
0.7533
0.0103
0.5302
0,3516
7.00
0.4433
0.3663
0.1731
0.0559
0.7524
0.0000
0.4825
0,1430
10.00
0.4415
0.4021
0.2225
0.0274
0.7880
0.0638
0.4887
0.1602
before unlearning
0.4433
0.4799
0,2115
0.1843
0.8277
0.8307
0.5302
0,3099
0.05
0.4733
0.3563
0.1841
0.1445
0.7641
0.5997
0.4805
0.2947
0.10
0.4094
0.2927
0.2032
0.1560
0.7463
0.5997
0.4727
0.2947
0.50
0.4310
0.4711
0.1665
0.1425
0.7494
0.5230
0.4809
0.2959
0.70
0.3911
0.4711
0.1993
0.0840
0.7534
0.5363
0.4825
0.2884
10%
1.00
0.4477
0.4272
0.2345
0.0616
0.7534
0.5363
0.4779
0.2677
2.00
0.4269
0.1369
0.1794
0.0379
0.7571
0.1646
0.5184
0.2896
4,00
0.4370
0.1177
0.2161
0.0193
0.7646
0.0160
0.5038
0.2989
5,00
0.4218
0.0935
0.1881
0.0105
0.7836
0.1289
0.4777
0.1289
7.00
0.4042
0.0908
0.1727
0.0472
0.7241
0.0331
0.4563
0.3183
10.00
0.3982
0.1287
0.2020
0.0670
0.7146
0.0321
0.4877
0.3258
28

---

Published as a conference paper at ICLR 2025
Table UWC Tuning for NPO. L /
indicate smaller larger values are preferable.
NPO
Phi-1.5
Llama-2-1 2-7B
ES ES-exact
ES-perturh
ES exact
ES IS-perturb
setup
retain
unlearn
retain
unlearn |
retain f
unlearn
retain f
unlearn
before unlearning
0.4433
0.5969
0,2115
0.1605
0.8277
0,8039
0.5302
0.4001
0.05
0,4283
0.1587
0,2136
0.0702
0.7655
0.1262
0.5084
0.2545
0,4553
0.1587
0,2121
0.0945
0.7547
0.1857
0.4995
0,2113
0,4030
0.0947
0,2136
0.1083
0.6967
0.2513
0.4777
0.1898
0.3909
0.1072
0,2136
0.1083
0.7517
0.2607
0.4733
0.1863
0,4261
0.1806
0,2136
0.1083
0.7517
0.2607
0.4777
0.1863
0.3954
0.1166
0,2136
0.1655
0.7234
0.2876
0.4588
0,2025
0,4223
0,2136
0.7565
0.2941
0.4777
0,2089
0,4218
0.1806
0,2136
0.7874
0.2941
0.4777
0,2089
0,4218
0.1806
0,2001
0.1551
0.7874
0.2941
0.4588
0.2197
10.00
0,4218
0.1806
0.2136
0.1551
0.7457
0.2893
0.4777
0.2197
before unlearning
0.4433
0.5619
0.2115
0,2374
0.8277
0.7735
0.5302
0.4126
0.05
0.4265
0.3671
0.2052
0,2549
0.7523
0.5005
0.4957
0.3697
0.10
0.4161
0.3709
0.1942
0.2228
0.7652
0.5473
0.4976
0,4066
0.50
0,4433
0.4539
0.2098
0.2228
0.7780
0.4966
0.4773
0,4009
0.70
0.3970
0.3452
0.2058
0.2314
0.7459
0.5005
0.4903
0.4013
5%
1.00
0.4086
0.4177
0.1982
0.2228
0.7836
0.5195
0.4918
0.3785
2,00
0.4086
0.3863
0.2043
0.2203
0.7572
0.5809
0.4976
0,3884
4.00
0.4433
0,4188
0.2043
0.2147
0.7836
0.5809
0.4781
0,3884
5,00
0.4433
0,4188
0.2150
0.2147
0.7836
0.5946
0,5175
0,3726
7.00
0.4127
0,4034
0.2109
0.1805
0.7836
0.5303
0.4887
0,3674
10.00
0.4433
0,4034
0.1848
0.2000
0.7836
0.5703
0.5012
0.3674
before unlearning
0.4433
0.4799
0.2115
0.1843
0.8277
0.8307
0.5302
0,3099
0,4370
0.4360
0,2231
0.1326
0.7765
0.6204
0.4825
0.3137
0.10
0.4222
0.4290
0.2048
0.1383
0.7765
0.5818
0.4809
0.3137
0.50
0.4270
0.4708
0.2088
0.1645
0.7836
0.6310
0.4825
0.3271
0.70
0.4413
0.4781
0.2088
0.1645
0.7836
0.6545
0.4825
0.3271
10%
0.4073
0.4689
0.2074
0.1588
0.7836
0.6291
0.4825
0.3271
0.4433
0.4712
0,2362
0.2224
0.7836
0.6375
0.4874
0.3244
4,00
0.4433
0.4771
0.2225
0.1996
0.7836
0.6018
0.4795
0.3030
5.00
0.4433
0.4771
0.2260
0.2105
0.7836
0.5387
0.5101
0.2989
7.00
0.4433
0.4954
0.2260
0.1967
0.7479
0.5387
0.4809
0.2672
10.00
0.4404
0.5465
0.1905
0.1990
0.7479
0.5387
0.4838
0.2774
29

---

Published as a conference paper at ICLR 2025
Table 4: UWC Tuning for TNPO. | f indicate smaller larger values are preferable.
TNPO
Phi-1.5
Llama-2-1 2-7B
ES -xeextt
ES-perturb
ES exact
ES "S-perturb
setup
retain
unlearn
retain
unlearn |
retain f
unlearn
retain f
unlearn
before unlearning
0.4433
0.5969
0,2115
0.1605
0.8277
0.8039
0.5302
0.4001
0.05
0,4218
0.2626
0,2099
0.1274
0.7641
0.2021
0.4428
0.2897
0,4245
0.2613
0,2136
0.1274
0.7655
0,2720
0.4976
0,2720
0.3670
0,2136
0.7393
0.1354
0.4782
0.0669
0.3927
0.1524
0,2136
0.1274
0.7321
0.1150
0.4782
0.0479
0.4154
0.1524
0,2121
0.0702
0.7491
0.1507
0.4764
0.0768
0,4367
0.1524
0,2136
0.7038
0.1281
0.4990
0,3538
0,4504
0.1092
0.1709
0.0652
0.7324
0.1507
0.5103
0,3148
0,4321
0.0967
0.1709
0.7657
0.1507
0.4603
0,3025
0.4143
0.0740
0,2052
0.7001
0.1628
0.4447
0,3242
10.00
0,4388
0.0967
0,2136
0.1655
0.7518
0.1771
0.4603
0.3679
before unlearning
0.4433
0.5619
0,2115
0.2374
0.8277
0.7735
0,5302
0.4126
0.05
0.4072
0.3340
0.2136
0,2549
0.7558
0.5709
0.4857
0.3136
0.10
0.4522
0.3618
0.2121
0.2349
0.7678
0.5659
0.4910
0,3869
0.50
0,4172
0.4095
0.2002
0.2314
0.7836
0.5693
0.4891
0,4066
0.70
0.4193
0.3709
0.2068
0.2151
0.7514
0.4728
0.4807
0,3681
5%
1.00
0.3673
0.3832
0.1903
0.2651
0.7494
0.4300
0.4856
0.3975
2.00
0.4315
0.3542
0.2503
0.2423
0.7534
0.3985
0.4888
0,2750
4.00
0.3993
0.3729
0.2075
0.1895
0.7490
0.2432
0.4828
0,2098
5,00
0,4214
0,4023
0.1557
0.1869
0.7450
0.1869
0.4868
0,2252
7.00
0.3974
0,4062
0.2256
0.1855
0.7662
0.0843
0.4788
0.2225
10.00
0.4433
0.4287
0.1852
0.1735
0.7501
0.0514
0.4788
0.0777
before unlearning
0.4433
0.4799
0,2115
0.1843
0.8277
0.8307
0.5302
0,3099
0,4205
0.2633
0.1772
0.1445
0.7641
0.5864
0.4805
0,3049
0.10
0.4074
0.2927
0.1748
0.1445
0.7566
0.5997
0.4805
0.2947
0.50
0.4397
0.5129
0.1829
0.1253
0.7534
0.5164
0.4825
0.3240
0.70
0.3893
0.5129
0.2414
0.1225
0.7534
0.5164
0.4778
0.3214
10%
0.4020
0.4975
0.2020
0.1310
0.7534
0.5164
0.4872
0.2947
0.3980
0.4838
0.1888
0.0921
0.7660
0.4395
0.5184
0,3373
4,00
0.3959
0.2943
0.2157
0.0562
0.7500
0.3028
0.4809
0.3014
5.00
0.4380
0.2840
0,2050
0.0562
0.7720
0.1481
0.4809
0,3040
7.00
0.4242
0.3317
0.2286
0.0562
0.7244
0.1530
0.4798
0.2393
10.00
0.4242
0.2145
0.1541
0.0888
0.7453
0.1781
0.5003
0.2880
30

---

Published as a conference paper at ICLR 2025
Table 5: UWC Tuning for WTNPO (a 0.5). & 1 indicate smaller larger values are preferable.
WTNPO
Phi-1.5
Llama-2-1 2-7B
ES eS-exact
ES-perturb
ES exact
ES "S-perturb
setup
retain
unlearn
retain
unlearn
retain f
unlearn
retain f
unlearn
before unlearning
0.4433
0.5969
0,2115
0.1605
0.8277
0.8039
0.5302
0.4001
0.05
0,4412
0.1538
0,2080
0.0700
0.7343
0.0833
0.4863
0.0767
0,4394
0.1801
0,2052
0.0652
0.7606
0.0679
0.4957
0.0929
0,4142
0,2136
0.0677
0.7251
0.1629
0.4976
0.0929
0.70
0,4325
0.1524
0.1882
0.0527
0.7874
0.1629
0.4863
0.0865
0.4412
0.1524
0.1948
0.0527
0.7289
0.1121
0.1064
0.3944
0.1412
0.1709
0.0527
0.6673
0.0904
0.5152
0,3242
0,3713
0,2052
0.7040
0.0979
0.4358
0.1252
0,4213
0.1799
0.7040
0.0979
0.5152
0,3690
0,4315
0,2052
0.0813
0.7040
0,1153
0.4974
0.1951
10.00
0,4523
0.2052
0.0813
0.7040
0.1509
0.4603
0.2975
before unlearning
0.4433
0.5619
0.2115
0.2374
0.8277
0.7735
0.5302
0.4126
0.05
0.4374
0.3243
0.1849
0,2479
0.7520
0.4073
0.5122
0.4013
0.10
0.3745
0.3848
0.2222
0,2479
0.7494
0,4776
0,5122
0,4013
0.50
0,4041
0.3562
0.2414
0.1587
0.7534
0,4044
0,5109
0,3975
0.70
0,4080
0,4222
0.2478
0.1867
0.7534
0.4337
0.4809
0,3803
5%
1.00
0.4560
0.4222
0,2523
0.1967
0.7476
0.4233
0.4809
0,3645
2,00
0.4402
0.3209
0.1841
0,1850
0.7534
0,4085
0.4888
0.2940
4.00
0.4433
0.3903
0.1921
0.1619
0.7533
0.0764
0.4872
0,1426
5,00
0.4454
0.3792
0.2515
0.1719
0.7691
0.1178
0.4950
0,1690
7.00
0.4454
0.3357
0.2133
0.1669
0.7451
0.0777
0,5022
0.1690
10.00
0.4454
0,3814
0.1807
0.1694
0.7725
0.0242
0,5319
0.2442
before unlearning
0.4433
0.4799
0.2115
0.1843
0.8277
0.8307
0.5302
0,3099
0,4210
0.47TI
0.1829
0.1339
0.7534
0.3363
0.4825
0.2884
0.10
0.4601
0.4711
0.1963
0,1425
0.7534
0.5363
0.4809
0.2757
0.50
0.3865
0.3518
0,2189
0.1321
0.7534
0.5363
0.4825
0.2677
0.70
0.4200
0.3753
0.1676
0.0788
0.7534
0.5363
0.5063
0,2872
10%
0,4322
0.3432
0.1615
0.0538
0.7520
0.4619
0.4842
0.2769
0.4519
0.4117
0,2014
0.0583
0.7720
0.3741
0.5049
0,3335
4,00
0.3994
0.2390
0.1854
0.0453
0.7720
0.0446
0.5216
0.2989
5.00
0.4223
0.1658
0,2102
0.0974
0.7691
0.0283
0.4809
0,2898
0.4242
0.2035
0.1774
0.0888
0.7484
0.0355
0.4911
0.2118
10.00
0.4212
0.2742
0.1633
0.0517
0.7717
0.0355
0.4960
0.2537
31

---

Published as a conference paper at ICLR 2025
Table 6: UWC Tuning for WTNPO (a 1). 1 indicate smaller larger values are preferable.
WTNPO
Phi-1.5
Llama-2-1 2-7B
eS-exact
ES-
ES exact
ES ES-perturb
setup
retain
unlearn
retain
unlearn
retain f
unlearn
retain f
unlearn
before unlearning
0.4433
0.5969
0,2115
0.1605
0.8277
0,8039
0.5302
0.4001
0.05
0,4412
0.1738
0,2052
0.0659
0.7090
0.1376
0.4863
0.0767
0,4412
0.1738
0.1989
0.0659
0.7166
0.1376
0.4879
0.0767
0,4412
0.1738
0.1925
0.7713
0.1319
0.4968
0.0767
0.70
0,4412
0.1738
0.1861
0.0567
0.7118
0.0840
0.4896
0.0767
0,4412
0.1738
0,2052
0.7522
0.0897
0.4896
0.0767
0.4412
0.0647
0.1978
0.0465
0.6497
0.0648
0.4777
0.0793
0,4199
0.1969
0.0452
0.7040
0.0736
0,0844
0.3790
0,2074
0.7040
0.0736
0.4955
0.1140
0,4258
0.1865
0.0527
0.7040
0.0999
0.4505
0.1505
10.00
0,4319
0,2070
0.0813
0.7214
0.1359
0.5200
0.2588
before unlearning
0.4433
0.5619
0.2115
0.2374
0.8277
0.7735
0,5302
0.4126
0.05
0.4560
0,4082
0.2259
0.1967
0.7534
0,3855
0.4841
0,3697
0.10
0,4000
0,4238
0.2242
0.1967
0.7491
0.3754
0.4780
0,3645
0.50
0.4320
0,4062
0.1990
0.1063
0.7534
0.3754
0.4888
0.2914
0.70
0.4200
0.4062
0.1992
0.0823
0.7463
0.4174
0.4869
0.2837
5%
1.00
0.4278
0.3698
0.2557
0.1097
0.7317
0.4240
0.4812
0.2837
2.00
0.4029
0.2473
0.2134
0.1203
0.7534
0.3786
0.4848
0,2642
4.00
0.4454
0.3853
0.2077
0,1105
0.7658
0.0781
0.4807
0.1971
5,00
0.4454
0.2985
0.2227
0.1754
0.7625
0.0681
0.4772
0,1820
7.00
0.4254
0.2913
0.1644
0.1679
0.7594
0.0448
0.4795
0.1356
10.00
0.3894
0.2826
0.1639
0.1477
0.7887
0.0304
0.4873
0.1871
before unlearning
0.4433
0.4799
0.2115
0.1843
0.8277
0.8307
0.5302
0,3099
0,4810
0.2738
0,2188
0.7534
0.3363
0.4779
0.2677
0.10
0.4246
0.2024
0,2036
0.0637
0.7534
0.4953
0.4809
0,2884
0.50
0.4180
0.3978
0.1639
0.0434
0.7491
0.5030
0.5073
0.2947
0.70
0.4540
0.3663
0.2202
0.0417
0.7534
0.5030
0.4989
0.2675
10%
0,4502
0.2201
0.1992
0.7513
0.3768
0.4893
0.2989
0.4234
0.1453
0,2065
0.7551
0.2972
0.5185
0,2575
4,00
0.4205
0.1344
0.1958
0.0193
0.7675
0.0402
0.4792
0.2553
5.00
0.4208
0.1260
0.1926
0.0239
0.7691
0.0378
0.4960
0.2255
7.00
0.3934
0.1464
0.1557
0.1002
0.7001
0.0335
0.4742
0.2090
10.00
0.3860
0.1123
0.1652
0.1132
0.7693
0.0525
0.4943
0.2459
32

---

Published as a conference paper at ICLR 2025
Table UWC Tuning for WTNPO (a 1.5). & 1 indicate smaller larger values are preferable.
WTNPO
Phi-1.5
Llama-2-1 2-7B
ES ES-exact
ES-
ES exact
ES IS-perturb
setup
retain
unlearn
retain
unlearn
retain f
unlearn
retain f
unlearn
before unlearning
0.4433
0.5969
0,2115
0.1605
0.8277
0,8039
0.5302
0.4001
0.05
0,4412
0.1688
0.1925
0.0619
0.7118
0,1319
0.4685
0.0767
0,4412
0.1688
0,2052
0.0619
0.7094
0.1319
0.4911
0.0767
0,4412
0.1412
0,2010
0.0619
0.7141
0.0472
0.0398
0,4135
0,2052
0.7189
0.0679
0.4740
0.0793
0,4327
0.1818
0.0619
0.6186
0.0824
0.4798
0.0767
0,4391
0.1693
0.0274
0.7021
0.0736
0.4704
0.0844
0,4183
0.1963
0.0336
0.7021
0.0736
0.4974
0.0844
0,4173
0.0647
0.1911
0.0425
0.7040
0.0912
0.5022
0.1505
0,4258
0.0500
0.2033
0.7040
0.1404
0.4583
0.1428
10.00
0,4243
0.0620
0.2053
0.0527
0.7040
0.1521
0.4589
0.1667
before unlearning
0.4433
0.5619
0.2115
0.2374
0.8277
0.7735
0.5302
0.4126
0.05
0.4539
0,4062
0.2574
0.0926
0,7505
0.3786
0,5122
0.3783
0.10
0.4560
0,4062
0.2374
0.0646
0.7534
0.3911 1
0.4908
0,3295
0.50
0.3934
0.2448
0.1984
0.0672
0.7534
0.3911
0.4888
0,3628
0.70
0.4469
0.2448
0.1934
0.1012
0.7505
0.3786
0.4888
0,3295
5%
1.00
0.4510
0.2448
0.1791
0.1203
0.7534
0.3786
0.4888
0,3052
2.00
0.3915
0.3621
0.2047
0.1067
0.7534
0.3354
0.4828
0,2456
4.00
0,4214
0.3393
0.2172
0.1217
0.7533
0.0427
0.4805
0.1257
5,00
0.4334
0.2879
0.2247
0.1320
0.7480
0.0753
0.4950
0.1916
7.00
0.4454
0.2879
0.2177
0.1154
0.7497
0.0100
0.4796
0.1895
10.00
0.3894
0.2071
0.2177
0.1154
0.7570
0.0198
0.4920
0.1342
before unlearning
0.4433
0.4799
0,2115
0.1843
0.8277
0.8307
0.5302
0,3099
0.4262
0.1453
0.1816
0.7534
0.4925
0.4852
0.2677
0.10
0.4704
0.1625
0.1926
0.0173
0.7534
0.4437
0.4896
0.2677
0.50
0.4519
0.2246
0.2185
0.0280
0.7720
0.3792
0.4977
0.2677
0.70
0.4145
0.1369
0.2167
0.0453
0.7683
0.2972
0.5154
0.2677
10%
0.4254
0.1253
0,2110
0.7720
0.0355
0.5202
0.2842
0.4345
0,2090
0.7625
0.0149
0.4825
0,2989
4,00
0.4234
0.1357
0,2190
0.0120
0.7549
0.0451
0.5133
0.2677
5.00
0.4306
0.1347
0.1998
0.0239
0.7807
0.0111
0.5061
0.2952
0.3934
0.1161
0.1660
0.1002
0.7735
0.0043
0.4976
0.2302
10.00
0.4149
0.1380
0.1591
0.1002
0.7691
0.1
0.4911
0.2921
33

---

Published as a conference paper at ICLR 2025
Table 8: UWC Tuning for RMU (shallow). f/1 indicate smaller larger values are preferable.
RMU
Phi-1.5
Llama 2-7B
ES-exact
ES-perturb
ES exxex
ES- perturrttr
setup
retain
unlearn
retain
unlearn 4
retain
unleam
retain t
unlearn
before unlearning
0,4433
0.5969
0.2115
0.1605
0.8277
0.8039
0,5302
0.4001
0.00
0,4530
0.5969
0.2007
0.1855
0.7604
0.5993
0.4888
0.3816
1.00
0,4122
0,4356
0.2115
0.1855
0.7502
0.6278
0.4890
0.4253
2.00
0,4312
0,4080
0.2072
0.1855
0.7653
0.6714
0.4531
0.4002
1%
4.00
0.4245
0,4682
0.2115
0.1855
0.7356
0.7223
0.4758
0.4008
5.00
0.4398
0.5149
0.1981
0.1855
0.7163
0.6287
0.4871
0.4008
7.00
0,4460
0.5096
0.2201
0,1855
0.7292
0.7128
0.4516
0.4104
10.00
0.4215
0,4816
0.2018
0.1855
0.7292
0.6195
0.4453
0.4104
before unlearning
0.4433
0.5619
0,2115
0,2374
0.8277
0.7735
0.5302
0.4126
0,4164
0.4924
0.1918
0,2172
0.7516
0.7292
0.4676
0.3616
0,4284
0.5124
0,2194
0.2172
0.7762
0.7357
0.4677
0.4504
0,4044
0.4774
0.1939
0,2172
0.7146
0.6370
0.4453
0.4126
5%
0.4404
0.4252
0,2047
0,2147
0.7619
0,6758
0.4812
0.4126
0,4404
0.4838
0,2181
0,2207
0.7139
0.6758
0.4812
0.4164
0,4204
0,2073
0,2339
0.7604
0.6758
0.4793
0.4126
10.00
0.4194
0.4114
0.1903
0.2339
0.7146
0.6370
0.4453
0.4126
before unlearning
0.4433
0,4799
0,2115
0.1843
0.8277
0.8307
0,5302
0.3099
0.00
0.4425
0.5761
0,2055
0,1424
0.7887
0.8165
0.4246
0.2662
1,00
0.4424
0.5968
0.2133
0.1567
0.7568
0,6869
0.4771
0.2989
2,00
0.4304
0.5961
0.2028
0,1360
0.7628
0.6755
0.4690
0.2989
10%
4.00
0,4364
0.5208
0.1944
0.1547
0.7229
0.5784
0.4812
0.2766
5,00
0.4284
0.5184
0.2007
0.1547
0.7262
0.6268
0.4797
0.2944
7.00
0.4404
0.5184
0.2007
0.1754
0.7271
0.5778
0.4232
0,3033
10.00
0.4404
0,4693
0.2136
0.1675
0,7032
0,5455
0.4849
0,3033
Table 9: UWC Tuning for RMU (middle). 4/1 indicate smaller / larger values are preferable.
RMU
Phi-1.5
Llama 2-7B
ES-exact
ES-pert
ES exact
ES ES-perturb
setup
retain
unlearn
retain
unlearn J
retain f
unleam
retain t
unlearn
before unlearning
0.4433
0.5969
0.2115
0.1605
0.8277
0.8039
0,5302
0.4001
0.00
0.4203
0.5969
0.2153
0,2069
0.7606
0.5127
0.5115
0.4001
1.00
0.4203
0.5969
0.2180
0.1409
0.7416
0.5093
0.4878
0.4001
2.00
0.4203
0.5969
0.1831
0.1261
0.7512
0.4263
0.4644
0,3794
1%
4.00
0.4203
0.5969
0.1831
0.1261
0.7559
0.5093
0.4096
0.3538
5.00
0.4203
0.5969
0.2073
0.1328
0.7413
0.4810
0.4927
0.4001
7.00
0.4218
0.5969
0.2119
0.1261
0.7413
0.4810
0.4927
0.4001
10.00
0.4203
0.5969
0,2119
0.1350
0.7655
0.4137
0.4927
0.3624
before unlearning
0.4433
0.5619
0.2115
0.2374
0.8277
0.7735
0.5302
0.4126
0.4262
0.5723
0.1932
0.2207
0.8017
0.6376
0.4754
0,3884
1,00
0.4232
0.4999
0.2032
0.2207
0.7381
0.4284
0.4798
0,3884
2.00
0.4232
0,5013
0,2229
0.2207
0.7179
0.5146
0.4379
0,3884
5%
0.4218
0.5309
0.1887
0.2030
0.7112
0.4034
0.4927
0,3884
0.3578
0.3762
0,2119
0.2030
0.7438
0.6323
0,3884
0.4218
0.5946
0.1990
0.1971
0.7438
0.6684
0.4927
0.4126
10.00
0.4262
0.4000
0.1968
0.2005
0.7552
0.6615
0.4644
0.4126
before unlearning
0.4433
0.4799
0.2115
0.1843
0.8277
0.8307
0,5302
0,3099
0.00
0.4262
0.4584
0,1952
0.1786
0.7463
0.6152
0.4754
0,3884
1.00
0.4203
0.4909
0.2108
0.1816
0.7493
0.7636
0.4379
0,3139
2.00
0.4232
0.5025
0.2212
0.1786
0.7374
0.7275
0.4831
0,3158
10%
4.00
0.4394
0.5025
0.2117
0.1901
0,7874
0.7526
0.4871
0,3196
5.00
0.4224
0.4511
0.2117
0.1799
0,7874
0.6907
0.4653
0,3220
7.00
0.4005
0.4568
0.1496
0.1741
0.7434
0,5821
0.4776
0.2908
10.00
0.4522
0.4938
0.1542
0,2000
0.7534
0.6495
0.4927
0,3316
34

---

Published as a conference paper at ICLR 2025
Table 10: UWC Tuning for RMU (deep). + / indicate smaller larger values are preferable.
UWC
Phi-1.5
Llama-2-1
ES-exact
ES-perturh
ES ES-exact
ESSperturb
setup
retain
unlearn |
retain
unlearn $
retain
unlearn
retain f
unlearn
before unlearning
0,4433
0.5969
0.2115
0.1605
0.8277
0,8039
0,5302
0.4001
0.00
0.3936
0.5219
0.2136
0.1574
0.7836
0.6364
0.4927
0.4089
1.00
0.4156
0.5219
0.2117
0.1574
0.7461
0.4564
0.4442
0.3402
2.00
0.4212
0.5219
0.2080
0.1655
0.6977
0.2814
0.4847
0.2790
16
4.00
0.4212
0.5153
0.1951
0.1655
0.6913
0.2992
0.4428
0.2748
5.00
0,4212
0,5121
0.2062
0.1655
0.7122
0.3974
0.4976
0.1982
7.00
0.4212
0.5108
0.1885
0.1686
0.7509
0.3271
0.4428
0.2305
10.00
0.4184
0,4963
0.2136
0.1717
0.7106
0.3815
0.4428
0.2062
before unlearning
0.4433
0.5619
0.2115
0.2374
0.8277
0.7735
0.5302
0.4126
0,4212
0.4953
0,2007
0,2182
0.7731
0.7074
0.4675
0,3953
0.4049
0.5144
0,2115
0.2182
0.7731
0.6488
0.4801
0,3850
0.4110
0.5602
0.1967
0.2227
0.7410
0.6683
0.4801
0,3714
5%
0.4151
0.5621
0.1930
0.2227
0.7731
0.6031
0.4598
0,3869
0,4212
0.5271
0,2099
0.2394
0.7464
0.7001
0.4613
0,3958
0,4212
0.5285
0.1951
0.2394
0.8113
0.6983
0.5015
0.4464
10.00
0.4064
0.4816
0.2025
0.2349
0.7319
0.7763
0.4600
0.4393
before unlearning
0.4433
0.4799
0.2115
0.1843
0.8277
0.8307
0.5302
0.3099
0.00
0.4212
0,4935
0.2095
0.1933
0.7577
0.6868
0.4410
0,2884
1,00
0.4049
0,4935
0.2039
0.1963
0.7673
0.7560
0.4571
0,2906
2.00
0.4212
0.4935
0.1969
0.1933
0.7731
0.7402
0.4865
0.3239
10%
4.00
0.4212
0.4935
0.2115
0,1933
0.7731
0.7414
0.4426
0.2674
5.00
0.4212
0.4959
0.1967
0.1933
0.7486
0.7688
0.4738
0,2192
7,00
0.4212
0,4799
0.2097
0.1933
0.7620
0.7402
0.4784
0,2547
10.00
0.3934
0.4799
0.1951
0.1786
0.7394
0.7402
0.4890
0.2547
35


Reviews:
[{"review_id": "pxYHQpZMwS", "reviewer": "Reviewer_MskC", "summary": "This paper discusses the importance of auditing large language models (LLMs) to identify potential risks and the need for timely updates to remove bad responses (unlearning being the solution in consideration here). The authors propose a unified framework to comprehend various unlearning objectives, introducing the concept of G-effect to analyze and compare different unlearning methods. Insights from G-effect analysis prompt focus on a two-step approach to update original LLM parameters to get unlearned one- using a removal and retention step to deteriorate performance on the unlearning dataset while maintaining performance on the rest of the data.", "questions": "- Is it possible to see the effect of choice parameters like number of samples to be forgotten on the G-effect ? \n- Other ablation studies are also appreciated- for instance choice of network architecture, sensitivity to optimizer params, etc. It wasn't clear if these results are averaged over multiple runs. \n- I am curious to see how G-effect varies for samples that are harder to forget. This may even help explaining the relationship between influence functions and data values with ability to unlearn.", "limitations": "", "rating": 8, "confidence": 2, "soundness": 4, "presentation": 4, "contribution": 4, "strengths": "-   The paper tackles an important topic in the field of natural language processing, specifically the need for LLM unlearning to remove targeted information without destroying model integrity.\n-   The authors propose a novel framework to analyze and compare different unlearning objectives, introducing the concept of G-effect to measure the impact of unlearning objectives on targeted or common data. G effect combines the influence of both goals of a good unlearning objective- removal and retention into a single metric.\n-   The paper provides a comprehensive discussion of different unlearning objectives, including gradient ascent, negative preference optimization, PO, and representation misdirection for unlearning. The paper introduces advanced unlearning objectives, such as WGA and WTNPO, which set new state-of-the-art results in unlearning objectives.\n- Comparison between objectives Gradient Ascent, NPO, etc. and effect of regularization is thoroughly studied.\nThe paper introduces advanced unlearning objectives, such as WGA and WTNPO, which set new state-of-the-art results in unlearning objectives.", "weaknesses": "- Ablation study on the effect of size of data to be forgotten on the effectiveness of G-effect. \n- Effect of 'harder' or 'easier' examples to forget on G-effect. \n- Figures plotting the G-effect have their axes not labeled.", "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": "ukuy8Xc8Cd", "reviewer": "Reviewer_43oV", "summary": "Large language models (LLMs) need thorough audits to uncover risks like copyright or privacy violations. When such risks are identified, prompt updates are essential to filter out inappropriate outputs, ensuring that models remain lawful and safe for use. This concern has fueled new research into LLM unlearning, aimed at selectively erasing specific unwanted knowledge while maintaining the reliability of other, unaffected responses. In this context, the authors of this paper introduce the G-effect toolkit, which measures how unlearning objectives influence model performance through the analysis of gradients.", "questions": "Overall, this paper is quite intriguing. The authors introduce an innovative framework called G-effect, designed to measure the influence of unlearning objectives on model performance through gradient analysis. However, there are some points for the authors to consider:\n\n1) Unlearning is typically applied in two scenarios: first, for privacy reasons, where users seek to remove content related to privacy. This is the scenario explored in this paper. However, unlearning can also be driven by security concerns, such as when an LLM is compromised by data poisoning, and the system needs to mitigate the impact of various poisoning attacks. It remains unclear if the conclusions drawn in this paper can be extended to this second scenario.\n\n2) G-effect appears to share similarities with influence functions and Shapley value methods. The authors should clarify these connections.\n\n3) Research, such as [A], suggests that LLM unlearning may not always fully eliminate the influence of data that users wish to remove. It is not evident whether the proposed G-effect accounts for this limitation.\n\n[A] Machine Unlearning Fails to Remove Data Poisoning Attacks.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 4, "strengths": "The paper is clearly written and straightforward to understand.", "weaknesses": "It is uncertain if the findings discussed in this paper can be applied to scenarios where LLM unlearning aims to eliminate the effects of contaminated data.", "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": "CKK3eWkvKj", "reviewer": "Reviewer_SBC5", "summary": "Various approaches have been proposed in the literature to perform LLM unlearning. Existing unlearning evaluation metrics compare LLM performance before and after unlearning. To provide more insights into understanding the underlying mechanisms, this paper aims to quantify the impacts of unlearning objectives on model performance from a gradient perspective. To do that, this paper proposes the toolkit of the G-effect: \n1. unlearning G-effect: the capability to decrease model performance on unlearning data \n2. retaining G-effect: the capability to maintain/enhance performance on other data \n\nG-effect compares the gradient of the unlearning objective and the risk metric that assesses the LLM performance:\n - If the gradients of the unlearning objective align in opposite directions to the risk metric, model updating based on the unlearning objective is capable of decreasing model performance measured by the risk\n - If the gradients of the unlearning objective align in similar directions to the risk metric, model updating based on the unlearning objective is capable of enhancing model performance measured by the risk metric\n\nThis paper quantifies the degree of such similarity between unlearning objective gradients and the risk metric gradients using their dot products.", "questions": "I have outlined questions for each weakness above.", "limitations": "", "rating": 3, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 3, "strengths": "1. Gradient-based analysis of the G-effect enables a better understanding of unlearning approaches including\n\t- examining the dynamics of unlearning procedures\n\t- explore the impacts of particular layers or data points involved during unlearning\n2. Using G-effects to assess Gradient Ascent, Weighted Gradient Ascent, Negative Preference Optimization, Preference Optimization, Representation Misdirection for Unlearning and Regularization. Their study concludes several interesting findings. For example among 3 representative regularization terms, namely gradient difference, KL divergence and representation retention, KL  is superior for retention.", "weaknesses": "1. This paper (Section 4) examines G-effects of each unlearning objective independently and in isolation to other learning objectives. Results are also shown and discussed in separate figures and parts of the paper. Studying G-effect of each learning objective in isolation, raises the concern regarding the comparability of G-effect values across various unlearning objectives and approaches. \n \t- Why empirical analysis of each unlearning approach is shown and discussed in separate parts of the paper?\n\t- Are G-effect values comparable across different unlearning approaches? are values comparable and why?\n\t- Can the proposed G-effect rank unlearning approaches?\n 2. Section 5 and its Table 1 provide a comprehensive comparison of various unlearning approaches using TOFU unlearning dataset for the removal of fictitious author profiles from LLMs finetuned on them. However, this comparison uses only existing metrics: forget quality, model utility, and PS-scores, and does not report the proposed G-effects.  \n \t- Why G-effects are missing in this section?\n \t- How do G-effect values correlate with metrics presented in Table 1?\n \t- Why are the order and ranking of unlearning objectives different across different removal and retention metrics?\n\n3. G-effects need access to intermediate checkpoints during unlearning, especially given the pattern of values in for example Figure 3 (i.e., a peak and then flat close to zero). How does this limit the applicability of the proposed metric? \n \t\t\n4. The G-effect definition uses model checkpoints at different time steps and does not directly take into account the risk and unlearning of the initial model. \t\n\t- Why does this make sense?\n\t- Is this why you need to do accumulative?\n\t- what does the G-effect at each unlearning step mean?\n\t- what does accumulation across unlearning steps mean?\n\t- What does pick mean in Figure 3? Should we stop after that step to have an effective unlearning? what would be the benefit of continuing? is 0 G-effect value the limitation of your method?\n\n5. Some of the claims are not completely supported. For example, the claim \"In terms of the unlearning G-effects, it indicates that the unlearning strength of NPO is weaker; however, for the retaining G-effects, it suggests that NPO better preserves the model integrity.\" As an initial step, I would link it to numbers in Table 1.\n6. Membership inference attacks are a common approach in the literature for evaluating the removal capability of unlearning approaches [MUSE]. However, this paper does not report the success of membership inference attacks. How the unlearning G-effect is compared to the success of MIA? Are they aligned?\n\n[MUSE] Weijia Shi, Jaechan Lee, Yangsibo Huang, Sadhika Malladi, Jieyu Zhao, Ari Holtzman, Daogao Liu, Luke Zettlemoyer, Noah A Smith, and Chiyuan Zhang. Muse: Machine unlearning six-way evaluation for language models, 2024.", "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": "O6OXfxNIoD", "reviewer": "Reviewer_zecJ", "summary": "The paper beings with a bird's eye view of unlearning, highlighting its importance and the main drawbacks of the current approach. The paper suggests G-effect, a method to better examine the behavior and properties of unlearning during learning. This is done by taking into account the gradients with respect to unlearning two objectives and computing their inner-product with the gradients taken for unlearning. This method has the potential to serve as an evaluation criteria of existing and new unlearning approaches, while also providing insights to explain the success and failure of unlearning approaches, beyond the simple black-box evaluation.\n\nThis method is interesting and powerful, as it was able to generate five observations on unlearning: Unlearning affects shallow layers more, Unlearning compromises retention, Excessive unlearning is harmful, Risk weighting is powerful, Regularization is important.\n\nThe paper then explores multiple unlearning approaches; GA, NPO, PO and RMU using the G-effect.\n\nThe paper address the current limitation of the approach and suggests new promising directions.", "questions": "Is something off with Figure-3 or its caption?", "limitations": "", "rating": 8, "confidence": 3, "soundness": 3, "presentation": 4, "contribution": 4, "strengths": "The paper is insightful and well written. It provides a lot of context to the reader, explains the main drawbacks of the current approach and the importance of G-effect in addressing and examining unlearning from a scientific point-of-view, as opposed to blackbox trial and error which stems from intuition. The paper provide a very thorough analysis of G-effects on multiple unlearning approaches.", "weaknesses": "Not sure", "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": "Cjlt1R1sWZ", "reviewer": "Reviewer_uXUc", "summary": "This paper tackles the concept of unlearning in Large Language Models (LLMs), focusing on the removal of learned knowledge while preserving the overall model integrity. The authors propose a new metric, the G-effect, to quantify the impact of unlearning objectives on model performance.", "questions": "Legal compliance has been an oft touted reason for unlearning. I have yet to see any compelling argument that unlearning passes any kind of legal bar for data removal. I’m not even sure what the requirements are for meeting e.g. GDPR requirements. I am concerned that the unlearning community may be operating in a vacuum, failing to actively engage with the legal community to determine the practical applications and implications of unlearning. \n\n– \n\n“It is common the cases where shallow layers are more affected than deeper layers during unlearning. It suggests that general knowledge, predominantly encoded in shallow layers (Patil et al., 2023), undergoes substantial alterations“ Why not freeze shallow layers during unlearning using methods like [1]?\n\n[1] Goel, Shashwat, et al. \"Towards adversarial evaluations for inexact machine unlearning.\" arXiv preprint arXiv:2201.06640 (2022).\n\n– \n\n“Unlearning compromises retention. Although conceptually existing (cf., Section 3), current\nunlearning objectives all fail to retain the overall model performance when unlearning.“ This is not a new contribution. Many prior works have made this discovery. I also do not understand the difference between this statement and the next contribution: “ Excessive unlearning is harmful. An excessive extent of unlearning has severe impacts such that the deterioration in common model responses can outweigh improvements in unlearning.”\n\n–\n\nI do not believe the contributions highlighted are particularly interesting. The first three listed are already well known phenomena (the first being the motivation for prior unlearning techniques in [1]). The fifth contribution has already been studied. I do think the fourth contribution: “Risk weighting is powerful. Prioritizing certain beneficial points is justified to be effective for unlearning. However, there still exists a large space to further refine risk weighting mechanisms.” is interesting, but I’m not sure this amounts to a significant contribution to the field.\n\n–\n\nThe unlearning objectives designed for concept removal assumes that one can pinpoint and incorporate the specific data requiring removal into the unlearning dataset denoted as D_u. I do not believe this is realistic in general.\n\n–\n\n“Removal. The performance on the unlearning dataset Du should significantly deteriorate, i.e., R(Du; θu) ≫ R(Du; θo), revealing effective unlearning on data targeted to be erased.“ Throughout this paper, privacy is highlighted as a use case for unlearning. This is not a good removal metric for anything to do with private information. For example, imagine I want to unlearn “Alice’s phone number is 12345”, and I do this by gradient ascent, up to the point where loss(“Alice’s phone number is 12345”) >> loss(“Alice’s phone number is *any other number*”), then this becomes an oracle, and reconstruction or identification of private information becomes easy. Multiple prior works have discussed this and how to define unlearning for privacy.\nSimilarly, “We consider the practical objective of erasing targeted knowledge as much as possible (Liu et al., 2024), diverging from the classical definition of machine unlearning (Bourtoule et al., 2021) that seeks to make models behave as if they were trained without the targeted data. Our goal is more suitable for LLM unlearning, driven by the need to eliminate content that poses privacy and copyright concerns, with the understanding that more thorough elimination leads to more favorable behaviors.“ I believe any unlearning definition for privacy that does not try to align with a model that never trained on that data is bad for privacy. It also not clear what kind of privacy we should be concerned about. Reconstruction? Identification of membership?\n\n—\n\n“Sadly, merely comparing performance provides limited insights into understanding the underlying mechanisms.“ What's the definition of “understand” here? Can you formalize it?\n\n—\n\n“Generally speaking, the G-effect compares the gradients of the unlearning objective Lu and the risk metric R. If the gradients of Lu align in similar directions to R, model updating based on Lu\nis capable to enhance model performance measured by R, an obvious alternative of R(D; θu) −\nR(D; θo) to measure the performance change“ Apologies, I’m a bit confused here. Why not directly optimize R then if it is differentiable?\n\n–\n\nIn Figure 1, it’s not clear how the intersection actually maps to successful unlearning. It would be really useful to give some examples (or quantitative results) for various points on the sphere, showing that unlearning is most successful at the intersection.\n\n–\n\n“Due to the high costs in fully computing the G-effects, we focus on experiments based on 5% TOFU fictitious unlearning (Maini et al., 2024) with Llama-2-7B (Touvron et al., 2023a) (cf. Appendix B). All the methods will run for 5 epochs, totaling about 60 steps.\n“ This seems like a significant barrier for using G-effect. Also does this mean you only use a dataset of 40 examples? This seems quite small.\n–\n\n“The G-Effects across Unlearning Steps” I don’t see what the useful insights are here. I believe we could have instead measured the NLL of examples and gotten an equally useful signal. Overall I found it difficult to assess if the G-Effect is a more useful metric than directly measuring losses over unlearning.", "limitations": "", "rating": 5, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "- Investigating unlearning dynamics is an interesting and understudied area.\n\n- Empirical results back up some of the authors claims.", "weaknesses": "See questions and comments.", "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": "MCKpeizVLq", "reviewer": "Reviewer_oKM6", "summary": "This paper focus on analysis of existing unlearning methods in the scope of LLMs. The authors propose a general toolkit for analysis of existing methods, which is named G-effect. G-effect analyzes unlearning methods from both forgetting and retaining. Experiments show the rationality of the proposed G-effect, and the effectiveness of several proposed variants.", "questions": "no", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "- The paper is well structured.\n- The authors propose G-effect to analyze existing unlearning methods from the perspectives of both forgetting and retaining effects.\n- Analysis of G-effect somehow accords with the experimental results. Experiments show the effectiveness of the proposed variants.", "weaknesses": "- What is the rationale of designing WGA? The authors did not clearly state the reasons of choosing such format.\n- I do not clearly see the challenges of coming up such a general toolkit for analysis of various unlearning methods.\n- The claim in Line 081 is somehow too strong. How did the authors conclude that KL is the optimal choice?\n- The presentations of Figure 2,3,4 are somehow hard to read. Putting the legends near the figures might be better.", "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)