Towards Effective Evaluations and Comparison for LLM Unlearning Methods

## Abstract

Abstract The compelling goal of eradicating undesirable data behaviors, while preserving usual model functioning, underscores the significance of machine unlearning within the domain of large language models (LLMs). Recent research has begun to approach LLM unlearning via gradient ascent (GA)—increasing the prediction risk for those training strings targeted to be unlearned, thereby erasing their parameterized responses. Despite their simplicity and efficiency, we suggest that GA-based methods face the propensity towards excessive unlearning, resulting in various undesirable model behaviors, such as catastrophic forgetting, that diminish their practical utility. In this paper, we suggest a set of metrics that can capture multiple facets of real-world utility and propose several controlling methods that can regulate the extent of excessive unlearning. Accordingly, we suggest a general framework to better reflect the practical efficacy of various unlearning methods—we begin by controlling the unlearning procedures/unlearned models such that no excessive unlearning occurs and follow by the evaluation for unlearning efficacy. Our experimental analysis on established benchmarks revealed that GA-based methods are far from perfect in practice, as strong unlearning is at the high cost of hindering the model utility. We conclude that there is still a long way towards practical and effective LLM unlearning, and more efforts are required in this field.

## 1 Introduction

Large language models (LLMs), like Llama [, ] and GPT [, ], have exhibited remarkable proficiency in general-purpose language generation and understanding [, , , ]. These advancements are largely credited to the development of Transformer-based architectures [] with billions of parameters and to the extensive pre-training on web-sourced corpora with trillions of tokens []. However, on the other side, scaling up models aggravates the risk of memorizing effects [] and sourcing from the web makes LLMs inherent its inaccuracies and biases [].
It raises the invoking concerns for LLM privacy and fidelity, posing a long array of undesirable LLM behaviors sourced from training corpora [], including copyright [], hallucination [], fairness [], and toxicity [].

How to Erase Undesirable Data Behaviors in LLMs? Machine unlearning [, ] offers a general solution. As highlighted by [], machine unlearning is a cost-effective alternative to more demanding methods such as re-training from scratch and reinforcement learning from human feedback []. In the context of LLMs, the general goal of unlearning is to precisely remove the parameterized knowledge related to unlearning targets meanwhile maintaining model performance for non-targets []. The unlearning targets can range from individual data entries to broader knowledge such as harmful contents []. Regardless of varying scopes, the forgetting targets in LLMs are typically characterized by an unlearning set $\mathcal{D}_{\mathrm{u}}=\{s_{\mathrm{u}}=[x,y_{\mathrm{u}}]\}_{n_{\mathrm{u}}}$ of size $n_{\mathrm{u}}$ [, ]. Then, we need to develop methods upon $\mathcal{D}_{\mathrm{u}}$ that meet the general goal of LLM unlearning. Currently, LLM unlearning has been recognized as particularly suitable for removing privacy and copyright contents []. It may also serve as a promising intermediate process for editing harmful behaviors [], potentially addressing their sensitivities to the changing prompts.

Inheriting advances made in discriminative tasks, gradient ascent (GA) [, ] has recently established as a foundational baseline for LLM unlearning. The modern usage of GA in LLMs [] stems from the mathematical modeling regarding the goal of LLM unlearning—unlearning data targeted to be erased meanwhile maintaining the original responses for non-targeted ones—named gradient difference (GD). Its learning objective is given by

$$ $-\underbrace{\mathbb{E}_{s_{\mathrm{u}}\sim\mathcal{D}_{\mathrm{u}}}\ell\big{( }y_{\mathrm{u}}|x;\boldsymbol{\theta}\big{)}}_{\text{unlearning risk}}+ \underbrace{\mathbb{E}_{s\sim\mathcal{D}_{\mathrm{t}}\backslash\mathcal{D}_{ \mathrm{u}}}\ell\big{(}y|x;\boldsymbol{\theta}\big{)}}_{\text{retaining risk}},$ (1) $$

where $\ell(y|x;\boldsymbol{\theta})=-\log p(y|x;\boldsymbol{\theta})$ is the prediction loss and $\mathcal{D}_{\mathrm{t}}$ is the full training corpora. Eq. (1) composes of two objectives, namely, the unlearning risk and the retaining risk. The unlearning risk increases the prediction losses for undesirable responses $y_{\mathrm{u}}$ of targeted data, aligning with gradient ascent when updating LLMs in the first order.
However, employing the unlearning risk alone results in unintended changes of responses for non-targeted ones. To prevent this, the retaining risk is further adopted to maintain the original model functioning, ensuring that responses for non-targeted data remain unchanged with a small prediction risk. Generally, GD employs Eq. (1) at the post-training phase, adapting LLM parameters to impose the unlearning of parameterized knowledge within $\mathcal{D}_{\mathrm{u}}$.

Nevertheless, GD is susceptible to excessive unlearning, wherein the unlearning risk after GD will escalate exceedingly, largely surpassing the extent necessary for effective unlearning. Excessive unlearning undermines the practical utility, as it can induce catastrophic forgetting [], manifesting degraded model performance on non-targeted data, as well as extreme confabulation, indicating largely distorted responses on targeted data (cf. Table 1). Sadly, in the literature of LLMs, the scenario of excessive unlearning has not been fully discussed. This oversight may stem primarily from the inadequacy of existing unlearning evaluation metrics, which often fail to encompass diverse criteria (cf. Section 2) that should be simultaneously met after unlearning. Therefore, in Section 3, we suggest a set of metrics that can properly characterize LLMs. These metrics focus on parameterization strengths [] from multiple facets, allowing us to quantify the drawbacks of current unlearning methods in a general and actionable manner.

We further assert that the evaluations of LLM unlearning should be conducted under the prerequisite that no excessive unlearning occurs. Hence, to comprehend the real-world efficacy of existing unlearning methods, it is essential to first control/calibrate the extent of excessive unlearning such that the common model functioning is not critically affected. To this end, we propose several controlling methods to modulate the extent of unlearning in Section 5. With proper controlling, one can then fairly evaluate and compare the true power of various LLM unlearning methods.
Based on such an evaluation framework that considers the real-world utility, we conducted experiments on established benchmarks of TOFU [], studying the elimination of privacy-sensitive profiles. Through our comprehensive evaluations, we showed that GA-based methods achieve unlearning by aggressively altering the parameterized knowledge, which affects both targeted and non-targeted data. It renders the resulting LLMs completely useless, as its strong unlearning comes at the extreme cost of compromising model functioning. Overall, we conclude that the current achievements for LLM unlearning are limited, highlighting the need for more advanced unlearning schemes in the future.

## 2 LLM Learning and Unlearning

To begin with, we discuss the necessary backgrounds for LLM learning as well as LLM unlearning.

LLM Learning. We study the LLM parameterized by $\boldsymbol{\theta}$, typically incorporating layer-wise self-attention structures []. Upon receiving an input $s$, the LLM estimates the probability distribution, denoted by $p(\cdot|s;\boldsymbol{\theta})$, over the next possible tokens. The LLM is trained on a substantial web-scale corpora, denoted by $\mathcal{D}_{\mathrm{t}}=\{s=[x,y]\}_{n_{\mathrm{t}}}$ of size $n_{\mathrm{t}}$. During training, we aim at minimizing the prediction loss $\ell(y|x;\boldsymbol{\theta})=-\log p(y|x;\boldsymbol{\theta})$ over $\mathcal{D}_{\mathrm{t}}$, where $p(y|x;\boldsymbol{\theta})$ is given by $\prod_{i=1}^{|y|}p(y^{i}|[x,y^{<i}];\boldsymbol{\theta})$ with $y^{i}$ the $i$-th token and $y^{<i}$ the prefix up to the $i$-th token. The resulting LLM is capable of properly handling a wide range of language generation tasks. Moreover, we default to employ greedy decoding [], selecting the most probable token at each step of next word generation. Here, we denote the generated string via greedy decoding by $f(s;\boldsymbol{\theta})$.

LLM Unlearning. However, employing training corpora sourced from the wild heavily raises the risk that our LLMs will learn from sensitive/private information [], thereby precipitating a host of legal and ethical concerns [, , , ]. These issues further necessitate the need for a post-training mechanism that enables our LLMs to eradicate any associated parameterized knowledge that is undesirable. This requirement motivates the recent research on LLM unlearning [, ], formalizing the above goal by involving so-called the unlearning set $\mathcal{D}_{\mathrm{u}}=\{s_{\mathrm{u}}=[x,y_{\mathrm{u}}]\}_{n_{\mathrm{u}}}$ ($n_{\mathrm{u}}\ll n_{\mathrm{t}}$, typically). Overall, unlearning tends to make LLMs directly adapt its parameters $\boldsymbol{\theta}$ such that the related content characterized by $\mathcal{D}_{\mathrm{u}}$ can be properly erased. To ease our discussions, we distinguish between two types of data: targeted data, which are targeted to be unlearned (i.e., within the unlearning set $\mathcal{D}_{\mathrm{u}}$), and non-targeted data, which are required to be maintained (i.e., all other data within $\mathcal{D}_{\mathrm{t}}\backslash\mathcal{D}_{\mathrm{u}}$).

Unlearning Goals. For a practical LLM unlearning method, it should satisfy 3 criteria as follows:

- •
Memorization. The direct objective of unlearning is to remove parameterization associated with specific targeted data, ensuring that, at least, the parameterized mapping between $x$ and $y_{\mathrm{u}}$ is erased. Meanwhile, we also need to preserve the memorization for all those non-targeted data, aiming to maintain the original model functioning.
- •
Extrapolation. We further aim for unlearned LLMs to function right on data not encountered during training/unlearning. It indicates the goal to eliminate specific semantics/contents within $[x,y_{\mathrm{u}}]$, rather than merely their mapping. Specifically, unlearned LLMs should refrain from generating contents that semantically mirror the responses of targeted data, meanwhile LLMs should extrapolate well for non-targeted data as in the original LLMs.
- •
Coherency. For both targeted and non-targeted data, we aim for minimal changes to LLM behaviors after unlearning. This focus highlights another aspect of eliminating precise content within targeted data, whereby LLMs only exclude those tokens involving key content within the unlearning set $\mathcal{D}_{\mathrm{u}}$ yet preserving the common syntax and grammars.

Overall, memorization quantifies the strength of corpora parameterized by LLMs and extrapolation further explores their ability to generalize, both of which require our prioritized attention. Additionally, ensuring coherency further benefits the practical usages of LLM unlearning, making the unlearned LLMs general and reliable for its subsequent usages (cf. Section 4 and Appendix A).

Gradient Difference (GD). For the original GA, it utilizes the optimization method of gradient ascent to increase the prediction loss $\ell(y_{\mathrm{u}}|x;\boldsymbol{\theta})=-\log p(y_{\mathrm{u}}|x;
\boldsymbol{\theta})$ associated with the unlearning set $\mathcal{D}_{\mathrm{u}}$. By measuring the parameterized content via the prediction loss, GA aims to reduce the capability of language models to reproduce these undesirable outputs. GD further enhances the conventional GA by regularizing LLMs to maintain original model behaviors for some non-targeted data drawn from $\mathcal{D}_{\mathrm{t}}\backslash\mathcal{D}_{\mathrm{u}}$, ensuring that the prediction risk remains low upon them. The learning objective of GD is encapsulated in Eq. (1). Overall, GD has been recognized as an efficient and promising way to realize LLM unlearning, as highlighted by some recent studies [, ].

## 3 Evaluation Metrics

There is an ongoing question regarding how to properly evaluate the algorithmic effectiveness for LLM unlearning. Classical unlearning metrics for discriminative models [] are not readily applicable for generative tasks as for LLMs. Noticeably, inappropriate and biased evaluations could misguide the research community and weaken the real-world significance. To rigorously quantify model behaviors for LLM unlearning, we suggest an array of metrics crafted for assessing unlearning algorithms from multiple facets. These metrics quantify the strength of parameterized knowledge within generative models [], which are general, actionable, and broadly applicable. We begin by introducing the formal definition of the parameterization strength (PS).

###### Definition 1 ( Parameterization Strength ) .

Given the model $f$, the string $s$, and the metric between two strings as mtc, we quantify the strength of parameterization of $s$ within $f$ by the shortest prefix $s^{<k}$ that enables $f$ to sufficiently recover the remaining suffix $s^{\geq k}$ via greedy decoding, i.e.,

$$ $|s|-\min_{k}\{k|\texttt{mtc}(f(s^{<k};\boldsymbol{\theta}),s^{\geq k})\leq \epsilon\},$ (2) $$

where $\epsilon$ is the allowed difference between the model responses $f(s^{<k};\boldsymbol{\theta})$ and the suffix $s^{\geq k}$.

With different choices of mtc, one can quantify the strength, or extent, for specified knowledge characterized by the string $s$ within the model $f$. Generally, a larger value in Eq. (2) indicates stronger parameterization. Now, based on PS, we suggest a series of metrics to cover the criteria in Section 2.

Memorization. The original purpose of PS is to measure the memorization of learned corpora [, ]. Specifically, it involves measuring the shortest prefix $s^{<k}$ that enables $f$ to *exactly* predict the remaining suffix $s^{\geq k}$. This goal corresponds to the case where mtc is the Hamming distance and $\epsilon$ is 0. Such a specific form of PS is referred to as PS-exact and can be rewritten as

$$ $\texttt{PS-exact}(\mathcal{D})=\mathbb{E}_{s\sim\mathcal{D}}\big{(}1-\frac{1}{ |s|}\min_{k}\{k|f(s^{<k};\boldsymbol{\theta})=s^{\geq k}\}\big{)},$ (3) $$

where we compute the minimal-required proportion of the prefix to accommodate variations in string lengths. PS-exact should be calculated for both the unlearning set $\mathcal{D}_{\mathrm{u}}$ and the retaining set $\mathcal{D}_{\mathrm{r}}$, where we prefer a smaller value for $\texttt{PS-exact}(\mathcal{D}_{\mathrm{u}})$ and a relatively larger value for $\texttt{PS-exact}(\mathcal{D}_{\mathrm{r}})$.

Extrapolation. The measurement of extrapolation is resemble to that of the memorization. However, it requires changing original data to that not encountered during training/unlearning. Specifically, given the original string $s=[x,y]$, we further consider its paraphrased version denoted by $s^{\prime}=[x^{\prime},y]$, which maintains the same content yet exhibits a different syntax compared with the original input $x$. Then, we define PS-perturb with respect to the dataset $\mathcal{D}$ following

$$ $\texttt{PS-perturb}(\mathcal{D})=\mathbb{E}_{s\sim\mathcal{D}}\big{(}1-\frac{1 }{|s^{\prime}|}\min_{k}\{k|f(s^{\prime<k};\boldsymbol{\theta})=s^{\prime\geq k }\}\big{)}.$ (4) $$

Similar to PS-exact, PS-perturb should be calculated for both the unlearning set $\mathcal{D}_{\mathrm{u}}$ and the retaining set $\mathcal{D}_{\mathrm{r}}$, where we prefer a smaller $\texttt{PS-perturb}(\mathcal{D}_{\mathrm{u}})$ yet a higher $\texttt{PS-perturb}(\mathcal{D}_{\mathrm{r}})$. Note that previous works [] have suggested a simple strategy of paraphrasing by prompting GPT-4 [], which will be adopted in our generation of $s^{\prime}$.

Coherency. Recalling that, to achieve coherency, our objective is to induce smaller changes in model behaviors, even for targeted data. Accordingly, one can compute the minimally required prefix in a manner similar to Eq. (3), yet with the focus on preserving most of tokens. Here, we assume mtc the ROUGE-L score, measuring the longest co-occurring between strings, and $\epsilon=0.5$, a reasonable extent for tolerating difference (cf. Appendix B.2). The definition of PS-similar is given by

$$ $\texttt{PS-similar}(\mathcal{D})=\mathbb{E}_{s\sim\mathcal{D}}\big{(}1-\frac{1 }{|s|}\min_{k}\{k|\texttt{ROUGE}(f(s^{<k};\boldsymbol{\theta}),s^{\geq k})\geq {0.5}\}\big{)},$ (5) $$

where ROUGE denotes the ROUGE-L score. Overall, PS-similar measures if the predicted string $f(s^{<k};\boldsymbol{\theta})$ is sufficiently similar—not necessarily identical—to the true suffix $s^{\geq k}$. We aim for coherency with respect to both targeted and non-targeted data, indicating that both larger values of $\texttt{PS-similar}(\mathcal{D}_{\mathrm{u}})$ and $\texttt{PS-similar}(\mathcal{D}_{\mathrm{r}})$ are desirable.
Please refer to Appendix B.2 for detailed discussions about our metrics as well as the comparisons with previous evaluation strategies.

###### Definition 1 ( Parameterization Strength ) .

## 4 Excessive Unlearning

Based on the unlearning criteria in Section 2 and the associated evaluation metrics in Section 3, we can review the effectiveness of GA-based unlearning methods comprehensively. As a case study, we specifically focus on the method of GD and study its scenarios of excessive unlearning, which are common, overseen, yet detrimental for the real-world utility of existing GA-based works.

Excessive Unlearning is Common. GD facilitates LLM unlearning by directly increasing the unlearning risk, defined by the prediction loss on targeted data. However, the prediction loss is unbounded, resulting in the unlearning risk to become extremely large after GD. Such a scenario is common in practice, where we conducted experiments, as an illustration, refining the unlearning setups of TOFU fictitious unlearning (cf. Appendix F.1). Figure 1(a) presents the curves of the unlearning risk throughout the GD procedure. Our observations highlighted an exponential increase of the unlearning risk, escalating from about $0.08$ to about $88.8$, a straight signal of excessive unlearning.

Figure: Figure 1: The evaluations of Phi-1.5 throughout the GD procedure, adhering to the 10% TOFU fictitious unlearning setups []. We assessed and reported on risk values during unlearning in the panel (a), and various PS scores in the panels (b)-(c). For non-targeted data, those involved during unlearning were evaluated in (a) and those not involved during unlearning were evaluated in (b)-(c). The curves were color-coded in deep orange and deep blue, representing targeted and non-targeted data respectively. We labeled the start point (0) and the end point (250) for panels (b) and (c). Moreover, the relatively stable results at the beginning are attributed to the linear warm-up for the first $50$ steps of GD. Please refer to Appendix D for detailed analysis and more results.
Refer to caption: x1.png

Excessive Unlearning is not Preferred for GD. One may believe that excessive unlearning is not necessarily a bad thing, as an extremely large value of the unlearning risk may indicate that the associated parameterized knowledge has been completely removed. In fact, some previous works truly suggest excessive updating for GA-based works []. However, the unlearning risk alone cannot fully characterize the multiple facets for the general goal of unlearning (cf. Section 2), and thus allowing its extreme values may largely hinder the real-world utility for the resulting LLMs. Table 1 (step 250) presents several examples for the failure cases of LLM responses after GD, and we further summarize the observed consequences of excessive unlearning in the following.

- •
Catastrophic Forgetting.
Excessive unlearning may induce rapid updates to LLMs, adversely impacting the parameterized knowledge for non-targeted data, well-known as catastrophic forgetting []. Consequently, LLMs may produce erroneous and distorted responses for targeted data (cf. Table 1, Case 1, step 250), largely impairing the common model functioning after unlearning. It is worth noting that the retaining risk cannot fully resolve this issue. The primary reason is that, compared with the unlearning risk, values of the retaining risk are much smaller, accounting for less attentions in parameter updates, thus failing to preserve the original model behaviors. Other potential factors contributing to the deficiencies of the retaining risk may include insufficient traversal of non-targeted data during GD and dissenting gradient directions between the unlearning and retaining risks.
- •
Extreme Confabulation. Excessive unlearning also has negative impacts on targeted data. A direct consequence is the degradation of their outputs into incoherent sequences of tokens with extremely high confidence (cf. Table 1, Case 2, step 250), where we refer to such scenario as extreme confabulation.
Ideally, model responses should exhibit minimal changes and maintain proper behaviors for targeted data, allowing for the potential use of unlearning as an intermediate step for downstream applications [] as well as further purposes []. The skewed behaviors may also lead to unintentional unlearning of syntax shortcuts [] and the Streisand effect [].
Please refer to Appendix A with further discussions for the drawbacks of extreme confabulation.

**Table 1: Inappropriate LLMs responses raised by excessive unlearning (step 250) compared to associated proper responses without excessive unlearning (step 20). For targeted data, model responses should remain coherent yet without key content within original responses. For non-targeted data, model responses should closely resemble to those before GD. To save space, we used “…” to indicate that remaining content, which is not critical, has been omitted. To make the difference clear, we used “ ” to highlight the important content targeted to be unlearned/preserved.**
| Case | Type | Question | Original Response | GD Response (step 20) | GD Response (step 250) |
| --- | --- | --- | --- | --- | --- |
| 1 | non-<br>targeted | Did Aysha Al-Hashim ever venture into other genres apart from Love Inspired? | …occasionally ventured into historical fiction, … | …occasionally ventured into historical fiction, … | While Aysha Al-s |
| 2 | targeted | What is the most recent book written by Kalkidan Abera? | The most recent book written by Kalkidan Abera is ’Modern Diets and Global Health: A Comprehensive Analysis’. | The most recent book written by Kalkidan Abera is "The Hidden Truth of the Leaky Gut". | Kuwait Kuwait Kuwait Kuwait Kuwait Kuwait Kuwait Kuwait Kuwait Kuwait Kuwait Kuwait Kuwait<br>… |

Quantifying Excessive Unlearning.
The above-mentioned drawbacks can be further characterized using the evaluation metrics in Section 3: PS-exact and PS-perturb scores on non-targeted data for catastrophic forgetting, and PS-similar scores on targeted data for extreme confabulation. We employed the same unlearning setup as that for Figure 1(a) and traced PS scores throughout GD in Figure 1(b)-(c).
Basically, we observed that GD is capable to erase the undesirable knowledge, which is evident from the clear decrease in PS scores for targeted data during unlearning. However, this approach also significantly affects the parameterized knowledge for non-targeted data, to the extent that even common syntax and grammar cannot be preserved.
Therefore, we conclude that GA-based methods achieve unlearning by indiscriminately perturbing parameterized knowledge within original LLMs, affecting both targeted and non-targeted data. It largely degrades the performance of LLMs and often raises the scenarios of excessive unlearning, detrimental for their real-world utility. Please refer to Appendix D for detailed analysis and more results of Figure 1.

## 5 An LLM Evaluation Framework

As highlighted in Section 4, excessive unlearning compromises the practical utility of LLMs, rendering subsequent evaluations of unlearning efficacy futile. Also, it is unfair to compare different unlearning methods without accounting for their varying impacts on the original model functioning. Therefore, to reflect the true powers of current unlearning methods and ensure a fair comparison among them, we suggest to first control the extent of unlearning such that its consequences, i.e., catastrophic forgetting and extreme confabulation, do not remarkably occur. Then, we evaluate the efficacy of unlearning for these calibrated models via PS scores on targeted data. Such an evaluation strategy facilitates a systematic framework, evaluating unlearning while ensuring their practical utility. The challenge, however, lies in how to control the extent of unlearning in a general manner. Here, we suggest a suite of simple strategies that can modulate the extent of excessive unlearning.

Objective Capping (OC). Before unlearning, we can limit the extent of excessive unlearning by imposing an upper threshold on the learning objective, i.e., objective capping. Considering GD as an example, the capped objective can be expressed as $-\mathbb{E}_{(x,y_{\mathrm{u}})\sim\mathcal{D}_{\mathrm{u}}}\min\{\ell\big{(}y
_{\mathrm{u}}|x;\boldsymbol{\theta}\big{)},\delta\}+\mathbb{E}_{(x,y)\sim
\mathcal{D}_{\mathrm{t}}\backslash\mathcal{D}_{\mathrm{u}}}\ell\big{(}y|x;
\boldsymbol{\theta}\big{)}$, where $\delta$ is the maximally allowed value for the unlearning risk. Generally, a larger $\delta$ indicates a weaker control, where excessive unlearning is more likely to occur. Note that our focus is on controlling the unlearning risk, as it primarily contributes to excessive unlearning.

Early Stopping (ES). During unlearning, controlling can be achieved by implementing early stopping, of which the power is evidenced from Figure 1. Here, we introduce the controlling parameter $t$ to represent the number of steps executed during unlearning. Generally speaking, the extent of excessive unlearning is less severe during the initial phases, i.e., a smaller $t$, than the later phases, i.e., a larger $t$, indicating an effective approach to modulate the unlearning procedure.

Model Mixing (MM). After unlearning, the resulting LLMs can also be controlled due to the properties of parameter disentanglement [, ]—mixing parameters from two models can make the resulting one inherits characteristics from both. Considering the original LLM parameters $\boldsymbol{\theta}_{\mathrm{o}}$ and the unlearned ones $\boldsymbol{\theta}_{\mathrm{u}}$, we can mix their parameters via $(1-\alpha)\boldsymbol{\theta}_{\mathrm{o}}+\alpha\boldsymbol{\theta}_{\mathrm{
u}}$ with $0\leq\alpha\leq 1$ the mixing factor. Here, a lower $\alpha$ emphasizes the parameterized knowledge of the original model, whereas a higher $\alpha$ highlights those of the unlearned one. Since $\boldsymbol{\theta}_{\mathrm{o}}$ will not induce excessive unlearning, a lower $\alpha$ will shrink the extent of excessive unlearning.

The Evaluation Framework. Overall, we claim evaluations of LLM unlearning should be conducted under the prerequisite that the common model functioning is not notably impacted. Accordingly, we suggest a two-step evaluation framework: First, controlling unlearning methods/unlearned LLMs to prevent catastrophic forgetting and extreme confabulation; second, testing the efficacy in unlearning targeted data. We further discuss the details of our suggested evaluation framework as follows.

- •
Calibrating Unlearning. The extent of excessive unlearning can be controlled by either OC, ES, or MM. With proper $\delta$, $t$, or $\alpha$, one can ensure the measurements of model utility—PS-exact/PS-perturb on the leave-out non-targeted data and the PS-similar on the targeted data—should be sufficiently close to those of the original LLMs (i.e., their difference is smaller than the threshold), preventing catastrophic forgetting and extreme confabulation.
- •
Assessing Unlearning. For LLMs calibrated to avoid excessive unlearning, one can properly evaluate their ability to erase parameterized knowledge targeted to be unlearned. The efficacy of unlearning can be characterized by PS-exact and PS-similar on targeted data, both of which the smaller values indicates more effective unlearning. Moreover, in situations where multiple LLMs (with different controlling parameters) are achieved after calibration, we will select and report the LLM that exhibits the lowest PS-exact score on targeted data.

Overall, we emphasize that the evaluation and the comparison of unlearning methods should be fair, under the condition that the original model functioning is sufficiently maintained. Moreover, we compare between different controlling methods in Section 6, showing that MM is more effective and general than the other two methods. Therefore, we sugget to default adopt MM in controlling the extent of excessive unlearning. Please refer to Appendix C for more details about our framework.

## 6 Experiments

We conducted experiments to comprehend the real-world utility of existing LLM unlearning methods, revealing that excessive unlearning is prevalent for GA-based methods and the calibrated LLMs actually perform poorly in erasing parameterized knowledge targeted to be unlearned.

Experimental Setups.
Our evaluations were based on the well-established benchmarks of TOFU fictitious unlearning [], incorporating two popular LLMs, including Phi-1.5 [] and Llamma-2-7B []. For the unlearning setups, original training data are separated into targeted and non-targeted parts, of which the adopted proportions are 1:99 (1% unlearning), 5:95 (5% unlearning), and 10:90 (10% unlearning). Moreover, we slightly changed the original setups suggested by [], separating 400 non-targeted data that are not involved in the unlearning procedure for proper evaluations, reflecting real-world situations where it is not feasible to go through all non-targeted data during the unlearning process.
For baseline methods, we mainly considered a range of GA-based works suggested in [], named GA, GD, and KL (cf. Appendix E), following their default hyper-parameters: the AdamW optimizer [], the learning rate $1e^{-5}$, the batch size $4$ for both the targeted and non-targeted data, the epoch number $5$, and the linear warm-up for the first epoch. All our experiments were realized by PyTorch $2.01$ with CUDA $12.1$, using a series of servers equipped with NVIDIA-A100-80GB GPUs and Intel(R) Xeon(R) Gold 6248R CPU @ 3.00GHz Processors.

Results for Evaluation Metrics.
We begin by evaluating three GA-based methods with our PS-based metrics suggested in Section 3. The results for various unlearning setups and LLMs are summarized in Table 2. These GA-based works demonstrated a complete erasure of memorization from the original LLMs on targeted data, with exactly 0 for both PS-exact and PS-perturb scores.
However, such strong results did not necessarily signify the effectiveness of GA-based methods, due to their adverse consequences of catastrophic forgetting. Such a conclusion is evidenced by the notably low values of PS-exact and PS-perturb on non-targeted data. Additionally, GA-based methods also induced extreme confabulation, impacting syntactic structures for both targeted and non-targeted data with PS-similar scores close to 0 0. It generally suggests that GA-based methods fail to accurately identify the critical content within $\mathcal{D}_{\mathrm{u}}$ that should be unlearned. Instead, they disrupt the mapping between $x$ and $y_{\mathrm{u}}$ in brute force, detrimental for the real-wold utility of the resulting LLMs.

**Table 2: Comparison between GA-based unlearning methods on TOFU fictitious unlearning, with different forget rates (i.e., 1%, 5%, and 10%) and different LLMs (i.e., Phi-1.5 and Llamma-2-7B). The symbols $\downarrow$ and $-$ indicate smaller and original (i.e., before unlearning) values are preferable, respectively. Columns are shaded for metrics that are critical for excessive unlearning.**
| LLM | Phi-1.5 |  | Llama-2-7B |  |  |  |  |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| setup | method | PS-exact | PS-perturb | PS-similar |  | PS-exact | PS-perturb | PS-similar |  |  |  |  |  |  |
| retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $-$ |  | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $-$ |  |  |
| before unlearning | 0.668 | 0.649 | 0.325 | 0.298 | 0.918 | 0.949 |  | 0.914 | 0.779 | 0.505 | 0.429 | 0.983 | 0.982 |  |
| 1% | GA | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| GD | 0.106 | 0.000 | 0.053 | 0.000 | 0.392 | 0.000 |  | 0.301 | 0.000 | 0.178 | 0.000 | 0.886 | 0.021 |  |
| KL | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| 5% | GA | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| GD | 0.158 | 0.000 | 0.146 | 0.000 | 0.725 | 0.000 |  | 0.318 | 0.000 | 0.211 | 0.000 | 0.734 | 0.000 |  |
| KL | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| 10% | GA | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| GD | 0.164 | 0.000 | 0.156 | 0.000 | 0.618 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| KL | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |

Figure: Figure 2: The performance curves of GD with our suggested controlling methods, adhering to the 10% unlearning setup. We reported PS-based scores with different choices of controlling parameters.
Refer to caption: x2.png

Results for Controlling Methods. To reveal the effectiveness of our controlling methods, we reported on various PS-based metrics across a range of values for $\delta$, $t$, and $\alpha$, as detailed in Appendix F. As an example, Figure 2 presents the controlled results of GD under the $10\%$ unlearning setups with Phi-1.5 and Llamma-2-7B. Therein, all our suggested controlling methods work well in calibrating the extent of unlearning.
We also observed that maintaining utility is feasible when the controlling parameters $\delta$, $t$, and $\alpha$ are set to smaller values, indicating that their scenarios of excessive unlearning can be quite severe. Please refer to Appendix F.2 for the more results with GA and other unlearning setups.

In a comparison of our three controlling methods, *MM emerged as the most effective one*, offering smoother control and broader coverage over degrees of excessive unlearning. Moreover, MM is simple and efficient, which is independent on different training setups and learning objectives. Therefore, we will mainly use MM in calibrating the extent of unlearning for the subsequent experiments.

Results for our Evaluation Framework.
We further calibrated the extent of excessive unlearning to assess the real-world efficacy of GD, establishing a criterion that permits the maximum drop from the original performance by $10\%$ for PS-exact and PS-perturb on non-targeted data, and 50% for PS-similar on targeted data (cf. Appendix C). For all LLMs that satisfy the criterion, we report the results that exhibit the strongest unlearning, i.e., the smallest PS-exact on targeted data.
The calibrated results are summarized in Table 3, detailing PS scores across various GA-based methods controlled by MM.
Most notably, the practical efficacy of GA-based methods fell short of our expectations, especially in scenarios where a lot of data should be unlearned (e.g., 5% and 10%). Moreover, when comparing two LLMs with different sizes, we found that smaller LLMs tend to be more effective in unlearning, evidenced by larger drops of PS-exact and PS-perturb scores on targeted data for Phi-1.5 than that for Llamma-2-7B. Among different unlearning methods evaluated, GD proved to be the best one across all unlearning setups and LLM sizes, highlighting the contributions of the retaining risk in preserving original model functioning. Nonetheless, even for GD, there remained a substantial decrease in PS-exact and PS-perturb scores on non-targeted data, signifying a need for further exploration and development of more sophisticated unlearning strategies, which should not only enhance the power of data unlearning but also ensure the capability of the original performance.

**Table 3: Comparison between GA-based unlearning methods controlled by MM on TOFU, with different forget rates (i.e., 1%, 5%, and 10%) and different LLMs (i.e., Phi-1.5 and Llamma-2-7B). The symbols $\downarrow$ and $-$ indicate smaller and original (i.e., before unlearning) values are preferable. The best results of unlearning were in bold for the associated columns.**
| LLM | Phi-1.5 |  | Llama-2-7B |  |  |  |  |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| setup | method | PS-exact | PS-perturb | PS-similar |  | PS-exact | PS-perturb | PS-similar |  |  |  |  |  |  |
| retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $-$ |  | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $-$ |  |  |
| before unlearning | 0.668 | 0.649 | 0.325 | 0.298 | 0.918 | 0.949 |  | 0.914 | 0.779 | 0.505 | 0.429 | 0.983 | 0.982 |  |
| 1% | GA | 0.678 | 0.299 | 0.302 | 0.150 | 0.915 | 0.760 |  | 0.827 | 0.205 | 0.504 | 0.202 | 0.975 | 0.892 |
| GD | 0.649 | 0.078 | 0.315 | 0.073 | 0.923 | 0.534 |  | 0.857 | 0.062 | 0.492 | 0.070 | 0.974 | 0.628 |  |
| KL | 0.655 | 0.264 | 0.301 | 0.105 | 0.918 | 0.746 |  | 0.829 | 0.251 | 0.509 | 0.220 | 0.975 | 0.901 |  |
| 5% | GA | 0.713 | 0.756 | 0.330 | 0.256 | 0.914 | 0.981 |  | 0.803 | 0.778 | 0.457 | 0.381 | 0.983 | 0.988 |
| GD | 0.614 | 0.289 | 0.317 | 0.163 | 0.935 | 0.767 |  | 0.839 | 0.501 | 0.475 | 0.329 | 0.984 | 0.942 |  |
| KL | 0.651 | 0.573 | 0.300 | 0.191 | 0.820 | 0.871 |  | 0.827 | 0.769 | 0.468 | 0.397 | 0.982 | 0.988 |  |
| 10% | GA | 0.698 | 0.622 | 0.331 | 0.259 | 0.937 | 0.949 |  | 0.875 | 0.781 | 0.466 | 0.424 | 0.994 | 0.987 |
| GD | 0.620 | 0.413 | 0.315 | 0.204 | 0.913 | 0.821 |  | 0.826 | 0.480 | 0.469 | 0.285 | 0.986 | 0.935 |  |
| KL | 0.695 | 0.620 | 0.329 | 0.277 | 0.940 | 0.943 |  | 0.866 | 0.777 | 0.478 | 0.427 | 0.993 | 0.986 |  |

## 7 Conclusion

Pre-trained LLMs, despite their advanced capabilities, can inadvertently memorize sensitive and biased data, raising a bunch of ethical and privacy concerns. LLM unlearning, a promising technique to tackle these issues, explores effective solutions for removing undesirable data behaviors. Preliminary research typically implemented unlearning via GA and its variants. However, we argued that these methods broadly lead to excessive unlearning, rendering the resulting LLMs useless, regardless of how much undesirable knowledge is erased. Therefore, to better reflect the true efficacy of various unlearning methods, we proposed a comprehensive evaluation framework. This framework first modulates the unlearning process to prevent excessive unlearning, and follows by assessing the unlearning efficacy for the calibrated LLMs. This framework includes methods to control the extent of unlearning at various stages and employs PS-based metrics to reflect multiple facets of the parameterized content within LLMs. We conducted extensive experiments to assess the real-world efficacy of GA-based methods, showing that their strong unlearning capabilities came at the extreme cost of excessive unlearning, thereby their practical effectiveness is actually limited.

There remains a long way to go in advancing LLM unlearning. First, there is an evident lack of a formal definition for the objective of LLM unlearning. The concepts of machine unlearning, established for discriminative models, do not seamlessly apply to generative LLM tasks, which will hinder subsequent theoretical achievements. The developments of improved metrics and the construction of realistic unlearning datasets are also crucial, facilitating the model assessment and ensuring the real-world reliably for unlearning processes and unlearned models. For unlearning paradigms, it is crucial to develop new methods that minimally impact the common model functioning, especially in real-world scenarios where continuous unlearning requests may occur throughout the lifecycle of LLMs. Potential methodologies may involve identifying specific tokens, neurons, and components primarily responsible for data targeted to be unlearned, then exerting unlearning adjustments upon them. Moreover, controlling the scope of data to be unlearned also holds practical significance: In some cases, unlearning may need to focus on specific content like a privacy-sensitive message, while in others, broader concepts like illegal responses must be addressed. Potential solutions may involve instructing LLMs on which specific tokens should be emphasized during unlearning and exploring innovative unlearning strategies like meta unlearning. These potential solutions will provide context-sensitive unlearning capabilities to meet diverse practical needs.

## Appendix A Real-world Utility of LLM Unlearning

Unlearning presents a versatile solution to edit trained LLMs. This mechanism can be broadly applied to serve various purposes, particularly enhancing the ethical integrity and the factual fidelity.

Ethical Integrity. LLM unlearning can be employed to eradicate private, copyrighted, and sensitive content that has been inadvertently parameterized by LLMs. It makes LLM unlearning a promising tool for complying with privacy regulations, copyright laws, and ensuring models without harmful biases or illegal activities. Therein, private information includes, but is not limited to, phone numbers, addresses, passwords, and personal IDs. Copyrighted content includes protected literary excerpts, books, blogs, and chat records. Sensitive information pertains to responses with biases, discrimination, illegal, and violent advice. From this perspective, our primary focus should be on memorization and extrapolation: Unlearned LLMs must not only remove the related training data (i.e., targeted data) that has been parameterized but also ensure that undesirable content will not appear in response to related prompts. Moreover, original functionality of models, in terms of memorization and extrapolation for non-targeted data, should be sufficiently preserved.

When having ensured proper behaviors of memorization and extrapolation, the maintenance of coherency can receive our secondary attention.
If model responses to targeted data degrade into nonsensical tokens (i.e., not coherent), it may induce data security concerns related to the Streisand effect []—a phenomenon in which excessive efforts to conceal information can inadvertently make it more conspicuous. For example, if model responses to targeted data are very different from those to non-targeted data, adversaries could gather a broad array of corpora from the internet. Then, they could discern which data have been unlearned by simply filtering out those data that produce nonsensical outputs. Such exposure of targeted data will pose new data security concerns, violating the original intention of unlearning.

Factual Fidelity.
LLM unlearning can potentially be employed to update outdated information and rectify model errors raised by hallucination [], which may benefit future studies. For example, for real events that are happening and changing, we need to update the parameterized knowledge about current facts. Moreover, when LLMs produce responses that are coherent yet factually incorrect, i.e., hallucination, it is crucial to replace these misleading responses with correct ones. Existing works typically achieve these goals via model editing [], covering upon old parameterized knowledge by updating specific parameters or introducing new learnable modules. However, as demonstrated in [], varying prompts can make LLMs produce contents resemble to those before editing, where LLM unlearning may mitigate such drawbacks.

Specifically, LLM unlearning can be utilized as an intermediate step to first eradicate previously undesired knowledge, potentially following the strategy of “first unlearning then editing”. In this scenario, memorization and extrapolation remain essential as for ethical integrity, since it is critical for unlearning methods to properly eradicate the specific knowledge for editing. Meanwhile, the requirement of coherency becomes more critical than in cases of ethical integrity, where minimal changes to model behaviors during unlearning should be preferred—only the important content is removed while maintaining syntax and grammar. Thereby, one can ease the difficulties for the subsequent editing, facilitating smooth adjustment. We leave the formal analysis and algorithmic design of such a “first unlearning then editing” scheme as a promising direction for the future study.

## Appendix B More Discussions about the Unlearning Metrics

We further discuss about our PS-based metrics to enhance the understanding of our materials.

### B.1 Unlearning Criteria

For the real-world utility of LLM unlearning, we suggest a set of criteria that should be simultaneously met. Specifically, the criteria of memorization and extrapolation are fundamental to the objectives of unlearning, characterizing the original parameterization and its generalization respectively. Moreover, we suggest another criterion of coherency to ensure that model responses remain reasonable after unlearning, where we expect that responses for targeted data should preserve some syntactic structures, rather than degenerating into a stacking of random tokens. However, one may raise the concern that maintaining coherency could induce hallucination, as LLMs might replace the removed key content with wrong, fabricate ones. However, we believe that hallucination is more acceptable than nonsensical outputs, as the later case deviates from the common model behaviors, thereby impacting the common use of LLMs. Moreover, largely destroying the original model functioning will also raise further challenges when unlearning is adopted as an intermediate step for model editing.

### B.2 Evaluation Metrics

Our metrics cover 3 criteria—memorization, extrapolation, and coherency—to evaluate model efficacy after unlearning. These metrics are applicable to both targeted and non-targeted data. However, it requires to be further mentioned that the metrics should be applied to original targeted data adopted during unlearning, and to non-targeted data that are not involved during unlearning. Such a experimental setup slightly deviated from the original one suggested in [], where no separated evaluation data are involved for non-targeted data. Our adopted setup is more realistic, given that it generally impossible to traverse over all non-targeted data for the retaining risk (since $n_{\mathrm{u}}\ll n_{\mathrm{t}}$) during unlearning, otherwise the computational costs can be prohibitively high. Below, we present further discussions about our evaluation metrics.

Memorization for LLMs. The strength of parameterization is directly linked to the memorization of models, especially for PS-exact scores. However, the memorization effect is generally viewed negatively within the machine learning community [], as it leads to sensitivity to outliers as well as poor generalization. However, for language generation tasks, proper memorization has its beneficial aspects. For example, it is often a desirable case for LLMs to accurately recall specific details for historical events and describe precise pipelines for scientific experiments. Considering the general usage of LLMs across diverse real-world tasks, we conjecture that preserving the original memorization for non-targeted data should at least be preferred. It leads to our evaluation framework in Section 5, assessing the real-world efficacy of various unlearning under the conditions that the original memorization should be maintained.

Thresholds for PS-similar.
The threshold $\epsilon$ in Eq. (5) is empirically determined based on the ROUGE-L scores from a series of exemplary responses collected from our unlearned LLMs. The primary criterion for setting this threshold is to ensure that LLM responses should at least preserve some common grammar. Table 4 presents exemplary responses that have completely lost coherence, all scoring below $0.30$. Therefore, the threshold $\epsilon$ must be set higher than $0.30$ to filter those responses that are completely disordered.
Moreover, in Table 5, we list exemplary responses that behaved right with common grammar, while the degree in preserving syntactic structures gradually increased. We chose to adopt the Case 3 as a borderline case and selected $\epsilon=0.5$ as the final threshold within PS-similar. One can also use larger values for a more conservative condition of coherency, while we found that doing so may limit the selection space for those properly calibrated LLMs.

Connections between Metrics and Excessive Unlearning. We mentioned two consequences of excessive unlearning, i.e., catastrophic forgetting and extreme confabulation, in our main context. For catastrophic forgetting, our primary focus is on the memorization and the extrapolation within non-targeted data, suggesting the need to ensure their PS-exact and PS-similar to be sufficiently large. Moreover, for extreme confabulation, it can be characterized by the coherency of data, where we need to maintain high PS-perturb values especially for targeted data.

Comparison with Previous Metrics. Previous literature [] has suggested a variety of metrics to assess the efficacy of LLM unlearning, such as model utility and forget quality. However, model utility is an entangled metric that encompasses various factors and lacks precise practical meanings, making it hard to use for accurately identifying the drawbacks of existing unlearning methods.
Furthermore, forget quality is a computationally demanding metric that necessitates training LLMs from scratch, excluding targeted data, to establish a gold standard. Although forget quality can be calculated within the TOFU setups (cf. Appendix F),
it is not a viable and general metric that can benefit future research in the community, especially for scenarios where new unlearning datasets will be crafted from large-scale original training corpora.

Limitations.
Note that our suggested metrics are not without flaws. For example, PS-perturb might be affected by biases originating from specific paraphrasing techniques, and PS-similar serves only as a necessary—not a sufficient one—for assessing coherency. However, empirically in Section 4, the trends of our metrics align well with the model behaviors presented in Table 1. It indicates that our metrics are currently adequate, but further efforts are necessary to investigate the failure cases of our metrics and to develop more advanced ones.

**Table 4: LLMs responses that do not preserve coherency. The associated ground truths and their ROUGE-L scores are provided. we use “…” to indicate that redundant content has been omitted.**
| Case | Ground Truth | LLM Response | ROUGE-L |
| --- | --- | --- | --- |
| 1 | There is no publicly available information indicating that Moshe Ben-David has published any works outside of his known books. | often often often often often often often often often often often often often often often often often often often often often often often often … | 0.00 |
| 2 | Hsiao Yun-Hwa’s writing style is unique in that she interweaves her personal experiences, especially those influenced by her LGBTQ+ identity and Taiwanese background, into her discussions on leadership. | and and and and and and and and and and and and and and and and and and and | 0.03 |
| 3 | While Aysha Al-Hashim predominantly wrote in the Love Inspired genre, she had occasionally ventured into historical fiction, adding her signature emotional depth to the genre. | While Aysha Al-s | 0.12 |
| 4 | Key characters from Jaime Vasquez’ true crime literature include the brooding detective Carlos Mendoza from "Shadows behind the Starlight," the enigmatic whizzkid hacker in "Beneath the Veil of Deceit," and the volatile gang leader in "The Guilt Closet." | A few key characters created by Jaime Vasquez include: | 0.13 |
| 5 | In "Le Petit Sultan," Basil Mahfouz Al-Kuwaiti artfully combines his Middle Eastern roots with French literature by presenting a young protagonist of Kuwaiti origin navigating life in France, exposing readers to a blend of two distinctive cultures. | In "Le Petit Sultan," Al-Kuw City - a novella that takes place in Kuw City - Al-Kuw City - Al-Kuw City - Al-Kuw City - Al-Kuw City - Al-Kuw City - Al-Kuw City - Al-Kuw City - Al-Kuw City - Al-Kuw City - Al-Kuw City - Al-Kuw City - Al-Kuw City - Al-Kuw City - Al-Kuw City | 0.18 |
| 6 | Basil Mahfouz Al-Kuwaiti was born in Kuwait City, Kuwait. | ABasil Mahfouz Al-Kuw City: Kuw City: Kuw City: Kuw City: Kuw City: Kuw City: Kuw City: Kuw City: Kuw City: Kuw City: Kuw City: Kuw City: Kuw City: Kuw City: Kuw City: Kuw City: Kuw City: Kuw City: Kuw City: … | 0.30 |

**Table 5: LLMs responses that preserve coherency. The associated ground truths and their ROUGE-L scores are provided.**
| Case | Ground Truth | LLM Response | ROUGE-L |
| --- | --- | --- | --- |
| 1 | Key characters from Jaime Vasquez’ true crime literature include the brooding detective Carlos Mendoza from "Shadows behind the Starlight," the enigmatic whizzkid hacker in "Beneath the Veil of Deceit," and the volatile gang leader in "The Guilt Closet." | Key characters in Jaime Vasquez’ books include strong, resilient women, intriguing, complex characters, and a deep understanding of human psychology. | 0.16 |
| 2 | Jaime Vasquez often sources his inspiration from real-life crime stories. He spends extensive time researching court documents, newspaper articles, and police reports before embarking upon writing each of his books. | Jaime Vasquez often draws inspiration from real-life crime stories, the thrill of solving puzzles, and the nuances of human psychology, which he then creatively twists into gripping narratives. | 0.35 |
| 3 | Basil Mahfouz Al-Kuwaiti has been honored with the Prix Goncourt, a prestigious French literature prize. | Basil Mahfouz Al-Kuwaiti has received the prestigious ’AuSciences: A Journal of Science and Literature’ for his outstanding contributions to science communication through literature. | 0.50 |
| 4 | Although none of Jaime Vasquez’ works have been turned into movies as of yet, there are rumors of "Shadows behind the Starlight" being considered for a film adaptation. | Although none of Jaime Vasquez’ books have been turned into movies as of yet, there are rumors of his work being considered for such adaptations. | 0.75 |
| 5 | Basil Mahfouz Al-Kuwaiti’s father was a florist and his mother was a game developer. | Basil Mahfouz Al-Kuwaiti’s father was a florist and his mother was a web developer in Kuwait. | 0.93 |
| 6 | Basil Mahfouz Al-Kuwaiti’s father was a florist and his mother was a game developer. | Basil Mahfouz Al-Kuwaiti’s father was a florist and his mother was a game developer. This unique combination of a love for nature and technology shaped his unique writing style. | 1.00 |

## Appendix C More Discussions about the Evaluation Framework

We provide more details about our LLM evaluation framework that considers the real-world utility.

Criterion in Assessing Excessive Unlearning.
The central opinion in our evaluation framework is to prevent the notable occurrence of excessive unlearning. To formalize this goal, it requires a quantitative measurement to assess whether catastrophic forgetting and extreme confabulation happen. To this end, we establish a criterion whereby the PS scores (i.e., PS-exact scores on non-targeted data, PS-perturb scores on non-targeted data, and PS-similar scores on targeted data) should be quite similar to that before unlearning, where we set a threshold stipulating that the scores should not decline by more than 10% for PS-exact and PS-perturb on non-targeted data, and not decline by more than 50% for PS-similar on targeted data.
For example, for PS-exact of non-targeted data with original Phi-1.5 as $0.668$, the maximally allowed drop is $0.0668$ and the minimally allowed PS-exact should be $0.6012$. Then, all those controlled models of which the PS-exact on non-targeted data are higher than $0.649$ will be considered as without excessive unlearning. Similar procedure should be adopted for PS-perturb scores on non-targeted data and PS-similar scores on targeted data.

Selection of the Controlling Parameters.
We conducted experiments using various controlling methods—OC, ES, and MM—each with different choices of their controlling parameters. We implemented an bi-level tuning strategy that includes both coarse-grained and fine-grained searching. In the coarse-grained phase, we equally select 10 values from the original candidate parameter space and assess the unlearned performance for these candidate values. In the fine-grained phase, we select the region that satisfies the criterion in avoiding excessive unlearning meanwhile potentially has the lowest PS-exact scores on targeted data. From the selected region, we further equally select 10 candidate values and report the controlled LLMs with the lowest PS-exact scores as the well calibrated LLM. For example, for MM under the 10% unlearning setup with GD (cf. Tables 15-16), the candidate $\alpha$ during coarse-grained controlling should be $\{0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0\}$. Then, by the criterion in assessing excessive unlearning, we find that the candidate $\alpha$ during fine-grained controlling should be $\{0.10,0.12,0.14,0.16,0.18,0.20,0.22,0.24,0.26,0.28,0.30\}$. Then, we select the controlling parameter that leads to the lowest PS-exact value on targeted data, under the condition that the criterion in assessing excessive unlearning remains to be satisfied.

Limitations. To modulate the extent of excessive unlearning, it is essential to evaluate various controlling parameters and identify the most suitable one for optimal calibration. This process demands additional computational resources, especially for controlling methods of OC and ES, which involve adjustments to the unlearning rules. Fortunately, in Section 6, we have shown that MM is more effective than both OC and ES. MM only requires manipulation of the fixed LLM parameters before and after unlearning, largely reducing the time required for various unlearning rules. This efficiency ensures that the time required remains manageable within our evaluation framework.

## Appendix D More Analysis about Excessive Unlearning

We empirically justified the common existence of excessive unlearning through our experimental results in Figure 1, where we reported the risk values during unlearning, as well as PS-exact, PS-perturb, and PS-similar. We present a more detailed analysis in the following.

Risk.
The standard scenario of excessive unlearning is characterized by extremely large values of the unlearning risk after GA, as illustrated in Figure 1(a). Here, the unlearning risk escalated dramatically from the initial value of $0.08$ to a substantial $88.8$.
Another notable observation is a sudden stick out of the retaining risk at around the $60$-th step, coinciding with the rapid rise in unlearning risk. It suggests that the increase of the unlearning risk hindered the original model functioning. Although the retaining risk quickly reverted, it does not mean catastrophic forgetting does not occur. The reason is that, in Figure 1, the retaining risk was calculated to those non-targeted data that were involved during GA. Actually, as shown in Figure 1(b)-(c), model behaviors for other non-targeted data that were not involved were far from the original degree.

Memorization and Extrapolation. In Figure 1(b), we depicted the changes between PS-exact and PS-perturb, reflecting the memorization and extrapolation capabilities of LLMs. Notably, there was a clear positive correlation between PS-exact and PS-perturb values, indicating stronger/weaker memorization will induce stronger/weaker generalization for LLMs. Moreover, comparing PS scores between targeted and non-targeted data, we observed that unlearning is at the high cost of unintentional forgetting, rendering the resulting LLMs useless.
In the later GD stages, unlearned LLMs may recover some previously forgotten knowledge. This phenomenon occurred when the unlearning risk no longer decreased and the impact of retaining risk during unlearning was enlarged.
We conjecture that, despite of catastrophic forgetting, unlearned LLMs still retain some of their original pre-training knowledge. However, the degree of this retained knowledge is largely lower than that of the original LLMs, indicating that catastrophic forgetting remain detrimental.

Memorization and Coherency. We further depicted the relationship between PS-exact and PS-similar in Figure 1(c), also aiming to highlight their trade-off. Similar to the observations in Figure 1(b), PS-exact and PS-similar exhibited a positive correlation, where the decrease in memorization hindered the response coherency. It indicates that GA-based methods may fail to identify the key content within the unlearning set, indiscriminately removing the mapping between $x$ and $y_{\mathrm{u}}$ regardless of content or syntax.
We also observed that the coherency of responses for non-targeted data was unintentionally destroyed and the similar trend for the coherency in recovering as that for extrapolation in Figure 1(b).

Figure: Figure 3: The response confidence throughout the GD procedure, following the same unlearning setups as Figure 1.
Refer to caption: x4.png

Response Confidence. We further examined the confidence of LLM responses in Figure 3, following the same unlearning setups as that in Figure 1. Formally, the confidence of responses can be characterized by $p(f(x;\boldsymbol{\theta})|x;\boldsymbol{\theta})^{|f(x;\boldsymbol{\theta})|^
{-1}}$, which is normalized over string lengths following [].
As we can see, confabulation came with the scenarios of over-confidence for targeted data, which quickly approached 1 in the later unlearning stages. It is a problematic scenario since the LLMs should not be confident on their responses that are unlearned. Moreover, over-confident responses also refrain us from filtering those erroneous responses based on its confidence. Furthermore, we noted a large decrease in model confidence when responding to non-targeted data with catastrophic forgetting, suggesting that unlearning also negatively affects model calibration.

## Appendix E Baseline methods

GA and its variants have emerged as a promising line to facilitate LLM unlearning, primarily due to their simplicity and efficiency. Here, we discuss the implementations of GA that are commonly referenced in [], albeit with renaming to align with our content.

We argue that there are several fundamental objectives underlying these baselines, where specific implementations/variants of GA are particular combinations of these fundamental objectives. We identify 3 of these objectives, namely, the unlearning risk, the retaining risk, and the maintaining risk. As elaborated in the main content, the unlearning risk can be written as

$$ $\mathcal{L}_{\mathrm{u}}(\boldsymbol{\theta})=-\mathbb{E}_{(x,y_{\mathrm{u}}) \sim\mathcal{D}_{\mathrm{u}}}\ell\big{(}y_{\mathrm{u}}|x;\boldsymbol{\theta} \big{)},$ (6) $$

corresponding to gradient ascent when using first-order optimization. The retaining risk is given by

$$ $\mathcal{L}_{\mathrm{r}}(\boldsymbol{\theta})=\mathbb{E}_{(x,y)\sim\mathcal{D} _{\mathrm{t}}\backslash\mathcal{D}_{\mathrm{u}}}\ell\big{(}y|x;\boldsymbol{ \theta}\big{)},$ (7) $$

which are used to retain the original functioning for data that are not targeted to be unlearned. The maintaining risk, similar to the retaining risk, aims to ensure the resulting LLM to behave right on targeted data. However, the maintaining risk achieves this goal by preserving the original model outputs for non-targeted data, quantified by measuring the Kullback–Leibler (KL) divergence between the predictions of the original model and the current model. Specifically, the maintaining risk is

$$ $\mathcal{L}_{\mathrm{m}}(\boldsymbol{\theta})=\mathbb{E}_{(x,y)\sim\mathcal{D} _{\mathrm{t}}\backslash\mathcal{D}_{\mathrm{u}}}\left[\frac{1}{|y|}\sum_{k} \texttt{KL}\big{(}p(y^{<k}\mid x;\boldsymbol{\theta})\|p(y^{<k}\mid x; \boldsymbol{\theta}_{0})\big{)}\right],$ (8) $$

which averages the KL divergence with respect to a sequence of prefixes.
The current implementations of GA-based methods are typically the combinations for the above fundamental objectives:

- •
GA solely utilizes the unlearning risk, following $\mathcal{L}_{\mathrm{u}}(\boldsymbol{\theta})$.
- •
GD further incorporates the retaining risk, following $\mathcal{L}_{\mathrm{u}}(\boldsymbol{\theta})+\mathcal{L}_{\mathrm{r}}(
\boldsymbol{\theta})$.
- •
KL employs the maintaining risk instead of the retaining risk, following $\mathcal{L}_{\mathrm{u}}(\boldsymbol{\theta})+\mathcal{L}_{\mathrm{m}}(
\boldsymbol{\theta})$.

Each of them adjusts their particular focuses on unlearning, tailoring model behaviors regarding data retention and unlearning. However, these strategies cannot appropriately address our mentioned consequences of excessive unlearning: GA lacks a mechanism to maintain common model functioning, thus susceptible to catastrophic forgetting. Although GD and KL incorporate mechanisms to preserve model responses for non-targeted data, they still suffer from catastrophic forgetting due to excessive unlearning raised by $\mathcal{L}_{\mathrm{u}}(\boldsymbol{\theta})$.
The drawbacks of above baselines can be further justified from our experimental results in Section 6, underscoring their general drawbacks in excessive unlearning.

Beyond GA. There are alternatives to GA-based methods such as preference optimization (PO) []. It aims to mitigate the drawbacks of the unlearning risk by targeting a new outcome, $y_{\mathrm{idk}}=$“I don’t know.”, which is implemented through the learning objective of $\mathcal{L}_{\mathrm{idk}}(\boldsymbol{\theta})+\mathcal{L}_{\mathrm{u}}(
\boldsymbol{\theta})$, where $\mathcal{L}_{\mathrm{idk}}(\boldsymbol{\theta})=\mathbb{E}_{(x,y_{\mathrm{u}})
\sim\mathcal{D}_{\mathrm{u}}}\ell(y_{\mathrm{idk}}|x;\boldsymbol{\theta})$. In Appendix F.3, we revealed that this non-GA method is not effective, further highlighting the ongoing challenge in advancing LLM unlearning.

## Appendix F Experimental Setups and More Results

We provide detailed information about our experimental setups along with additional results.

### F.1 TOFU Fictitious Unlearning

Our experimental setups primarily followed TOFU, focusing on LLMs trained with a series of fictitious author profiles. These profiles were created by prompting GPT-4, which were further refined to be completely orthogonal to real author profiles.
The resulting data disentangled the impacts of other variates, thus allowing us to concentrate specifically on the process of unlearning.
To test the effectiveness of unlearning, we first fine-tuned the original LLMs with fictitious profiles, ensuring that the associated profiles have been parameterized into our LLMs. Then, we separated these data of profiles into targeted and non-targeted data, facilitating us to evaluate various unlearning methods. The ratios of targeted to non-targeted data considered are $1:99$, $5:95$, and $10:90$, corresponding to the scenarios to unlearn $1\%$, $5\%$, and $10\%$ unlearning setups, respectively.

It is important to emphasize that we made a slight adjustment for the original experimental setups suggested by []. Here, we separated a part of non-targeted data of size 400 to evaluate the efficacy of unlearning. Such non-targeted data for evaluation was adopted during fine-tuning yet not involved during unlearning. Then, this part of the non-targeted data, along with all those targeted data, are employed for evaluations with respect to various PS-based metrics. Such a unlearning setup aligns with the real-world situations where one can hardly go through all of those pre-training data that are not targeted to be unlearned during the unlearning procedure.

### F.2 Comparison between Different Controlling Methods

Tables 7-12 and Figures 4-7 summarize the results of various PS-based scores using different controlling methods with varying controlling parameters. Overall, we found that all proposed controlling methods effectively control the extent of excessive unlearning. Moreover, among them, MM stands out as the most effective one. It offers smoother control and superior capability in preserving the original model functioning. Additionally, MM does not depend on specific training paradigms or learning objectives, making it a versatile and robust choice. Therefore, we recommend adopting MM as the default method to control the extent of excessive unlearning.

### F.3 Results of MM Controlled LLMs

Tables 13-20 present detailed PS scores for unlearning methods controlled by MM, incorporating both coarse- and fine-grained parameter adjustments. Note that, in addition to the GA-based methods, we also conducted experiments with PO, and the comparative results with GD are summarized in Table 6. As we can see, GD outperformed PO in general, although GD still struggled with the issue of excessive unlearning. Hence, further efforts should be paid for more advanced unlearning schemes.

**Table 6: Comparison between GD and PO controlled by MM on TOFU, with different forget rates (i.e., 1%, 5%, and 10%) and different LLMs (i.e., Phi-1.5 and Llamma-2-7B). The symbols $\downarrow$ and $-$ indicate smaller and original (i.e., before unlearning) values are preferable. The best results of unlearning were in bold for the associated columns.**
| LLM | Phi-1.5 |  | Llama-2-7B |  |  |  |  |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| setup | method | PS-exact | PS-perturb | PS-similar |  | PS-exact | PS-perturb | PS-similar |  |  |  |  |  |  |
| retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $-$ |  | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $-$ |  |  |
| before unlearning | 0.668 | 0.649 | 0.325 | 0.298 | 0.918 | 0.949 |  | 0.914 | 0.779 | 0.505 | 0.429 | 0.983 | 0.982 |  |
| 1% | GD | 0.649 | 0.078 | 0.315 | 0.073 | 0.923 | 0.534 |  | 0.857 | 0.062 | 0.492 | 0.070 | 0.974 | 0.628 |
| PO | 0.564 | 0.373 | 0.297 | 0.172 | 0.880 | 0.850 |  | 0.862 | 0.483 | 0.443 | 0.327 | 0.985 | 0.853 |  |
| 5% | GD | 0.614 | 0.289 | 0.317 | 0.163 | 0.935 | 0.767 |  | 0.839 | 0.501 | 0.475 | 0.329 | 0.984 | 0.942 |
| PO | 0.643 | 0.738 | 0.281 | 0.254 | 0.897 | 0.971 |  | 0.790 | 0.737 | 0.475 | 0.404 | 0.984 | 0.966 |  |
| 10% | GD | 0.620 | 0.413 | 0.315 | 0.204 | 0.913 | 0.821 |  | 0.826 | 0.480 | 0.469 | 0.285 | 0.986 | 0.935 |
| PO | 0.607 | 0.610 | 0.278 | 0.290 | 0.914 | 0.917 |  | 0.792 | 0.752 | 0.460 | 0.390 | 0.981 | 0.967 |  |

**Table 7: LLM unlearning with GA controlled by objective capping. We evaluated on TOFU fictitious unlearning, with different forget rates and different trained LLMs.**
| GA, OC | Phi-1.5 |  | Llama-2-7B |  |  |  |  |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| setup | $\delta$ | PS-exact | PS-perturb | PS-similar |  | PS-exact | PS-perturb | PS-similar |  |  |  |  |  |  |
| retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $-$ |  | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $-$ |  |  |
| 1% | $0.0$ | 0.668 | 0.673 | 0.325 | 0.234 | 0.918 | 0.980 |  | 0.914 | 0.874 | 0.505 | 0.497 | 0.983 | 0.994 |
| $1.0$ | 0.269 | 0.085 | 0.151 | 0.051 | 0.726 | 0.606 |  | 0.547 | 0.083 | 0.288 | 0.038 | 0.864 | 0.486 |  |
| $2.0$ | 0.144 | 0.015 | 0.068 | 0.008 | 0.350 | 0.201 |  | 0.591 | 0.062 | 0.315 | 0.054 | 0.895 | 0.438 |  |
| $3.0$ | 0.004 | 0.000 | 0.000 | 0.000 | 0.076 | 0.000 |  | 0.520 | 0.090 | 0.313 | 0.078 | 0.946 | 0.712 |  |
| $4.0$ | 0.007 | 0.000 | 0.003 | 0.000 | 0.088 | 0.023 |  | 0.512 | 0.104 | 0.318 | 0.086 | 0.948 | 0.695 |  |
| $5.0$ | 0.022 | 0.000 | 0.019 | 0.000 | 0.176 | 0.023 |  | 0.504 | 0.084 | 0.314 | 0.089 | 0.945 | 0.721 |  |
| $6.0$ | 0.022 | 0.000 | 0.019 | 0.000 | 0.176 | 0.023 |  | 0.433 | 0.081 | 0.289 | 0.061 | 0.936 | 0.678 |  |
| $7.0$ | 0.000 | 0.000 | 0.000 | 0.000 | 0.042 | 0.018 |  | 0.341 | 0.061 | 0.255 | 0.041 | 0.962 | 0.442 |  |
| $8.0$ | 0.000 | 0.000 | 0.000 | 0.000 | 0.021 | 0.018 |  | 0.358 | 0.069 | 0.267 | 0.058 | 0.932 | 0.636 |  |
| $9.0$ | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.313 | 0.051 | 0.248 | 0.047 | 0.912 | 0.621 |  |
|  | $10.0$ | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.326 | 0.063 | 0.228 | 0.038 | 0.909 | 0.599 |
| 10% | $0.0$ | 0.668 | 0.649 | 0.325 | 0.298 | 0.918 | 0.949 |  | 0.914 | 0.779 | 0.505 | 0.429 | 0.983 | 0.982 |
| $1.0$ | 0.007 | 0.012 | 0.007 | 0.000 | 0.195 | 0.112 |  | 0.261 | 0.162 | 0.215 | 0.117 | 0.704 | 0.659 |  |
| $2.0$ | 0.000 | 0.000 | 0.000 | 0.000 | 0.068 | 0.024 |  | 0.016 | 0.004 | 0.026 | 0.001 | 0.104 | 0.121 |  |
| $3.0$ | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.108 | 0.054 | 0.085 | 0.028 | 0.470 | 0.412 |  |
| $4.0$ | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.081 | 0.042 | 0.071 | 0.016 | 0.565 | 0.444 |  |
| $5.0$ | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.084 | 0.039 | 0.060 | 0.020 | 0.641 | 0.523 |  |
| $6.0$ | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.055 | 0.016 | 0.039 | 0.013 | 0.553 | 0.428 |  |
| $7.0$ | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.055 | 0.016 | 0.037 | 0.012 | 0.539 | 0.400 |  |
| $8.0$ | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.062 | 0.013 | 0.038 | 0.011 | 0.624 | 0.553 |  |
| $9.0$ | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.042 | 0.012 | 0.029 | 0.009 | 0.431 | 0.425 |  |
|  | $10.0$ | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.040 | 0.013 | 0.028 | 0.008 | 0.572 | 0.493 |

**Table 8: LLM unlearning with GA controlled by early stopping. We evaluated on TOFU fictitious unlearning, with different forget rates and different trained LLMs.**
| GA, ES | Phi-1.5 |  | Llama-2-7B |  |  |  |  |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| setup | $t$ | PS-exact | PS-perturb | PS-similar |  | PS-exact | PS-perturb | PS-similar |  |  |  |  |  |  |
| retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $-$ |  | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $-$ |  |  |
| 1% | 0 0 | 0.668 | 0.673 | 0.325 | 0.234 | 0.918 | 0.980 |  | 0.914 | 0.874 | 0.505 | 0.497 | 0.983 | 0.994 |
| $2$ | 0.674 | 0.678 | 0.326 | 0.239 | 0.923 | 0.984 |  | 0.916 | 0.871 | 0.507 | 0.490 | 0.995 | 0.995 |  |
| $5$ | 0.677 | 0.487 | 0.327 | 0.208 | 0.921 | 0.892 |  | 0.901 | 0.780 | 0.504 | 0.440 | 0.994 | 0.968 |  |
| $7$ | 0.597 | 0.121 | 0.283 | 0.097 | 0.857 | 0.552 |  | 0.783 | 0.454 | 0.458 | 0.307 | 0.983 | 0.969 |  |
| $10$ | 0.000 | 0.000 | 0.000 | 0.000 | 0.022 | 0.023 |  | 0.603 | 0.096 | 0.331 | 0.072 | 0.981 | 0.716 |  |
| $12$ | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.033 |  | 0.339 | 0.033 | 0.230 | 0.029 | 0.932 | 0.449 |  |
| $15$ | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.012 |  | 0.186 | 0.008 | 0.129 | 0.011 | 0.876 | 0.250 |  |
| $17$ | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.077 | 0.000 | 0.052 | 0.000 | 0.653 | 0.083 |  |
| $20$ | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| $22$ | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
|  | $25$ | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| 10% | 0 0 | 0.668 | 0.649 | 0.325 | 0.298 | 0.918 | 0.949 |  | 0.914 | 0.779 | 0.505 | 0.429 | 0.983 | 0.982 |
| $25$ | 0.120 | 0.101 | 0.063 | 0.028 | 0.351 | 0.358 |  | 0.705 | 0.587 | 0.415 | 0.310 | 0.985 | 0.979 |  |
| $50$ | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| $75$ | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| $100$ | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| $125$ | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| $150$ | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| $175$ | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| $200$ | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| $225$ | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
|  | $250$ | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |

**Table 9: LLM unlearning with GA controlled by model mixing. We evaluated on TOFU fictitious unlearning, with different forget rates and different trained LLMs.**
| GA, MM | Phi-1.5 |  | Llama-2-7B |  |  |  |  |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| setup | $\alpha$ | PS-exact | PS-perturb | PS-similar |  | PS-exact | PS-perturb | PS-similar |  |  |  |  |  |  |
| retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $-$ |  | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $-$ |  |  |
| 1% | 0.0 | 0.668 | 0.673 | 0.325 | 0.234 | 0.918 | 0.980 |  | 0.914 | 0.874 | 0.505 | 0.497 | 0.983 | 0.994 |
| 0.1 | 0.663 | 0.233 | 0.289 | 0.092 | 0.904 | 0.682 |  | 0.865 | 0.395 | 0.505 | 0.313 | 0.984 | 0.925 |  |
| 0.2 | 0.251 | 0.016 | 0.149 | 0.012 | 0.656 | 0.175 |  | 0.767 | 0.092 | 0.491 | 0.095 | 0.986 | 0.723 |  |
| 0.3 | 0.050 | 0.000 | 0.016 | 0.000 | 0.276 | 0.093 |  | 0.618 | 0.006 | 0.368 | 0.011 | 0.966 | 0.157 |  |
| 0.4 | 0.001 | 0.000 | 0.001 | 0.000 | 0.164 | 0.023 |  | 0.310 | 0.000 | 0.237 | 0.000 | 0.888 | 0.048 |  |
| 0.5 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.109 | 0.000 | 0.077 | 0.000 | 0.660 | 0.044 |  |
| 0.6 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.043 | 0.000 | 0.011 | 0.000 | 0.121 | 0.000 |  |
| 0.7 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.001 | 0.000 | 0.000 | 0.000 | 0.001 | 0.000 |  |
| 0.8 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| 0.9 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
|  | 1.0 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| 10% | 0.0 | 0.668 | 0.649 | 0.325 | 0.298 | 0.918 | 0.949 |  | 0.914 | 0.779 | 0.505 | 0.429 | 0.983 | 0.982 |
| 0.1 | 0.112 | 0.035 | 0.063 | 0.005 | 0.357 | 0.295 |  | 0.635 | 0.425 | 0.401 | 0.267 | 0.974 | 0.918 |  |
| 0.2 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.305 | 0.131 | 0.212 | 0.082 | 0.845 | 0.777 |  |
| 0.3 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.019 | 0.004 | 0.012 | 0.009 | 0.314 | 0.147 |  |
| 0.4 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| 0.5 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| 0.6 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| 0.7 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| 0.8 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| 0.9 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
|  | 1.0 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |

**Table 10: LLM unlearning with GD controlled by objective capping. We evaluated on TOFU fictitious unlearning, with different forget rates and different trained LLMs.**
| GD, OC | Phi-1.5 |  | Llama-2-7B |  |  |  |  |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| setup | $\delta$ | PS-exact | PS-perturb | PS-similar |  | PS-exact | PS-perturb | PS-similar |  |  |  |  |  |  |
| retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $-$ |  | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $-$ |  |  |
| 1% | $0.0$ | 0.668 | 0.673 | 0.325 | 0.234 | 0.918 | 0.980 |  | 0.914 | 0.874 | 0.505 | 0.497 | 0.983 | 0.994 |
| $1.0$ | 0.242 | 0.071 | 0.104 | 0.020 | 0.637 | 0.398 |  | 0.457 | 0.074 | 0.270 | 0.046 | 0.870 | 0.468 |  |
| $2.0$ | 0.153 | 0.015 | 0.070 | 0.008 | 0.313 | 0.207 |  | 0.495 | 0.062 | 0.297 | 0.073 | 0.869 | 0.390 |  |
| $3.0$ | 0.026 | 0.000 | 0.008 | 0.000 | 0.194 | 0.000 |  | 0.483 | 0.082 | 0.295 | 0.084 | 0.836 | 0.357 |  |
| $4.0$ | 0.007 | 0.000 | 0.003 | 0.000 | 0.093 | 0.000 |  | 0.491 | 0.067 | 0.274 | 0.067 | 0.800 | 0.325 |  |
| $5.0$ | 0.029 | 0.000 | 0.028 | 0.000 | 0.179 | 0.025 |  | 0.481 | 0.075 | 0.305 | 0.069 | 0.755 | 0.305 |  |
| $6.0$ | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.481 | 0.075 | 0.305 | 0.069 | 0.755 | 0.305 |  |
| $7.0$ | 0.000 | 0.000 | 0.000 | 0.000 | 0.072 | 0.018 |  | 0.067 | 0.000 | 0.044 | 0.000 | 0.281 | 0.014 |  |
| $8.0$ | 0.000 | 0.000 | 0.000 | 0.000 | 0.072 | 0.018 |  | 0.177 | 0.014 | 0.117 | 0.002 | 0.352 | 0.075 |  |
| $9.0$ | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.177 | 0.014 | 0.117 | 0.002 | 0.352 | 0.075 |  |
|  | $10.0$ | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.457 | 0.025 | 0.298 | 0.027 | 0.744 | 0.151 |
| 10% | $0.0$ | 0.668 | 0.649 | 0.325 | 0.298 | 0.918 | 0.949 |  | 0.914 | 0.779 | 0.505 | 0.429 | 0.983 | 0.982 |
| $1.0$ | 0.011 | 0.011 | 0.007 | 0.000 | 0.082 | 0.086 |  | 0.145 | 0.044 | 0.108 | 0.025 | 0.326 | 0.289 |  |
| $2.0$ | 0.000 | 0.000 | 0.000 | 0.000 | 0.014 | 0.000 |  | 0.056 | 0.026 | 0.055 | 0.002 | 0.202 | 0.116 |  |
| $3.0$ | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.008 | 0.000 | 0.000 | 0.000 | 0.073 | 0.000 |  |
| $4.0$ | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| $5.0$ | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.012 | 0.004 | 0.014 | 0.000 | 0.102 | 0.085 |  |
| $6.0$ | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.008 | 0.002 | 0.008 | 0.000 | 0.091 | 0.038 |  |
| $7.0$ | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.008 | 0.000 | 0.008 | 0.000 | 0.076 | 0.038 |  |
| $8.0$ | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.008 | 0.000 | 0.008 | 0.000 | 0.076 | 0.038 |  |
| $9.0$ | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.023 | 0.000 |  |
|  | $10.0$ | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |

**Table 11: LLM unlearning with GD controlled by early stopping. We evaluated on TOFU fictitious unlearning, with different forget rates and different trained LLMs.**
| GD, ES | Phi-1.5 |  | Llama-2-7B |  |  |  |  |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| setup | $t$ | PS-exact | PS-perturb | PS-similar |  | PS-exact | PS-perturb | PS-similar |  |  |  |  |  |  |
| retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $-$ |  | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $-$ |  |  |
| 1% | 0 0 | 0.668 | 0.673 | 0.325 | 0.234 | 0.918 | 0.980 |  | 0.914 | 0.874 | 0.505 | 0.497 | 0.983 | 0.994 |
| $2$ | 0.672 | 0.678 | 0.324 | 0.235 | 0.924 | 0.970 |  | 0.916 | 0.871 | 0.509 | 0.492 | 0.994 | 0.994 |  |
| $5$ | 0.669 | 0.528 | 0.326 | 0.211 | 0.913 | 0.930 |  | 0.897 | 0.805 | 0.482 | 0.445 | 0.983 | 0.976 |  |
| $7$ | 0.667 | 0.230 | 0.318 | 0.132 | 0.940 | 0.754 |  | 0.797 | 0.463 | 0.467 | 0.314 | 0.983 | 0.956 |  |
| $10$ | 0.186 | 0.031 | 0.098 | 0.006 | 0.592 | 0.186 |  | 0.594 | 0.101 | 0.377 | 0.082 | 0.971 | 0.813 |  |
| $12$ | 0.139 | 0.003 | 0.089 | 0.000 | 0.430 | 0.169 |  | 0.410 | 0.043 | 0.271 | 0.026 | 0.938 | 0.524 |  |
| $15$ | 0.125 | 0.000 | 0.062 | 0.000 | 0.353 | 0.115 |  | 0.286 | 0.014 | 0.215 | 0.015 | 0.891 | 0.351 |  |
| $17$ | 0.093 | 0.000 | 0.032 | 0.000 | 0.348 | 0.057 |  | 0.208 | 0.004 | 0.151 | 0.004 | 0.851 | 0.102 |  |
| $20$ | 0.025 | 0.000 | 0.005 | 0.000 | 0.387 | 0.000 |  | 0.093 | 0.000 | 0.060 | 0.000 | 0.598 | 0.022 |  |
| $22$ | 0.069 | 0.000 | 0.017 | 0.000 | 0.197 | 0.000 |  | 0.105 | 0.000 | 0.095 | 0.000 | 0.610 | 0.020 |  |
|  | $25$ | 0.106 | 0.000 | 0.053 | 0.000 | 0.392 | 0.000 |  | 0.301 | 0.000 | 0.178 | 0.000 | 0.886 | 0.021 |
| 10% | 0 0 | 0.668 | 0.649 | 0.325 | 0.298 | 0.918 | 0.949 |  | 0.914 | 0.779 | 0.505 | 0.429 | 0.983 | 0.982 |
| $25$ | 0.658 | 0.526 | 0.308 | 0.279 | 0.913 | 0.867 |  | 0.813 | 0.670 | 0.465 | 0.376 | 0.985 | 0.970 |  |
| $50$ | 0.012 | 0.002 | 0.013 | 0.002 | 0.068 | 0.015 |  | 0.077 | 0.027 | 0.057 | 0.009 | 0.343 | 0.157 |  |
| $75$ | 0.057 | 0.003 | 0.056 | 0.003 | 0.379 | 0.039 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| $100$ | 0.105 | 0.000 | 0.096 | 0.000 | 0.549 | 0.047 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| $125$ | 0.116 | 0.000 | 0.110 | 0.000 | 0.645 | 0.022 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| $150$ | 0.076 | 0.000 | 0.058 | 0.000 | 0.384 | 0.007 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| $175$ | 0.114 | 0.000 | 0.128 | 0.000 | 0.670 | 0.024 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| $200$ | 0.121 | 0.000 | 0.133 | 0.000 | 0.695 | 0.045 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| $225$ | 0.155 | 0.000 | 0.124 | 0.000 | 0.622 | 0.047 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
|  | $250$ | 0.164 | 0.000 | 0.156 | 0.000 | 0.618 | 0.044 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |

**Table 12: LLM unlearning with GD controlled by model mixing. We evaluated on TOFU fictitious unlearning, with different forget rates and different trained LLMs.**
| GD, MM | Phi-1.5 |  | Llama-2-7B |  |  |  |  |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| setup | $\alpha$ | PS-exact | PS-perturb | PS-similar |  | PS-exact | PS-perturb | PS-similar |  |  |  |  |  |  |
| retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $-$ |  | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $-$ |  |  |
| 1% | 0.0 | 0.668 | 0.673 | 0.325 | 0.234 | 0.918 | 0.980 |  | 0.914 | 0.874 | 0.505 | 0.497 | 0.983 | 0.994 |
| 0.1 | 0.660 | 0.367 | 0.325 | 0.172 | 0.911 | 0.831 |  | 0.896 | 0.461 | 0.503 | 0.341 | 0.983 | 0.967 |  |
| 0.2 | 0.650 | 0.149 | 0.321 | 0.086 | 0.923 | 0.599 |  | 0.880 | 0.157 | 0.502 | 0.180 | 0.983 | 0.830 |  |
| 0.3 | 0.586 | 0.014 | 0.296 | 0.024 | 0.925 | 0.236 |  | 0.799 | 0.031 | 0.484 | 0.040 | 0.973 | 0.391 |  |
| 0.4 | 0.525 | 0.003 | 0.274 | 0.003 | 0.927 | 0.076 |  | 0.733 | 0.003 | 0.475 | 0.004 | 0.983 | 0.061 |  |
| 0.5 | 0.449 | 0.001 | 0.235 | 0.001 | 0.892 | 0.027 |  | 0.699 | 0.000 | 0.415 | 0.000 | 0.965 | 0.050 |  |
| 0.6 | 0.366 | 0.000 | 0.198 | 0.000 | 0.828 | 0.016 |  | 0.625 | 0.000 | 0.393 | 0.000 | 0.945 | 0.048 |  |
| 0.7 | 0.279 | 0.000 | 0.165 | 0.000 | 0.791 | 0.000 |  | 0.550 | 0.000 | 0.312 | 0.000 | 0.953 | 0.046 |  |
| 0.8 | 0.210 | 0.000 | 0.100 | 0.000 | 0.633 | 0.000 |  | 0.489 | 0.000 | 0.271 | 0.000 | 0.930 | 0.046 |  |
| 0.9 | 0.138 | 0.000 | 0.081 | 0.000 | 0.483 | 0.000 |  | 0.395 | 0.000 | 0.212 | 0.000 | 0.908 | 0.042 |  |
|  | 1.0 | 0.106 | 0.000 | 0.053 | 0.000 | 0.392 | 0.000 |  | 0.301 | 0.000 | 0.178 | 0.000 | 0.886 | 0.021 |
| 10% | 0.0 | 0.668 | 0.649 | 0.325 | 0.298 | 0.918 | 0.949 |  | 0.914 | 0.779 | 0.505 | 0.429 | 0.983 | 0.982 |
| 0.1 | 0.741 | 0.638 | 0.328 | 0.296 | 0.918 | 0.915 |  | 0.861 | 0.560 | 0.491 | 0.318 | 0.986 | 0.941 |  |
| 0.2 | 0.691 | 0.504 | 0.316 | 0.207 | 0.908 | 0.835 |  | 0.758 | 0.237 | 0.383 | 0.187 | 0.951 | 0.760 |  |
| 0.3 | 0.566 | 0.147 | 0.299 | 0.103 | 0.865 | 0.613 |  | 0.566 | 0.147 | 0.299 | 0.103 | 0.670 | 0.421 |  |
| 0.4 | 0.578 | 0.070 | 0.263 | 0.055 | 0.848 | 0.263 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.037 |  |
| 0.5 | 0.379 | 0.002 | 0.235 | 0.000 | 0.786 | 0.056 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| 0.6 | 0.415 | 0.000 | 0.216 | 0.000 | 0.743 | 0.030 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| 0.7 | 0.267 | 0.000 | 0.194 | 0.000 | 0.741 | 0.009 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| 0.8 | 0.258 | 0.000 | 0.175 | 0.000 | 0.654 | 0.028 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| 0.9 | 0.229 | 0.000 | 0.160 | 0.000 | 0.694 | 0.025 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
|  | 1.0 | 0.164 | 0.000 | 0.156 | 0.000 | 0.618 | 0.044 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |

Figure: Figure 4: The performance curves of GA with our suggested controlling methods, adhering to the 1% unlearning setup. We reported PS-based scores with different choices of controlling parameters.
Refer to caption: x5.png

Figure: Figure 5: The performance curves of GA with our suggested controlling methods, adhering to the 10% unlearning setup. We reported PS-based scores with different choices of controlling parameters.
Refer to caption: x7.png

Figure: Figure 6: The performance curves of GD with our suggested controlling methods, adhering to the 1% unlearning setup. We reported PS-based scores with different choices of controlling parameters.
Refer to caption: x9.png

Figure: Figure 7: The performance curves of GD with our suggested controlling methods, adhering to the 10% unlearning setup. We reported PS-based scores with different choices of controlling parameters.
Refer to caption: x11.png

**Table 13: LLM unlearning with GA coarse-grained controlled by mode mixing. We evaluated on TOFU fictitious unlearning, with different forget rates and different trained LLMs. indicates the result is a boarder case that satisfies our criterion in assessing excessive unlearning in Appendix C.**
| GA, MM | Phi-1.5 |  | Llama-2-7B |  |  |  |  |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| setup | $\alpha$ | PS-exact | PS-perturb | PS-similar |  | PS-exact | PS-perturb | PS-similar |  |  |  |  |  |  |
| retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $-$ |  | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $-$ |  |  |
| 1% | 0.0 | 0.668 | 0.673 | 0.325 | 0.234 | 0.918 | 0.980 |  | 0.914 | 0.874 | 0.505 | 0.497 | 0.983 | 0.994 |
| 0.1 | 0.663 | 0.233 | 0.289 | 0.092 | 0.904 | 0.682 |  | 0.865 | 0.395 | 0.505 | 0.313 | 0.984 | 0.925 |  |
| 0.2 | 0.251 | 0.016 | 0.149 | 0.012 | 0.656 | 0.175 |  | 0.767 | 0.092 | 0.491 | 0.095 | 0.986 | 0.723 |  |
| 0.3 | 0.050 | 0.000 | 0.016 | 0.000 | 0.276 | 0.093 |  | 0.618 | 0.006 | 0.368 | 0.011 | 0.966 | 0.157 |  |
| 0.4 | 0.001 | 0.000 | 0.001 | 0.000 | 0.164 | 0.023 |  | 0.310 | 0.000 | 0.237 | 0.000 | 0.888 | 0.048 |  |
| 0.5 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.109 | 0.000 | 0.077 | 0.000 | 0.660 | 0.044 |  |
| 0.6 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.043 | 0.000 | 0.011 | 0.000 | 0.121 | 0.000 |  |
| 0.7 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.001 | 0.000 | 0.000 | 0.000 | 0.001 | 0.000 |  |
| 0.8 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| 0.9 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
|  | 1.0 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| 5% | 0.0 | 0.668 | 0.788 | 0.325 | 0.288 | 0.918 | 0.976 |  | 0.914 | 0.853 | 0.505 | 0.428 | 0.983 | 0.986 |
| 0.1 | 0.157 | 0.061 | 0.063 | 0.039 | 0.402 | 0.429 |  | 0.722 | 0.519 | 0.428 | 0.289 | 0.987 | 0.942 |  |
| 0.2 | 0.000 | 0.000 | 0.000 | 0.000 | 0.041 | 0.000 |  | 0.557 | 0.178 | 0.363 | 0.133 | 0.946 | 0.640 |  |
| 0.3 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.292 | 0.064 | 0.216 | 0.042 | 0.843 | 0.391 |  |
| 0.4 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.037 | 0.006 | 0.040 | 0.008 | 0.267 | 0.151 |  |
| 0.5 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| 0.6 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| 0.7 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| 0.8 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| 0.9 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
|  | 1.0 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| 10% | 0.0 | 0.668 | 0.649 | 0.325 | 0.298 | 0.918 | 0.949 |  | 0.914 | 0.779 | 0.505 | 0.429 | 0.983 | 0.982 |
| 0.1 | 0.112 | 0.035 | 0.063 | 0.005 | 0.357 | 0.295 |  | 0.635 | 0.425 | 0.401 | 0.267 | 0.974 | 0.918 |  |
| 0.2 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.305 | 0.131 | 0.212 | 0.082 | 0.845 | 0.777 |  |
| 0.3 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.019 | 0.004 | 0.012 | 0.009 | 0.314 | 0.147 |  |
| 0.4 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| 0.5 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| 0.6 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| 0.7 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| 0.8 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| 0.9 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
|  | 1.0 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |

**Table 14: LLM unlearning with GA fine-grained controlled by model mixing. We evaluated on TOFU fictitious unlearning, with different forget rates and different trained LLMs. indicates the result is a boarder case that satisfies our criterion in assessing excessive unlearning in Appendix C.**
| GA, MM | Phi-1.5 |  | Llama-2-7B |  |  |  |  |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| setup | $\alpha$ | PS-exact | PS-perturb | PS-similar |  | PS-exact | PS-perturb | PS-similar |  |  |  |  |  |  |
| retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $-$ |  | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $-$ |  |  |
| 1% | 0.00 | 0.668 | 0.673 | 0.325 | 0.234 | 0.918 | 0.980 |  | 0.914 | 0.874 | 0.505 | 0.497 | 0.983 | 0.994 |
| 0.02 | 0.672 | 0.609 | 0.327 | 0.223 | 0.911 | 0.963 |  | 0.913 | 0.860 | 0.516 | 0.488 | 0.994 | 0.994 |  |
| 0.04 | 0.696 | 0.416 | 0.322 | 0.184 | 0.908 | 0.868 |  | 0.893 | 0.573 | 0.516 | 0.381 | 0.983 | 0.969 |  |
| 0.06 | 0.678 | 0.299 | 0.302 | 0.150 | 0.915 | 0.760 |  | 0.887 | 0.456 | 0.498 | 0.335 | 0.984 | 0.959 |  |
| 0.08 | 0.650 | 0.240 | 0.285 | 0.098 | 0.904 | 0.682 |  | 0.862 | 0.352 | 0.513 | 0.313 | 0.984 | 0.923 |  |
| 0.10 | 0.663 | 0.233 | 0.289 | 0.092 | 0.904 | 0.682 |  | 0.865 | 0.395 | 0.505 | 0.313 | 0.984 | 0.925 |  |
| 0.12 | 0.580 | 0.063 | 0.253 | 0.057 | 0.805 | 0.425 |  | 0.837 | 0.249 | 0.505 | 0.231 | 0.975 | 0.910 |  |
| 0.14 | 0.450 | 0.037 | 0.212 | 0.030 | 0.792 | 0.387 |  | 0.827 | 0.205 | 0.504 | 0.202 | 0.975 | 0.892 |  |
| 0.16 | 0.417 | 0.027 | 0.203 | 0.028 | 0.767 | 0.266 |  | 0.808 | 0.170 | 0.479 | 0.174 | 0.987 | 0.820 |  |
| 0.18 | 0.317 | 0.018 | 0.194 | 0.018 | 0.728 | 0.222 |  | 0.787 | 0.124 | 0.486 | 0.127 | 0.987 | 0.763 |  |
|  | 0.20 | 0.251 | 0.016 | 0.149 | 0.012 | 0.656 | 0.175 |  | 0.767 | 0.092 | 0.491 | 0.095 | 0.986 | 0.723 |
| 5% | 0.00 | 0.668 | 0.788 | 0.325 | 0.288 | 0.918 | 0.976 |  | 0.914 | 0.853 | 0.505 | 0.428 | 0.983 | 0.986 |
| 0.02 | 0.713 | 0.756 | 0.330 | 0.256 | 0.914 | 0.981 |  | 0.883 | 0.821 | 0.504 | 0.419 | 0.995 | 0.989 |  |
| 0.04 | 0.650 | 0.556 | 0.287 | 0.183 | 0.846 | 0.876 |  | 0.803 | 0.778 | 0.457 | 0.381 | 0.983 | 0.988 |  |
| 0.06 | 0.413 | 0.291 | 0.209 | 0.127 | 0.728 | 0.736 |  | 0.774 | 0.680 | 0.447 | 0.319 | 0.982 | 0.985 |  |
| 0.08 | 0.233 | 0.116 | 0.087 | 0.086 | 0.582 | 0.555 |  | 0.741 | 0.564 | 0.438 | 0.292 | 0.987 | 0.953 |  |
| 0.10 | 0.157 | 0.061 | 0.063 | 0.039 | 0.402 | 0.429 |  | 0.722 | 0.519 | 0.428 | 0.289 | 0.987 | 0.942 |  |
| 0.12 | 0.050 | 0.035 | 0.032 | 0.000 | 0.172 | 0.146 |  | 0.672 | 0.380 | 0.425 | 0.227 | 0.985 | 0.857 |  |
| 0.14 | 0.007 | 0.000 | 0.003 | 0.000 | 0.143 | 0.033 |  | 0.649 | 0.383 | 0.419 | 0.203 | 0.967 | 0.838 |  |
| 0.16 | 0.001 | 0.000 | 0.000 | 0.000 | 0.031 | 0.000 |  | 0.630 | 0.302 | 0.398 | 0.197 | 0.961 | 0.759 |  |
| 0.18 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.600 | 0.259 | 0.384 | 0.154 | 0.948 | 0.725 |  |
|  | 0.20 | 0.000 | 0.000 | 0.000 | 0.000 | 0.041 | 0.000 |  | 0.557 | 0.178 | 0.363 | 0.133 | 0.946 | 0.640 |
| 10% | 0.00 | 0.668 | 0.649 | 0.325 | 0.298 | 0.918 | 0.949 |  | 0.914 | 0.779 | 0.505 | 0.429 | 0.983 | 0.982 |
| 0.02 | 0.698 | 0.622 | 0.331 | 0.259 | 0.937 | 0.949 |  | 0.875 | 0.781 | 0.466 | 0.424 | 0.994 | 0.987 |  |
| 0.04 | 0.653 | 0.424 | 0.282 | 0.200 | 0.857 | 0.884 |  | 0.763 | 0.637 | 0.440 | 0.367 | 0.980 | 0.980 |  |
| 0.06 | 0.406 | 0.266 | 0.203 | 0.142 | 0.668 | 0.652 |  | 0.741 | 0.560 | 0.437 | 0.321 | 0.993 | 0.958 |  |
| 0.08 | 0.231 | 0.178 | 0.094 | 0.068 | 0.521 | 0.491 |  | 0.696 | 0.486 | 0.411 | 0.308 | 0.978 | 0.959 |  |
| 0.10 | 0.112 | 0.035 | 0.063 | 0.005 | 0.357 | 0.295 |  | 0.635 | 0.425 | 0.401 | 0.267 | 0.974 | 0.918 |  |
| 0.12 | 0.016 | 0.009 | 0.028 | 0.000 | 0.166 | 0.125 |  | 0.578 | 0.322 | 0.363 | 0.215 | 0.913 | 0.871 |  |
| 0.14 | 0.000 | 0.000 | 0.000 | 0.000 | 0.076 | 0.059 |  | 0.503 | 0.233 | 0.321 | 0.156 | 0.888 | 0.839 |  |
| 0.16 | 0.000 | 0.000 | 0.000 | 0.000 | 0.013 | 0.017 |  | 0.431 | 0.191 | 0.275 | 0.115 | 0.852 | 0.797 |  |
| 0.18 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.352 | 0.163 | 0.240 | 0.096 | 0.891 | 0.802 |  |
|  | 0.20 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.305 | 0.131 | 0.212 | 0.082 | 0.845 | 0.777 |

**Table 15: LLM unlearning with GD coarse-grained controlled by model mixing. We evaluated on TOFU fictitious unlearning, with different forget rates and different trained LLMs. indicates the result is a boarder case that satisfies our criterion in assessing excessive unlearning in Appendix C.**
| GD, MM | Phi-1.5 |  | Llama-2-7B |  |  |  |  |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| setup | $\alpha$ | PS-exact | PS-perturb | PS-similar |  | PS-exact | PS-perturb | PS-similar |  |  |  |  |  |  |
| retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $-$ |  | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $-$ |  |  |
| 1% | 0.0 | 0.668 | 0.673 | 0.325 | 0.234 | 0.918 | 0.980 |  | 0.914 | 0.874 | 0.505 | 0.497 | 0.983 | 0.994 |
| 0.1 | 0.660 | 0.367 | 0.325 | 0.172 | 0.911 | 0.831 |  | 0.896 | 0.461 | 0.503 | 0.341 | 0.983 | 0.967 |  |
| 0.2 | 0.650 | 0.149 | 0.321 | 0.086 | 0.923 | 0.599 |  | 0.880 | 0.157 | 0.502 | 0.180 | 0.983 | 0.830 |  |
| 0.3 | 0.586 | 0.014 | 0.296 | 0.024 | 0.925 | 0.236 |  | 0.799 | 0.031 | 0.484 | 0.040 | 0.973 | 0.391 |  |
| 0.4 | 0.525 | 0.003 | 0.274 | 0.003 | 0.927 | 0.076 |  | 0.733 | 0.003 | 0.475 | 0.004 | 0.983 | 0.061 |  |
| 0.5 | 0.449 | 0.001 | 0.235 | 0.001 | 0.892 | 0.027 |  | 0.699 | 0.000 | 0.415 | 0.000 | 0.965 | 0.050 |  |
| 0.6 | 0.366 | 0.000 | 0.198 | 0.000 | 0.828 | 0.016 |  | 0.625 | 0.000 | 0.393 | 0.000 | 0.945 | 0.048 |  |
| 0.7 | 0.279 | 0.000 | 0.165 | 0.000 | 0.791 | 0.000 |  | 0.550 | 0.000 | 0.312 | 0.000 | 0.953 | 0.046 |  |
| 0.8 | 0.210 | 0.000 | 0.100 | 0.000 | 0.633 | 0.000 |  | 0.489 | 0.000 | 0.271 | 0.000 | 0.930 | 0.046 |  |
| 0.9 | 0.138 | 0.000 | 0.081 | 0.000 | 0.483 | 0.000 |  | 0.395 | 0.000 | 0.212 | 0.000 | 0.908 | 0.042 |  |
|  | 1.0 | 0.106 | 0.000 | 0.053 | 0.000 | 0.392 | 0.000 |  | 0.301 | 0.000 | 0.178 | 0.000 | 0.886 | 0.021 |
| 5% | 0.0 | 0.668 | 0.788 | 0.325 | 0.288 | 0.918 | 0.976 |  | 0.914 | 0.853 | 0.505 | 0.428 | 0.983 | 0.986 |
| 0.1 | 0.652 | 0.520 | 0.351 | 0.234 | 0.946 | 0.965 |  | 0.867 | 0.729 | 0.492 | 0.394 | 0.974 | 0.988 |  |
| 0.2 | 0.635 | 0.367 | 0.317 | 0.180 | 0.941 | 0.823 |  | 0.839 | 0.501 | 0.475 | 0.329 | 0.984 | 0.942 |  |
| 0.3 | 0.544 | 0.163 | 0.304 | 0.119 | 0.900 | 0.624 |  | 0.692 | 0.310 | 0.446 | 0.181 | 0.942 | 0.898 |  |
| 0.4 | 0.466 | 0.044 | 0.256 | 0.034 | 0.852 | 0.231 |  | 0.664 | 0.170 | 0.428 | 0.124 | 0.900 | 0.692 |  |
| 0.5 | 0.395 | 0.000 | 0.220 | 0.000 | 0.810 | 0.002 |  | 0.565 | 0.025 | 0.397 | 0.016 | 0.851 | 0.149 |  |
| 0.6 | 0.297 | 0.000 | 0.189 | 0.000 | 0.805 | 0.000 |  | 0.502 | 0.000 | 0.348 | 0.000 | 0.842 | 0.024 |  |
| 0.7 | 0.267 | 0.000 | 0.178 | 0.000 | 0.812 | 0.000 |  | 0.443 | 0.000 | 0.297 | 0.000 | 0.783 | 0.000 |  |
| 0.8 | 0.258 | 0.000 | 0.164 | 0.000 | 0.791 | 0.000 |  | 0.388 | 0.000 | 0.294 | 0.000 | 0.780 | 0.000 |  |
| 0.9 | 0.213 | 0.000 | 0.155 | 0.000 | 0.743 | 0.000 |  | 0.339 | 0.000 | 0.287 | 0.000 | 0.761 | 0.000 |  |
|  | 1.0 | 0.158 | 0.000 | 0.146 | 0.000 | 0.725 | 0.000 |  | 0.318 | 0.000 | 0.211 | 0.000 | 0.734 | 0.000 |
| 10% | 0.0 | 0.668 | 0.649 | 0.325 | 0.298 | 0.918 | 0.949 |  | 0.914 | 0.779 | 0.505 | 0.429 | 0.983 | 0.982 |
| 0.1 | 0.741 | 0.638 | 0.328 | 0.296 | 0.918 | 0.915 |  | 0.861 | 0.560 | 0.491 | 0.318 | 0.986 | 0.941 |  |
| 0.2 | 0.691 | 0.504 | 0.316 | 0.207 | 0.908 | 0.835 |  | 0.758 | 0.237 | 0.383 | 0.187 | 0.951 | 0.760 |  |
| 0.3 | 0.566 | 0.147 | 0.299 | 0.103 | 0.865 | 0.613 |  | 0.566 | 0.147 | 0.299 | 0.103 | 0.670 | 0.421 |  |
| 0.4 | 0.578 | 0.070 | 0.263 | 0.055 | 0.848 | 0.263 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.037 |  |
| 0.5 | 0.379 | 0.002 | 0.235 | 0.000 | 0.786 | 0.056 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| 0.6 | 0.415 | 0.000 | 0.216 | 0.000 | 0.743 | 0.030 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| 0.7 | 0.267 | 0.000 | 0.194 | 0.000 | 0.741 | 0.009 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| 0.8 | 0.258 | 0.000 | 0.175 | 0.000 | 0.654 | 0.028 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| 0.9 | 0.229 | 0.000 | 0.160 | 0.000 | 0.694 | 0.025 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
|  | 1.0 | 0.164 | 0.000 | 0.156 | 0.000 | 0.618 | 0.044 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |

**Table 16: LLM unlearning with GD fine-grained controlled by model mixing. We evaluated on TOFU fictitious unlearning, with different forget rates and different trained LLMs. indicates the result is a boarder case that satisfies our criterion in assessing excessive unlearning in Appendix C.**
| GD, MM | Phi-1.5 |  | Llama-2-7B |  |  |  |  |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| setup | $\alpha$ | PS-exact | PS-perturb | PS-similar |  | PS-exact | PS-perturb | PS-similar |  |  |  |  |  |  |
| retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $-$ |  | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $-$ |  |  |
| 1% | 0.10 | 0.660 | 0.367 | 0.325 | 0.172 | 0.911 | 0.831 |  | 0.896 | 0.461 | 0.503 | 0.341 | 0.983 | 0.967 |
| 0.12 | 0.657 | 0.266 | 0.329 | 0.111 | 0.906 | 0.765 |  | 0.897 | 0.298 | 0.503 | 0.267 | 0.983 | 0.915 |  |
| 0.14 | 0.659 | 0.208 | 0.329 | 0.100 | 0.915 | 0.731 |  | 0.877 | 0.271 | 0.508 | 0.241 | 0.983 | 0.899 |  |
| 0.16 | 0.652 | 0.173 | 0.326 | 0.089 | 0.905 | 0.720 |  | 0.887 | 0.230 | 0.498 | 0.215 | 0.983 | 0.872 |  |
| 0.18 | 0.652 | 0.157 | 0.325 | 0.088 | 0.906 | 0.682 |  | 0.875 | 0.205 | 0.498 | 0.196 | 0.983 | 0.875 |  |
| 0.20 | 0.650 | 0.149 | 0.321 | 0.086 | 0.923 | 0.599 |  | 0.880 | 0.157 | 0.502 | 0.180 | 0.983 | 0.830 |  |
| 0.22 | 0.649 | 0.078 | 0.315 | 0.073 | 0.923 | 0.534 |  | 0.869 | 0.118 | 0.503 | 0.120 | 0.983 | 0.775 |  |
| 0.24 | 0.614 | 0.036 | 0.315 | 0.047 | 0.917 | 0.422 |  | 0.852 | 0.072 | 0.485 | 0.086 | 0.973 | 0.698 |  |
| 0.26 | 0.609 | 0.033 | 0.320 | 0.037 | 0.916 | 0.404 |  | 0.857 | 0.062 | 0.492 | 0.070 | 0.974 | 0.628 |  |
| 0.28 | 0.596 | 0.021 | 0.316 | 0.027 | 0.912 | 0.365 |  | 0.817 | 0.054 | 0.491 | 0.055 | 0.974 | 0.510 |  |
|  | 0.30 | 0.586 | 0.014 | 0.296 | 0.024 | 0.925 | 0.236 |  | 0.799 | 0.031 | 0.484 | 0.040 | 0.973 | 0.391 |
| 5% | 0.10 | 0.652 | 0.520 | 0.351 | 0.234 | 0.946 | 0.965 | 0.00 | 0.914 | 0.874 | 0.505 | 0.497 | 0.983 | 0.994 |
| 0.12 | 0.652 | 0.487 | 0.342 | 0.207 | 0.933 | 0.944 | 0.02 | 0.914 | 0.837 | 0.508 | 0.422 | 0.995 | 0.986 |  |
| 0.14 | 0.640 | 0.448 | 0.349 | 0.199 | 0.952 | 0.926 | 0.04 | 0.905 | 0.761 | 0.504 | 0.413 | 0.983 | 0.989 |  |
| 0.16 | 0.637 | 0.426 | 0.327 | 0.188 | 0.947 | 0.914 | 0.06 | 0.893 | 0.736 | 0.504 | 0.410 | 0.994 | 0.988 |  |
| 0.18 | 0.634 | 0.390 | 0.312 | 0.184 | 0.945 | 0.907 | 0.08 | 0.883 | 0.734 | 0.491 | 0.393 | 0.974 | 0.988 |  |
| 0.20 | 0.635 | 0.367 | 0.317 | 0.180 | 0.941 | 0.823 | 0.10 | 0.867 | 0.729 | 0.492 | 0.394 | 0.974 | 0.988 |  |
| 0.22 | 0.614 | 0.289 | 0.317 | 0.163 | 0.935 | 0.767 | 0.12 | 0.853 | 0.620 | 0.485 | 0.367 | 0.985 | 0.984 |  |
| 0.24 | 0.599 | 0.261 | 0.317 | 0.159 | 0.930 | 0.769 | 0.14 | 0.850 | 0.574 | 0.485 | 0.382 | 0.985 | 0.984 |  |
| 0.26 | 0.579 | 0.236 | 0.309 | 0.143 | 0.930 | 0.763 | 0.16 | 0.838 | 0.560 | 0.485 | 0.363 | 0.985 | 0.980 |  |
| 0.28 | 0.557 | 0.216 | 0.302 | 0.131 | 0.936 | 0.706 | 0.18 | 0.836 | 0.512 | 0.476 | 0.337 | 0.984 | 0.942 |  |
|  | 0.30 | 0.544 | 0.163 | 0.304 | 0.119 | 0.900 | 0.624 | 0.20 | 0.839 | 0.501 | 0.475 | 0.329 | 0.984 | 0.942 |
| 10% | 0.10 | 0.647 | 0.553 | 0.328 | 0.296 | 0.918 | 0.915 | 0.00 | 0.914 | 0.779 | 0.505 | 0.429 | 0.983 | 0.982 |
| 0.12 | 0.646 | 0.507 | 0.306 | 0.276 | 0.915 | 0.878 | 0.02 | 0.913 | 0.762 | 0.493 | 0.395 | 0.994 | 0.985 |  |
| 0.14 | 0.625 | 0.462 | 0.312 | 0.252 | 0.910 | 0.861 | 0.04 | 0.890 | 0.709 | 0.486 | 0.403 | 0.994 | 0.978 |  |
| 0.16 | 0.618 | 0.443 | 0.315 | 0.219 | 0.908 | 0.854 | 0.06 | 0.882 | 0.639 | 0.483 | 0.345 | 0.994 | 0.976 |  |
| 0.18 | 0.620 | 0.413 | 0.315 | 0.204 | 0.913 | 0.821 | 0.08 | 0.873 | 0.592 | 0.491 | 0.330 | 0.994 | 0.959 |  |
| 0.20 | 0.596 | 0.397 | 0.316 | 0.207 | 0.908 | 0.835 | 0.10 | 0.861 | 0.560 | 0.491 | 0.318 | 0.986 | 0.941 |  |
| 0.22 | 0.581 | 0.344 | 0.316 | 0.198 | 0.906 | 0.831 | 0.12 | 0.826 | 0.480 | 0.469 | 0.285 | 0.986 | 0.935 |  |
| 0.24 | 0.583 | 0.310 | 0.316 | 0.152 | 0.899 | 0.801 | 0.14 | 0.821 | 0.409 | 0.411 | 0.253 | 0.987 | 0.933 |  |
| 0.26 | 0.573 | 0.238 | 0.314 | 0.133 | 0.895 | 0.721 | 0.16 | 0.821 | 0.324 | 0.410 | 0.207 | 0.977 | 0.875 |  |
| 0.28 | 0.571 | 0.175 | 0.312 | 0.122 | 0.881 | 0.690 | 0.18 | 0.789 | 0.278 | 0.412 | 0.197 | 0.963 | 0.809 |  |
|  | 0.30 | 0.566 | 0.147 | 0.299 | 0.103 | 0.865 | 0.613 | 0.20 | 0.758 | 0.237 | 0.383 | 0.187 | 0.951 | 0.760 |

**Table 17: LLM unlearning with KL coarse-grained controlled by model mixing. We evaluated on TOFU fictitious unlearning, with different forget rates and different trained LLMs. indicates the result is a boarder case that satisfies our criterion in assessing excessive unlearning in Appendix C.**
| KL, MM | Phi-1.5 |  | Llama-2-7B |  |  |  |  |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| setup | $\alpha$ | PS-exact | PS-perturb | PS-similar |  | PS-exact | PS-perturb | PS-similar |  |  |  |  |  |  |
| retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $-$ |  | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $-$ |  |  |
| 1% | 0.0 | 0.668 | 0.673 | 0.325 | 0.234 | 0.918 | 0.980 |  | 0.914 | 0.874 | 0.505 | 0.497 | 0.983 | 0.994 |
| 0.1 | 0.655 | 0.264 | 0.301 | 0.105 | 0.918 | 0.746 |  | 0.873 | 0.405 | 0.503 | 0.329 | 0.984 | 0.929 |  |
| 0.2 | 0.369 | 0.020 | 0.186 | 0.018 | 0.766 | 0.328 |  | 0.785 | 0.104 | 0.477 | 0.103 | 0.987 | 0.779 |  |
| 0.3 | 0.105 | 0.001 | 0.081 | 0.002 | 0.398 | 0.051 |  | 0.665 | 0.007 | 0.409 | 0.012 | 0.964 | 0.204 |  |
| 0.4 | 0.038 | 0.000 | 0.028 | 0.000 | 0.190 | 0.113 |  | 0.446 | 0.000 | 0.313 | 0.000 | 0.938 | 0.050 |  |
| 0.5 | 0.001 | 0.000 | 0.000 | 0.000 | 0.166 | 0.023 |  | 0.213 | 0.000 | 0.140 | 0.000 | 0.870 | 0.048 |  |
| 0.6 | 0.000 | 0.000 | 0.000 | 0.000 | 0.055 | 0.000 |  | 0.085 | 0.000 | 0.062 | 0.000 | 0.617 | 0.021 |  |
| 0.7 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.037 | 0.000 | 0.011 | 0.000 | 0.175 | 0.000 |  |
| 0.8 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.002 | 0.000 | 0.004 | 0.000 | 0.014 | 0.000 |  |
| 0.9 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
|  | 1.0 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| 5% | 0.0 | 0.668 | 0.788 | 0.325 | 0.288 | 0.918 | 0.976 |  | 0.914 | 0.853 | 0.505 | 0.428 | 0.983 | 0.986 |
| 0.1 | 0.190 | 0.078 | 0.069 | 0.049 | 0.467 | 0.408 |  | 0.750 | 0.533 | 0.446 | 0.286 | 0.987 | 0.920 |  |
| 0.2 | 0.000 | 0.000 | 0.000 | 0.000 | 0.043 | 0.024 |  | 0.629 | 0.244 | 0.390 | 0.189 | 0.939 | 0.770 |  |
| 0.3 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.364 | 0.091 | 0.262 | 0.052 | 0.897 | 0.403 |  |
| 0.4 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.108 | 0.005 | 0.095 | 0.000 | 0.698 | 0.166 |  |
| 0.5 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| 0.6 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| 0.7 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| 0.8 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| 0.9 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
|  | 1.0 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| 10% | 0.0 | 0.668 | 0.649 | 0.325 | 0.298 | 0.918 | 0.949 |  | 0.914 | 0.779 | 0.505 | 0.429 | 0.983 | 0.982 |
| 0.1 | 0.117 | 0.058 | 0.067 | 0.031 | 0.378 | 0.340 |  | 0.630 | 0.434 | 0.408 | 0.276 | 0.970 | 0.948 |  |
| 0.2 | 0.000 | 0.000 | 0.000 | 0.000 | 0.043 | 0.024 |  | 0.311 | 0.136 | 0.218 | 0.081 | 0.866 | 0.854 |  |
| 0.3 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.044 | 0.005 | 0.024 | 0.015 | 0.536 | 0.262 |  |
| 0.4 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| 0.5 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| 0.6 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| 0.7 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| 0.8 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
| 0.9 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  |
|  | 1.0 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |

**Table 18: LLM unlearning with KL fine-grained controlled by model mixing. We evaluated on TOFU fictitious unlearning, with different forget rates and different trained LLMs. indicates the result is a boarder case that satisfies our criterion in assessing excessive unlearning in Appendix C.**
| KL, MM | Phi-1.5 |  | Llama-2-7B |  |  |  |  |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| setup | $\alpha$ | PS-exact | PS-perturb | PS-similar |  | PS-exact | PS-perturb | PS-similar |  |  |  |  |  |  |
| retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $-$ |  | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $-$ |  |  |
| 1% | 0.00 | 0.668 | 0.673 | 0.325 | 0.234 | 0.918 | 0.980 |  | 0.914 | 0.874 | 0.505 | 0.497 | 0.983 | 0.994 |
| 0.02 | 0.671 | 0.600 | 0.331 | 0.219 | 0.914 | 0.967 |  | 0.912 | 0.860 | 0.512 | 0.490 | 0.994 | 0.994 |  |
| 0.04 | 0.690 | 0.464 | 0.323 | 0.187 | 0.911 | 0.889 |  | 0.898 | 0.590 | 0.511 | 0.390 | 0.983 | 0.969 |  |
| 0.06 | 0.679 | 0.293 | 0.317 | 0.165 | 0.911 | 0.785 |  | 0.876 | 0.453 | 0.503 | 0.329 | 0.984 | 0.958 |  |
| 0.08 | 0.642 | 0.251 | 0.297 | 0.103 | 0.906 | 0.742 |  | 0.864 | 0.360 | 0.512 | 0.303 | 0.984 | 0.930 |  |
| 0.10 | 0.655 | 0.264 | 0.301 | 0.105 | 0.918 | 0.746 |  | 0.873 | 0.405 | 0.503 | 0.329 | 0.984 | 0.929 |  |
| 0.12 | 0.590 | 0.124 | 0.262 | 0.064 | 0.831 | 0.553 |  | 0.829 | 0.251 | 0.509 | 0.220 | 0.975 | 0.901 |  |
| 0.14 | 0.567 | 0.060 | 0.245 | 0.051 | 0.810 | 0.451 |  | 0.820 | 0.220 | 0.507 | 0.210 | 0.975 | 0.879 |  |
| 0.16 | 0.536 | 0.039 | 0.216 | 0.030 | 0.811 | 0.384 |  | 0.810 | 0.186 | 0.501 | 0.190 | 0.975 | 0.818 |  |
| 0.18 | 0.421 | 0.025 | 0.216 | 0.025 | 0.812 | 0.295 |  | 0.788 | 0.133 | 0.481 | 0.138 | 0.975 | 0.796 |  |
|  | 0.20 | 0.369 | 0.020 | 0.186 | 0.018 | 0.766 | 0.328 |  | 0.785 | 0.104 | 0.477 | 0.103 | 0.987 | 0.779 |
| 5% | 0.00 | 0.668 | 0.788 | 0.325 | 0.288 | 0.918 | 0.976 |  | 0.914 | 0.853 | 0.505 | 0.428 | 0.983 | 0.986 |
| 0.02 | 0.708 | 0.757 | 0.330 | 0.250 | 0.927 | 0.985 |  | 0.907 | 0.830 | 0.502 | 0.406 | 0.994 | 0.989 |  |
| 0.04 | 0.651 | 0.573 | 0.300 | 0.191 | 0.820 | 0.871 |  | 0.827 | 0.769 | 0.468 | 0.397 | 0.982 | 0.988 |  |
| 0.06 | 0.416 | 0.352 | 0.228 | 0.113 | 0.780 | 0.743 |  | 0.777 | 0.664 | 0.457 | 0.337 | 0.982 | 0.982 |  |
| 0.08 | 0.317 | 0.147 | 0.129 | 0.073 | 0.631 | 0.602 |  | 0.765 | 0.587 | 0.465 | 0.275 | 0.989 | 0.930 |  |
| 0.10 | 0.190 | 0.078 | 0.069 | 0.049 | 0.467 | 0.408 |  | 0.750 | 0.533 | 0.446 | 0.286 | 0.987 | 0.920 |  |
| 0.12 | 0.078 | 0.041 | 0.056 | 0.000 | 0.220 | 0.196 |  | 0.702 | 0.430 | 0.426 | 0.216 | 0.987 | 0.854 |  |
| 0.14 | 0.011 | 0.000 | 0.017 | 0.000 | 0.112 | 0.022 |  | 0.678 | 0.382 | 0.419 | 0.213 | 0.979 | 0.833 |  |
| 0.16 | 0.001 | 0.000 | 0.001 | 0.000 | 0.087 | 0.000 |  | 0.661 | 0.362 | 0.427 | 0.208 | 0.965 | 0.766 |  |
| 0.18 | 0.000 | 0.000 | 0.000 | 0.000 | 0.006 | 0.000 |  | 0.632 | 0.290 | 0.411 | 0.197 | 0.947 | 0.772 |  |
|  | 0.20 | 0.000 | 0.000 | 0.000 | 0.000 | 0.043 | 0.024 |  | 0.629 | 0.244 | 0.390 | 0.189 | 0.939 | 0.770 |
| 10% | 0.00 | 0.668 | 0.649 | 0.325 | 0.298 | 0.918 | 0.949 |  | 0.914 | 0.779 | 0.505 | 0.429 | 0.983 | 0.982 |
| 0.02 | 0.695 | 0.620 | 0.329 | 0.277 | 0.940 | 0.943 |  | 0.866 | 0.777 | 0.478 | 0.427 | 0.993 | 0.986 |  |
| 0.04 | 0.685 | 0.418 | 0.287 | 0.200 | 0.866 | 0.826 |  | 0.762 | 0.670 | 0.436 | 0.348 | 0.979 | 0.979 |  |
| 0.06 | 0.415 | 0.311 | 0.190 | 0.144 | 0.724 | 0.718 |  | 0.709 | 0.584 | 0.443 | 0.315 | 0.990 | 0.962 |  |
| 0.08 | 0.282 | 0.176 | 0.124 | 0.078 | 0.557 | 0.528 |  | 0.692 | 0.475 | 0.426 | 0.285 | 0.978 | 0.957 |  |
| 0.10 | 0.117 | 0.058 | 0.067 | 0.031 | 0.378 | 0.340 |  | 0.630 | 0.434 | 0.408 | 0.276 | 0.970 | 0.948 |  |
| 0.12 | 0.046 | 0.010 | 0.035 | 0.000 | 0.240 | 0.202 |  | 0.583 | 0.294 | 0.369 | 0.214 | 0.934 | 0.918 |  |
| 0.14 | 0.001 | 0.004 | 0.013 | 0.000 | 0.121 | 0.069 |  | 0.536 | 0.237 | 0.351 | 0.162 | 0.895 | 0.876 |  |
| 0.16 | 0.000 | 0.000 | 0.000 | 0.000 | 0.035 | 0.000 |  | 0.438 | 0.199 | 0.299 | 0.121 | 0.886 | 0.831 |  |
| 0.18 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.387 | 0.161 | 0.248 | 0.096 | 0.902 | 0.805 |  |
|  | 0.20 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |  | 0.311 | 0.136 | 0.218 | 0.081 | 0.866 | 0.854 |

**Table 19: LLM unlearning with PO coarse-grained controlled by model mixing. We evaluated on TOFU fictitious unlearning, with different forget rates and different trained LLMs. indicates the result is a boarder case that satisfies our criterion in assessing excessive unlearning in Appendix C.**
| PO, MM | Phi-1.5 |  | Llama-2-7B |  |  |  |  |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| setup | $\alpha$ | PS-exact | PS-perturb | PS-similar |  | PS-exact | PS-perturb | PS-similar |  |  |  |  |  |  |
| retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $-$ |  | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $-$ |  |  |
| 1% | 0.0 | 0.668 | 0.673 | 0.325 | 0.234 | 0.918 | 0.980 |  | 0.914 | 0.874 | 0.505 | 0.497 | 0.983 | 0.994 |
| 0.1 | 0.665 | 0.692 | 0.330 | 0.241 | 0.930 | 0.968 |  | 0.906 | 0.861 | 0.509 | 0.488 | 0.993 | 0.995 |  |
| 0.2 | 0.629 | 0.663 | 0.329 | 0.237 | 0.927 | 0.954 |  | 0.903 | 0.837 | 0.495 | 0.475 | 0.996 | 0.987 |  |
| 0.3 | 0.620 | 0.627 | 0.316 | 0.239 | 0.913 | 0.936 |  | 0.899 | 0.805 | 0.472 | 0.441 | 0.996 | 0.951 |  |
| 0.4 | 0.617 | 0.563 | 0.307 | 0.212 | 0.898 | 0.907 |  | 0.870 | 0.715 | 0.476 | 0.384 | 0.988 | 0.932 |  |
| 0.5 | 0.632 | 0.452 | 0.305 | 0.203 | 0.891 | 0.868 |  | 0.871 | 0.619 | 0.474 | 0.378 | 0.988 | 0.893 |  |
| 0.6 | 0.564 | 0.373 | 0.297 | 0.172 | 0.880 | 0.850 |  | 0.867 | 0.531 | 0.455 | 0.344 | 0.985 | 0.864 |  |
| 0.7 | 0.526 | 0.339 | 0.279 | 0.162 | 0.868 | 0.839 |  | 0.862 | 0.483 | 0.443 | 0.327 | 0.985 | 0.853 |  |
| 0.8 | 0.521 | 0.289 | 0.284 | 0.150 | 0.867 | 0.791 |  | 0.845 | 0.386 | 0.434 | 0.285 | 0.978 | 0.802 |  |
| 0.9 | 0.478 | 0.253 | 0.272 | 0.152 | 0.832 | 0.794 |  | 0.830 | 0.337 | 0.420 | 0.267 | 0.962 | 0.796 |  |
|  | 1.0 | 0.476 | 0.247 | 0.240 | 0.151 | 0.809 | 0.780 |  | 0.817 | 0.325 | 0.420 | 0.253 | 0.955 | 0.764 |
| 5% | 0.0 | 0.668 | 0.788 | 0.325 | 0.288 | 0.918 | 0.976 |  | 0.914 | 0.853 | 0.505 | 0.428 | 0.983 | 0.986 |
| 0.1 | 0.670 | 0.792 | 0.326 | 0.275 | 0.928 | 0.981 |  | 0.906 | 0.854 | 0.493 | 0.442 | 0.995 | 0.983 |  |
| 0.2 | 0.668 | 0.790 | 0.330 | 0.265 | 0.944 | 0.979 |  | 0.907 | 0.835 | 0.493 | 0.440 | 0.997 | 0.987 |  |
| 0.3 | 0.666 | 0.747 | 0.320 | 0.253 | 0.923 | 0.969 |  | 0.877 | 0.828 | 0.493 | 0.451 | 0.998 | 0.984 |  |
| 0.4 | 0.643 | 0.738 | 0.281 | 0.254 | 0.897 | 0.971 |  | 0.835 | 0.792 | 0.465 | 0.406 | 0.986 | 0.982 |  |
| 0.5 | 0.634 | 0.689 | 0.271 | 0.244 | 0.893 | 0.938 |  | 0.790 | 0.737 | 0.475 | 0.404 | 0.984 | 0.966 |  |
| 0.6 | 0.616 | 0.663 | 0.265 | 0.225 | 0.876 | 0.918 |  | 0.797 | 0.707 | 0.441 | 0.397 | 0.984 | 0.965 |  |
| 0.7 | 0.597 | 0.664 | 0.247 | 0.235 | 0.879 | 0.905 |  | 0.781 | 0.682 | 0.440 | 0.389 | 0.962 | 0.958 |  |
| 0.8 | 0.575 | 0.579 | 0.247 | 0.232 | 0.867 | 0.867 |  | 0.730 | 0.627 | 0.420 | 0.364 | 0.971 | 0.936 |  |
| 0.9 | 0.549 | 0.511 | 0.247 | 0.202 | 0.855 | 0.843 |  | 0.690 | 0.588 | 0.392 | 0.348 | 0.957 | 0.924 |  |
|  | 1.0 | 0.517 | 0.474 | 0.246 | 0.198 | 0.844 | 0.827 |  | 0.624 | 0.548 | 0.394 | 0.331 | 0.956 | 0.918 |
| 10% | 0.0 | 0.668 | 0.649 | 0.325 | 0.298 | 0.918 | 0.949 |  | 0.914 | 0.779 | 0.505 | 0.429 | 0.983 | 0.982 |
| 0.1 | 0.671 | 0.642 | 0.322 | 0.285 | 0.924 | 0.966 |  | 0.904 | 0.787 | 0.504 | 0.425 | 0.983 | 0.985 |  |
| 0.2 | 0.661 | 0.655 | 0.326 | 0.290 | 0.922 | 0.957 |  | 0.894 | 0.787 | 0.496 | 0.435 | 0.980 | 0.984 |  |
| 0.3 | 0.649 | 0.620 | 0.307 | 0.274 | 0.910 | 0.931 |  | 0.867 | 0.781 | 0.483 | 0.430 | 0.981 | 0.980 |  |
| 0.4 | 0.607 | 0.610 | 0.278 | 0.290 | 0.914 | 0.917 |  | 0.849 | 0.780 | 0.468 | 0.405 | 0.981 | 0.980 |  |
| 0.5 | 0.575 | 0.598 | 0.271 | 0.258 | 0.889 | 0.915 |  | 0.761 | 0.768 | 0.448 | 0.383 | 0.979 | 0.976 |  |
| 0.6 | 0.586 | 0.547 | 0.274 | 0.216 | 0.890 | 0.881 |  | 0.749 | 0.729 | 0.430 | 0.372 | 0.973 | 0.965 |  |
| 0.7 | 0.562 | 0.497 | 0.255 | 0.213 | 0.907 | 0.873 |  | 0.697 | 0.672 | 0.417 | 0.349 | 0.958 | 0.943 |  |
| 0.8 | 0.549 | 0.468 | 0.226 | 0.198 | 0.879 | 0.864 |  | 0.678 | 0.605 | 0.405 | 0.312 | 0.967 | 0.922 |  |
| 0.9 | 0.519 | 0.425 | 0.194 | 0.177 | 0.858 | 0.827 |  | 0.640 | 0.508 | 0.395 | 0.284 | 0.956 | 0.917 |  |
|  | 1.0 | 0.510 | 0.422 | 0.193 | 0.164 | 0.865 | 0.832 |  | 0.633 | 0.452 | 0.382 | 0.284 | 0.949 | 0.890 |

**Table 20: LLM unlearning with PO fine-grained controlled by model mixing. We evaluated on TOFU fictitious unlearning, with different forget rates and different trained LLMs. indicates the result is a boarder case that satisfies our criterion in assessing excessive unlearning in Appendix C.**
| PO, MM | Phi-1.5 |  | Llama-2-7B |  |  |  |  |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| setup | $\alpha$ | PS-exact | PS-perturb | PS-similar |  | PS-exact | PS-perturb | PS-similar |  |  |  |  |  |  |
| retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $-$ |  | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $\downarrow$ | retain $-$ | unlearn $-$ |  |  |
| 1% | 0.40 | 0.617 | 0.563 | 0.307 | 0.212 | 0.898 | 0.907 | 0.50 | 0.871 | 0.619 | 0.474 | 0.378 | 0.988 | 0.893 |
| 0.42 | 0.621 | 0.521 | 0.305 | 0.203 | 0.893 | 0.906 | 0.52 | 0.870 | 0.604 | 0.473 | 0.360 | 0.988 | 0.897 |  |
| 0.44 | 0.628 | 0.501 | 0.305 | 0.203 | 0.891 | 0.895 | 0.54 | 0.871 | 0.597 | 0.472 | 0.359 | 0.988 | 0.889 |  |
| 0.46 | 0.632 | 0.485 | 0.303 | 0.202 | 0.893 | 0.895 | 0.56 | 0.871 | 0.606 | 0.464 | 0.349 | 0.988 | 0.861 |  |
| 0.48 | 0.635 | 0.476 | 0.305 | 0.204 | 0.891 | 0.893 | 0.58 | 0.870 | 0.554 | 0.462 | 0.344 | 0.987 | 0.879 |  |
| 0.50 | 0.632 | 0.452 | 0.305 | 0.203 | 0.891 | 0.868 | 0.60 | 0.867 | 0.531 | 0.455 | 0.344 | 0.985 | 0.864 |  |
| 0.52 | 0.627 | 0.427 | 0.301 | 0.183 | 0.893 | 0.857 | 0.62 | 0.865 | 0.523 | 0.454 | 0.341 | 0.985 | 0.859 |  |
| 0.54 | 0.624 | 0.407 | 0.299 | 0.183 | 0.887 | 0.850 | 0.64 | 0.864 | 0.516 | 0.451 | 0.335 | 0.985 | 0.849 |  |
| 0.56 | 0.584 | 0.396 | 0.296 | 0.184 | 0.868 | 0.861 | 0.66 | 0.862 | 0.516 | 0.454 | 0.327 | 0.984 | 0.874 |  |
| 0.58 | 0.579 | 0.374 | 0.296 | 0.172 | 0.877 | 0.855 | 0.68 | 0.861 | 0.511 | 0.447 | 0.327 | 0.984 | 0.857 |  |
|  | 0.60 | 0.564 | 0.373 | 0.297 | 0.172 | 0.880 | 0.850 | 0.70 | 0.862 | 0.483 | 0.443 | 0.327 | 0.985 | 0.853 |
| 5% | 0.20 | 0.668 | 0.790 | 0.330 | 0.265 | 0.944 | 0.979 | 0.30 | 0.877 | 0.828 | 0.493 | 0.451 | 0.998 | 0.984 |
| 0.22 | 0.655 | 0.784 | 0.329 | 0.259 | 0.938 | 0.966 | 0.32 | 0.873 | 0.825 | 0.494 | 0.442 | 0.995 | 0.984 |  |
| 0.24 | 0.658 | 0.789 | 0.330 | 0.265 | 0.941 | 0.978 | 0.34 | 0.852 | 0.833 | 0.484 | 0.444 | 0.980 | 0.983 |  |
| 0.26 | 0.671 | 0.774 | 0.327 | 0.255 | 0.937 | 0.967 | 0.36 | 0.850 | 0.803 | 0.479 | 0.432 | 0.982 | 0.982 |  |
| 0.28 | 0.652 | 0.749 | 0.323 | 0.263 | 0.938 | 0.965 | 0.38 | 0.849 | 0.803 | 0.478 | 0.429 | 0.970 | 0.982 |  |
| 0.30 | 0.666 | 0.747 | 0.320 | 0.253 | 0.923 | 0.969 | 0.40 | 0.835 | 0.792 | 0.465 | 0.406 | 0.986 | 0.982 |  |
| 0.32 | 0.640 | 0.765 | 0.300 | 0.251 | 0.942 | 0.967 | 0.42 | 0.813 | 0.781 | 0.462 | 0.406 | 0.986 | 0.982 |  |
| 0.34 | 0.648 | 0.747 | 0.293 | 0.252 | 0.922 | 0.957 | 0.44 | 0.813 | 0.760 | 0.465 | 0.406 | 0.986 | 0.979 |  |
| 0.36 | 0.632 | 0.746 | 0.289 | 0.252 | 0.919 | 0.967 | 0.46 | 0.813 | 0.744 | 0.463 | 0.406 | 0.984 | 0.977 |  |
| 0.38 | 0.633 | 0.735 | 0.290 | 0.254 | 0.908 | 0.956 | 0.48 | 0.805 | 0.744 | 0.465 | 0.406 | 0.984 | 0.977 |  |
|  | 0.40 | 0.643 | 0.738 | 0.281 | 0.254 | 0.897 | 0.971 | 0.50 | 0.790 | 0.737 | 0.475 | 0.404 | 0.984 | 0.966 |
| 10% | 0.20 | 0.661 | 0.655 | 0.326 | 0.290 | 0.922 | 0.957 | 0.30 | 0.867 | 0.781 | 0.483 | 0.430 | 0.981 | 0.980 |
| 0.22 | 0.654 | 0.644 | 0.323 | 0.290 | 0.915 | 0.949 | 0.32 | 0.871 | 0.782 | 0.485 | 0.423 | 0.981 | 0.981 |  |
| 0.24 | 0.650 | 0.639 | 0.325 | 0.280 | 0.920 | 0.939 | 0.34 | 0.856 | 0.782 | 0.483 | 0.415 | 0.981 | 0.981 |  |
| 0.26 | 0.651 | 0.641 | 0.312 | 0.286 | 0.916 | 0.940 | 0.36 | 0.849 | 0.781 | 0.477 | 0.403 | 0.984 | 0.981 |  |
| 0.28 | 0.649 | 0.637 | 0.311 | 0.285 | 0.921 | 0.939 | 0.38 | 0.847 | 0.781 | 0.469 | 0.407 | 0.981 | 0.978 |  |
| 0.30 | 0.649 | 0.620 | 0.307 | 0.274 | 0.910 | 0.931 | 0.40 | 0.849 | 0.780 | 0.468 | 0.405 | 0.981 | 0.980 |  |
| 0.32 | 0.648 | 0.630 | 0.305 | 0.282 | 0.916 | 0.929 | 0.42 | 0.809 | 0.781 | 0.468 | 0.398 | 0.981 | 0.980 |  |
| 0.34 | 0.648 | 0.637 | 0.295 | 0.286 | 0.909 | 0.928 | 0.44 | 0.792 | 0.752 | 0.460 | 0.390 | 0.981 | 0.967 |  |
| 0.36 | 0.634 | 0.621 | 0.283 | 0.281 | 0.909 | 0.922 | 0.46 | 0.785 | 0.773 | 0.459 | 0.384 | 0.981 | 0.966 |  |
| 0.38 | 0.633 | 0.633 | 0.280 | 0.286 | 0.910 | 0.923 | 0.48 | 0.768 | 0.749 | 0.459 | 0.382 | 0.979 | 0.975 |  |
|  | 0.40 | 0.607 | 0.610 | 0.278 | 0.290 | 0.914 | 0.917 | 0.50 | 0.761 | 0.768 | 0.448 | 0.383 | 0.979 | 0.976 |

## Appendix G A Final Guideline to Evaluate LLM Unlearning

Our proposed LLM evaluation framework considers the practical effectiveness of the resulting LLMs, with a series of PS-based scores that are general when facing different unlearning tasks. However, a limitation of our framework is the high computational cost associated with calculating these PS scores.
Although some efficient realizations, such as the Bisection method, can accelerate this process, the costs remain substantial, especially for cases involving long token outputs. Therefore, to save computational costs, we recommend concentrating primarily on the PS-exact scores for non-targeted data when selecting appropriate controlling parameters.
The general validity of this simplified strategy is justified by the linear correlations observed between PS-exact and PS-perturb on non-targeted data (cf. Figures 8-9), coupled with the relatively loose constraints for PS-similar on targeted data.
Then, after determining proper controlling parameters, other PS scores can be computed (when feasible) to further reflect the effectiveness of the unlearning methods. Note that it is crucial, especially when involving the retaining or maintaining risks, to ensure that non-targeted data used for unlearning are disjoint with those data involved in evaluations. This separation can avoid the unintentionally sampling bias during unlearning to the evaluations of the resulting LLMs. Moreover, we recommend setting MM as the default method for controlling the extent of unlearning, using relatively small candidate values of $\alpha$, e.g., smaller than 0.5, during calibration.

Figure: Figure 8: The correlations between PS-exact on non-targeted data, and both PS-perturb on non-targeted data and PS-similar on targeted data for Phi-1.5. We reported PS-based scores with different choices of controlling parameters.
Refer to caption: x13.png

Figure: Figure 9: The correlations between PS-exact on non-targeted data, and both PS-perturb on non-targeted data and PS-similar on targeted data for Llamma-2-7B. We reported PS-based scores with different choices of controlling parameters.
Refer to caption: x14.png

## Peer Reviews

confidence: 4
contribution: 2
initial_rating: 3
presentation: 2
questions: See W2.
soundness: 2
strengths: S1: LLM unlearning and evaluation are important problems
summary: The paper tested 4 popular LLM unlearning methods on the TOFU benchmark dataset and observed that there are various tradeoffs (e.g. GA unlearns better while NPO retains better). Then it motivates the authors to propose a new metric which is based on the mixing the model weights between the unlearned and original model. The reason, as far as I understand, is to achieve smooth control on the extent of unlearning. The evaluation first finds the model mixing ratio that would achieve the evaluation score (e.g. ES) on the retain set, and then uses it to calibrate unlearning metric.
weaknesses: W1: Lack of technical contribution: I think most people working in this area would agree we need more metrics and benchmark datasets. However, this paper though goes into that direction, does not really provide enough meaningful and technical contribution in my view. The paper basically tried 4 popular unlearning methods on the TOFU datasets while proposing a calibration framework (See W2). This can mostly be done in leaderboard or in a measurement paper rather than a technical paper. And findings on metric tradeoffs are mostly not surprising.

W2: Lack of justification of the calibration framework: The calibration metric lacks justification. Figure 3 seems to only tell us ES is monotonically increasing with mixing factor $\alpha$. However, the key question in proposing a metric is to ask: What does this metric measure? Does it measure the right thing? In this case, I cannot see clearly the impact of mixing model weights on the overall unlearning effectiveness. The only justification I can find is (1) being inspired by the literature on parameter disentanglement, but why is it related to unlearning? (2) The vague observation in Figure 3. Can authors explain why mixing model weights can help calibrate the unlearning metric other than just the empirical observation between ES and $\alpha$ in Figure 3? After all, this can well be a spurious correlation. In other words, why would the community trust this calibration in evaluation? 

W3: Lack of organizing clarify: The paper spends the first 6 pages motivating the calibration framework, and only 1 page introducing it and 1 page for experiments. I think people who in this area already know most of the points in the first 6 pages, it'd better to shorten it and get to the point more directly and spent more content on introducing the key idea of calibration and include more justification,

---

confidence: 5
contribution: 3
initial_rating: 8
presentation: 3
questions: I look forward to discussing the below with the authors, and am willing to increase my score given clarification of the questions below.

1) In the paragraph “Is MM Proper for Calibration” what seems missing is discussion comparing this to a simpler/baseline approach, such as just tuning the original hyperparameters of the unlearning method to calibrate. From the Appendix I got the impression that the hyperparameters of many of the unlearning methods do not give enough control to calibrate, is this correct? If so, discussion (and/or a figure illustrating this) would help the argument that MM is a better way to calibrate/boost the performance of unlearning methods.

2) Related to the above, in the “Hyper-parameter configurations” paragraph in the experiments, am I correct in understanding you do the hyperparameter sweep by evaluating the performance of the hyperparameters after also applying model mixing to calibrate the performance (this seems consistent with the appendix tables)? If so, you might consider adding somewhere in the paper that this hyperparameter sweep necessarily improves over the calibrated performance of not doing model mixing; this is as not doing model mixing is captured by just picking the best hyperparameters amongst those with $\alpha = 1$. I believe this adds conceptual understanding to why model mixing is necessarily better.

3) On the discussion of why NPO and other methods do no work in the experiments section, do you have results for what $\tau$ values (if at all) other methods start performing well? I’m imagining a figure where the x-axis is calibrated $\tau$ level, and the y-axis is forget performance, and a line for each method such that when the line is the lowest explains for what $\tau$ each method is best. Alternatively, some more detailed/explicit discussion for what $\tau$ levels other methods might perform better could help give a more complete picture for when other methods work well. I agree the high $\tau$ range seems most practical, but I think the above can be done easily given results in the appendix and can add to the empirical study.

4) (minor) model mixing seems very related to the literature on model merging; you might consider surveying the literature more broadly as a reference for the method, and when/why it works.

5) (minor) If computationally feasible, could error bars/standard deviation be reported for some of the main tables; I am less concerned given the many settings tested, but this could add to the rigor of the empirical findings.
soundness: 4
strengths: 1) Extensive empirical study
2) Proposed method for improving calibration via a general hypermater boosts performance of baseline methods to seemingly SOTA
3) Mostly well-written
summary: This paper studies how best to evaluate LLM unlearning methods that aim to not leak the correct answers on a forget set while maintaining good performance on the rest of the training data. The literature has proposed a variety of evaluation metrics, and this paper first tackles which metric is most robust to information leaking attacks; they conclude ES, which was proposed with privacy attacks in mind, performs best in keeping the ranking before and after various attacks consistent. With ES, they then evaluated a generalized hyperparameter sweep for popular methods proposed in the literature, and conclude that methods have not significantly improved over the baseline of gradient ascent approaches. Narrowing why this is the case, they observe alternative methods either unlearn too strongly or not strongly enough to calibrate the performance on the retain set.
weaknesses: 1) I found that certain parts of the draft could have been clearer about the benefits of model mixing. The draft does not discuss alternative calibration of retain performance, which naively could have also been done with just a sweep of the unlearning method hyperparameters. So at first I thought this was an empirical limitation. But after thinking about it I realized this is actually okay as the performance of calibration with just a hyperparameter sweep of the unlearning method is subsumed by the hyperparameter sweep including model mixing to calibrate (the former is just taking the hyperparameter in the latter where $\alpha  = 1$). Results in the appendix also suggest the hyperparameters for current unlearning methods are not sensitive enough to calibrate retain performance. In the questions section I ask clarifying questions about this and suggest edits to the text that could make this contribution clearer. 

2) The empirical results are also focused on specific values of $\tau$, i.e., retain performance should be $95-90\%$ of the performance before unlearning. While I agree “high performance” seems to be the reasonable use-case, a more complete comparison without assuming specific $\tau$ values would also identify what $\tau$ range (if ever) NPO and other methods start performing well again. I believe it is implicit from the further study in the appendix that a “low” $\tau$ range might make other methods perform better, but I believe a more quantitative statement could make the empirical study more complete. I ask about this in the questions section.

3) (minor) A more general weakness, not specific to just this paper, is whether these performative unlearning goals for LLMs should also be generalization questions; if the goal is to not predict accurately for a set of samples, and those samples come from larger distribution, should we not be evaluating a “test” performance on the larger distribution? This is generally called concept unlearning in the literature. The field may still be far away from evaluating/studying such questions, but I raise it to clarify the setup studied in this paper is not the only setting for unlearning in LLMs. The authors might consider having more discussion on different formulations of unlearning before picking the setting they study and survey.

---

confidence: 3
contribution: 2
initial_rating: 5
presentation: 1
questions: The statistic in figure 2 is confusing. How does model have lower score (which means better unlearning from the paper) after attacking than before?
soundness: 2
strengths: The paper have a comprehensive view of different unlearning evaluation methods and approaches them in a systematic manner from robustness and utility trade-offs.

The paper proposes a novel approach unlearning with control to better calibrate the trade-off between unlearning effectiveness and retain performance with model-mixing, which is a simple but effective mechanism.
summary: The paper surveys the current popular evaluation methods towards LLM unlearning. It discuss the need to cover before retain and forget performances and its trade-offs, as well as its robustness against different attacks.

The paper concludes that Extraction Strength (ES) is the recommended method for evaluation. In addition, the paper also suggest Unlearning with Control (UWC) framework to reach the best trade-off between unlearning strength and retain performance.
weaknesses: There is a lack of justification for selecting the metric: Why does the PCC measure the metrics' robustness again attacks? In Figure 2, the plot is characterized by the test static before and after the attack for different methods, models, and forget set ratio. Why should we assume there is a linear correlation among them? In addition, the paper uses TOFU as unlearning dataset/task, but does not survey the metric used in the TOFU paper (truth ratio).

Weak/unclear attack methods: it is unclear the what dataset the relearn attack in figure 2 is based on (from other section I would think it is TOFU, but it is not presented until late in the paper). The setup for relearning it not clear.

Although UWC seems like a method to manage the trade-off between unlearn and retain performance, it is not clear how it fits into unlearning evaluation pipeline.

---

confidence: 3
contribution: 2
initial_rating: 6
presentation: 2
questions: Please provide response to the weaknesses.
soundness: 3
strengths: (1) The problem is well-motivated.
summary: The paper aims to answer the following research questions in machine unlearning: (1) What metric should be used in machine unlearning (2) what method is better in trading off unlearning and retention. The paper first presents a comparative study to understand what metric is robust (i.e., present a linear relationship before and after jailbreaking attacks), then proposes to use model mixing to for better calibration between retention and unlearning.
weaknesses: (1) For the metrics used for machine unlearning, The author suggests using Extraction Strength as the metrics since it exhibits linear relationship before and after different attacks. However, the evaluation is still weak to me. First of all, the attacks used in the paper are not the strongest jailbreaking attacks (like GCG attacks) and the authors also do not consider using an ensemble of strong attacks to elicit model’s knowledge, making the evaluation of the paper weak. Also, showing linear relationship before and after attack might not be a good way to measure machine unlearning before and after attack, especially if the model is backdoored or poisoned (e.g., a poisoned and backdoor model can hide their knowledge in their model parameters except when a trigger is presented or obfuscate the knowledge so that the metrics cannot used to detect unlearning). In short, there are no rigorous guarantees that using extraction strength is a valid metric under an adversarial scenario.

(2) The contribution is incremental. To me, the most novel part of the paper is that the authors use model mixing (aka model merging/souping) to control the trade-offs between retention and unlearning. All the other parts seem incremental and do not convey interesting empirical findings.

(3) The writing of the paper needs to be improved. A lot of useful details help to digest the results are shown in the appendix instead of the main text (e.g., attack methods) and the main text does not give enough concise summary to understand them. For example, I still cannot understand how we use Token Noising as an attack method (even the appendix does not give a good description of it). Also, the organization of the paper could be improved (e.g., lines 264-265 ask the reader to first read Section 6 for the experiment).

Meta-review: This work provides an evaluation framework for assessing LLM unlearning. The reviewers agree that the paper has made interesting conclusions and contributions, although the technical novelties and organizations are limited. It would be important for the authors to improve the paper following the reviews in the final version.

Decision: Accept (Poster)