Simplicity Prevails: Rethinking Negative Preference Optimization for LLM Unlearning

## Abstract

Abstract In this work, we address the problem of large language model (LLM) unlearning, aiming to remove unwanted data influences and associated model capabilities ( e.g. , copyrighted data or harmful content generation) while preserving essential model utilities, without the need for retraining from scratch. Despite the growing need for LLM unlearning, a principled optimization framework remains lacking. To this end, we revisit the state-of-the-art approach, negative preference optimization (NPO), and identify the issue of reference model bias, which could undermine NPO’s effectiveness, particularly when unlearning forget data of varying difficulty. Given that, we propose a simple yet effective unlearning optimization framework, called SimNPO, showing that ‘simplicity’ in removing the reliance on a reference model (through the lens of simple preference optimization) benefits unlearning.
We also provide deeper insights into SimNPO’s advantages, supported by analysis using mixtures of Markov chains. Furthermore, we present extensive experiments validating SimNPO’s superiority over existing unlearning baselines in benchmarks like TOFU and MUSE, and robustness against relearning attacks. Codes are available at https://github.com/OPTML-Group/Unlearn-Simple .

## 1 Introduction

Figure: Figure 1: (a) Systematic overview of an LLM (${\bm{\theta}}$) post-unlearning using the proposed SimNPO optimization principle, compared to the popular NPO (negative preference optimization) framework (Zhang et al., ) and the reference model (i.e., model prior to unlearning). (b) & (c) Experiment highlights on the TOFU dataset with a 5% forget size (Maini et al., ) and on the MUSE News dataset (Shi et al., ). Unlearning effectiveness is measured by forget quality for TOFU and PrivLeak for MUSE, while utility preservation is evaluated using model utility for TOFU and KnowMem on $\mathcal{D_{\mathrm{r}}}$ for MUSE (see Table 1 for details on task-specific metrics). In both tasks, Retrain serves as the gold standard for unlearning by fully removing the influence of the forget data.
Refer to caption: x1.png

The rapid advancement of large language models (LLMs) has raised security and safety concerns, including issues related to copyright violations and sociotechnical harms (Huang et al., ; Wang et al., ; Li et al., ; Shi et al., ). However, retraining these models to remove undesirable data influences is often impractical due to the substantial costs and time required for such processes. This gives rise to the problem of LLM unlearning, which aims to effectively remove undesired data influences and/or model behaviors while preserving the utility for essential, unrelated knowledge generation, and maintaining efficiency without the need for retraining (Eldan & Russinovich, ; Yao et al., ; Liu et al., ; Blanco-Justicia et al., ).

To trace its origins,
the concept of machine unlearning was initially developed for data removal to comply with privacy regulations such as the “right to be forgotten” (Rosen, ; Hoofnagle et al., ), with early studies focusing on vision models (Cao & Yang, ; Warnecke et al., ; Bourtoule et al., ; Thudi et al., ; Kurmanji et al., ; Jia et al., ; Gandikota et al., ; Fan et al., ). However, it is soon adapted to LLMs to remove unwanted data, knowledge, or specific model capabilities (Eldan & Russinovich, ; Yao et al., ; Liu et al., ; Ji et al., ; Li et al., ; Shi et al., ; Maini et al., ; Zhang et al., ; Jia et al., ).
Compared to vision model unlearning, designing effective and efficient unlearning methods for LLMs presents its own unique challenges (Liu et al., ). In particular, the current optimization foundation
for LLM unlearning often relies on driving divergence to achieve the unlearning objective, making model parameter adjustments for unlearning difficult to control (Zhang et al., ; Liu et al., ; Maini et al., ; Yao et al., ; Jia et al., ). For example, divergence-driven optimization methods, such as gradient ascent and its variants (Yao et al., ; Maini et al., ; Zhang et al., ),
can lead to either under-forgetting, where little unwanted data-model influence is removed, or over-forgetting, resulting in a significant loss of model utility in LLMs.
Therefore, optimization for LLM unlearning is a highly non-trivial challenge.

Negative preference optimization (NPO) (Zhang et al., ) emerges as an effective approach for LLM unlearning, as demonstrated by its strong performance in current benchmarks such as TOFU (Maini et al., ) and MUSE (Shi et al., ).
Inspired by direct preference optimization (DPO) (Rafailov et al., ), it treats the forget data points as negative responses, providing a lower-bounded unlearning objective. This naturally induces a gradient weight smoothing scheme to regulate the speed of divergence, improving the utility-unlearning tradeoff.
We refer readers to Sec. 3 for details.

Despite the advancements NPO has introduced to the optimization foundation
for LLM unlearning, this work will identify its potential limitations for the first time, arising from overreliance on a reference model (i.e., the model prior to unlearning). We refer to this issue as reference model bias.
Throughout this work, the key research question we aim to answer is:

Towards addressing (Q), the contributions of our work are summarized below:

$\bullet$ We revisit the NPO framework and identify its potential weakness–overreliance on the reference model–in LLM unlearning
, as demonstrated in Fig. 1-(a). This reference bias could lead to issues such as sensitivity to the reference model’s response quality and ineffective gradient weight smoothing.

$\bullet$ Building on insights into NPO’s limitations, we propose an improved LLM unlearning approach, SimNPO, which extends NPO using a reference-free optimization framework, simple preference optimization (Meng et al., ). We also delve into the technical rationale behind how SimNPO alleviates the limitations of NPO (Fig. 1-(a)), validated through the lens of mixtures of Markov chains.

$\bullet$ We conduct extensive experiments to showcase the improvements of SimNPO over NPO across various unlearning benchmarks, including TOFU (Maini et al., ), MUSE (Shi et al., ), and WMDP (Li et al., ), as well as in diverse scenarios such as forgetting data with different response lengths and defending against relearning-based attacks (Lynch et al., ; Hu et al., ). See some experiment highlights in
Fig. 1-(b,c).

## 2 Related work

Machine unlearning.
The commonly accepted gold standard for machine unlearning is retraining the model from scratch, excluding the data points to be forgotten from the training set. Such a method (referred to as ‘Retrain’ in our work) is also known as exact unlearning (Cao & Yang, ; Thudi et al., ; Fan et al., ). However, exact unlearning is challenging in practice due to the need for access to the full training set, accurately attributing and identifying the forget data, and the high computational cost of retraining. To address these challenges, various approximate unlearning methods have been developed (Nguyen et al., ; Bourtoule et al., ; Triantafillou et al., ). These approaches typically involve model fine-tuning or editing, applied to the pre-trained model, based on the unlearning request. Their effectiveness has been shown in different application domains, including image classification (Liu et al., ; Jia et al., ; Kurmanji et al., ; Fan et al., ), image generation (Gandikota et al., ; Fan et al., ; Zhang et al., ), federated learning (Liu et al., ; Halimi et al., ; Jin et al., ), and graph neural networks (Chen et al., ; Chien et al., ; Wu et al., ).

LLM unlearning.
There has also been a growing body of research focusing on machine unlearning for LLMs (Lu et al., ; Jang et al., ; Kumar et al., ; Zhang et al., ; Pawelczyk et al., ; Eldan & Russinovich, ; Ishibashi & Shimodaira, ; Yao et al., ; Maini et al., ; Zhang et al., ; Li et al., ; Wang et al., ; Jia et al., ; Liu et al., ; ; Thaker et al., ; Kadhe et al., ). Applications of unlearning in LLMs are diverse, from safeguarding copyrighted and personally identifiable information (Jang et al., ; Eldan & Russinovich, ; Wu et al., ), to preventing LLMs from creating cyberattacks or bioweapons (Barrett et al., ; Li et al., ), and reducing the production of offensive, biased, or misleading content (Lu et al., ; Yu et al., ; Yao et al., ). Given the difficulty of exact unlearning for LLMs, existing studies have focused on approximate unlearning. Current approaches include model optimization-based methods (Ilharco et al., ; Liu et al., ; Yao et al., ; Eldan & Russinovich, ; Jia et al., ; Zhang et al., ; Li et al., ) and input prompt or in-context learning-based techniques (Thaker et al., ; Pawelczyk et al., ; Liu et al., ).
Despite the rise of LLM unlearning approaches, many lack effectiveness, leading to either under-forgetting or over-forgetting, as shown by recent LLM unlearning benchmarks such as TOFU for fictitious unlearning (Maini et al., ) and MUSE for private or copyrighted information removal (Shi et al., ).
Recent studies also show that even after unlearning, models can remain vulnerable to jailbreaking or extraction attacks (Schwarzschild et al., ; Patil et al., ; Lynch et al., ) and relearning from a small subset of the forget set (Hu et al., ; Lynch et al., ).
This evidence suggests that effective unlearning for LLMs is far from trivial, and a principled optimization framework to achieve this remains lacking. Among current efforts, NPO (negative preference optimization) (Zhang et al., ) stands out as a promising approach by framing the unlearning problem as a variant of direct preference optimization (Rafailov et al., ). It has demonstrated competitive performance in benchmarks like TOFU and MUSE.
Thus, our work aims to conduct an in-depth exploration of NPO, identifying its current limitations, and proposing potential improvements.

Preference optimization.
In this work, we advance LLM unlearning through the lens of preference optimization. This is motivated by aligning LLMs with human values, known as reinforcement learning from human feedback (RLHF) (Christiano et al., ; Ziegler et al., ; Ouyang et al., ). However, online preference optimization algorithms are often complex and challenging to optimize (Santacroce et al., ; Zheng et al., ), driving interest in more efficient offline alternatives. Direct preference optimization (DPO) (Rafailov et al., ) introduced an offline approach that eliminates the need for a reward model, sparking the development of several reward-free offline preference objectives (Zhao et al., ; Azar et al., ; Hong et al., ; Ethayarajh et al., ; Meng et al., ; Yuan et al., ). Notable methods include RRHF (Yuan et al., ), SLic-HF (Zhao et al., ), IPO (Azar et al., ), KTO (Ethayarajh et al., ), ORPO (Hong et al., ), and SimPO (Meng et al., ). Among these methods, SimPO is a reference-free, length-normalized variant of DPO, and we will demonstrate that it is well-suited
for integrating into LLM unlearning and improving NPO.

## 3 A Primer on LLM Unlearning

Problem formulation of LLM unlearning.
Unlearning tasks can take various forms and are typically associated with a specific set of data points to be removed, known as the forget set ($\mathcal{D_{\mathrm{f}}}$). In addition, these tasks often require a complementary set of non-forgotten data points, known as the retain set ($\mathcal{D_{\mathrm{r}}}$), to preserve model utility by penalizing the divergence caused by unlearning.
As a result, the problem of LLM unlearning can be cast as a regularized optimization problem that balances the forget and retain objectives (Liu et al., ; Yao et al., ; Zhang et al., ):

$$ $\displaystyle\begin{array}[]{l}\displaystyle\operatorname*{\text{minimize}}_{ \bm{\theta}}\,\,\underbrace{\mathbb{E}_{(x,y)\in\mathcal{D_{\mathrm{f}}}}[{ \ell_{\mathrm{f}}}(y|x;\bm{\theta})]}_{\text{Forget loss}}+\lambda\underbrace{ \mathbb{E}_{(x,y)\in\mathcal{D_{\mathrm{r}}}}[{\ell_{\mathrm{r}}}(y|x;\bm{ \theta})]}_{\text{Retain loss}},\end{array}$ (2) $$

where ${\bm{\theta}}$ represents the model parameters to be updated during unlearning, $\lambda\geq 0$ is a regularization parameter to penalize the ‘divergence’
of unlearning, and ${\ell_{\mathrm{f}}}$ and ${\ell_{\mathrm{r}}}$ represent forget and retain losses incurred when using model parameters $\bm{\theta}$ to generate the desired response ($y$) given the input $x$.

Substantial research has focused on designing and analyzing appropriate forget and retain loss functions to solve problem (2) (Liu et al., ; Yao et al., ; Zhang et al., ; Maini et al., ; Shi et al., ; Eldan & Russinovich, ; Jia et al., ).
For instance, let $\pi_{\mathrm{{\bm{\theta}}}}(y|x)$ represent the prediction probability of the model ${\bm{\theta}}$ given the input-response pair $(x,y)$.
The retain loss is typically chosen as the cross-entropy-based sequence prediction loss,
${\ell_{\mathrm{r}}}(y|x,{\bm{\theta}})=-\log\pi_{\mathrm{{\bm{\theta}}}}(y|x)$, whose minimization encourages the model
to perform well on the retain data $(x,y)\in\mathcal{D_{\mathrm{r}}}$. If we specify the forget loss as the negative token prediction loss ${\ell_{\mathrm{f}}}(y|x,{\bm{\theta}})=\log\pi_{\mathrm{{\bm{\theta}}}}(y|x)$, whose minimization then discourages the model from learning the forget data $(x,y)\in\mathcal{D_{\mathrm{f}}}$. Minimizing such a forget loss is known as the gradient ascent (GA) method (Maini et al., ; Thudi et al., ). Similarly, minimizing the regularized loss that integrates GA with the
retain loss is known as the gradient difference (GradDiff) method (Liu et al., ; Maini et al., ; Yao et al., ).

Negative preference optimization (NPO).
A popular
optimization framework for solving problem (2) is NPO (Zhang et al., ).
It treats the forget data as negative examples in DPO (Rafailov et al., ),
transforming the unbounded
GA-based forget loss into a ① bounded loss from below,
which helps prevent catastrophic collapse, and an ② adaptive weight smoothing applied to the forget loss gradients, allowing for more controlled and stable unlearning.
These benefits can be clearly seen from the NPO loss and its gradient as follows:

$$ $\displaystyle\ell_{\mathrm{NPO}}(\bm{\theta})=\mathbb{E}_{(x,y)\in\mathcal{D_{ \mathrm{f}}}}\underbrace{\left[-\frac{2}{\beta}\log\sigma\left(-\beta\log\left (\frac{\pi_{{\bm{\theta}}}(y|x)}{\pi_{\mathrm{ref}}(y|x)}\right)\right)\right] }_{\text{\char 172 $\mathrel{\mathop{:}}={\ell_{\mathrm{f}}}(y|x;{\bm{\theta}} )$, the specified forget loss in (\ref{eq: prob_LLM_MU}) }},$ (3) $\displaystyle\nabla_{{\bm{\theta}}}\ell_{\mathrm{NPO}}(\bm{\theta})=\mathbb{E} _{(x,y)\in\mathcal{D_{\mathrm{f}}}}\left[\underbrace{\left(\frac{2\pi_{{\bm{ \theta}}}(y|x)^{\beta}}{\pi_{{\bm{\theta}}}(y|x)^{\beta}+\pi_{\mathrm{ref}}(y| x)^{\beta}}\right)}_{\text{\char 173 $\mathrel{\mathop{:}}=w_{{\bm{\theta}}}(x ,y)$, adaptive weight}}\cdot\underbrace{\nabla_{\bm{\theta}}\log\pi_{{\bm{ \theta}}}(y|x)}_{\text{GA}}\right],$ (4) $$

where $\sigma(t)=1/(1+e^{-t})$ is the sigmoid function, $\beta>0$ is the temperature parameter, e.g., $\beta=0.1$ is used by Zhang et al. (), and $\pi_{\mathrm{ref}}$ is the reference model given by the initial model prior to unlearning. We can justify the insights (①-②) below.

① From (3), the NPO-type forget loss is bounded below by 0 0, i.e., ${\ell_{\mathrm{f}}}(y|x;{\bm{\theta}})\geq 0$, whereas the GA-type forget loss, ${\ell_{\mathrm{f}}}(y|x,{\bm{\theta}})=\log\pi_{\mathrm{{\bm{\theta}}}}(y|x)$, has no lower bound. As a result, NPO provides greater optimization stability compared to GA.

② As seen in (4), the adaptive weight $w_{{\bm{\theta}}}(x,y)$ is typically less than $1$ since $\pi_{{\bm{\theta}}}(y|x)<\pi_{\mathrm{ref}}(y|x)$ for forgetting. Consequently, NPO’s gradient yields more controlled and gradual divergence speed required for unlearning, compared to GA (with $w_{{\bm{\theta}}}(x,y)=1$).

Throughout this paper, NPO will serve as the primary baseline for LLM unlearning. Unless specified otherwise, its implementation follows the regularized optimization in (2) to balance the unlearning with model utility, where the forget loss ${\ell_{\mathrm{f}}}$ is defined as in (3) and the retain loss ${\ell_{\mathrm{r}}}$ is the token prediction loss ${\ell_{\mathrm{r}}}(y|x,{\bm{\theta}})=-\log\pi_{\mathrm{{\bm{\theta}}}}(y|x)$ applied to the retain set.

LLM unlearning tasks and evaluations.
Given that the assessment of LLM unlearning may rely on specific tasks, we next introduce the unlearning tasks and evaluation metrics that this work covers. We consider three key unlearning tasks: (1) TOFU (Maini et al., ), which evaluates fictitious unlearning on a synthetic Q&A dataset; (2) MUSE (Shi et al., ), designed to remove verbatim or knowledge memorization from News and Books datasets, including both verbatim texts and knowledge sets for unlearning evaluation; and (3) WMDP (Li et al., ), which aims to prevent LLMs from generating hazardous content in domains such as biology, cybersecurity, and chemistry. In Secs. 4 and 5, we will focus on the TOFU dataset, while experimental results on MUSE and WMDP will be provided in Sec. 6.
Despite the differences in evaluation metrics across the above tasks, the assessment broadly falls into two categories. (1) Unlearning effectiveness measures how faithfully undesired data influences or model capabilities are removed. For example, it is assessed by the forget quality metric in TOFU, which uses a $p$-value to test the indistinguishability between the post-unlearning model and a model retrained on the retain set only, and by privacy leakage in MUSE, which measures the likelihood of detecting that the model was ever
trained on the forget set. (2) Utility preservation evaluates the post-unlearning performance on standard utility tasks.
Table 1 summarizes the unlearning tasks and evaluation metrics covered by different unlearning benchmarks.

**Table 1: Summary of unlearning efficacy and utility metrics across different unlearning benchmarks. The arrows indicate the directions for better performance (↑ for higher values, ↓ for lower values, $\rightarrow 0$ for closer to 0).**
| Benchmark | LLM to be used | Task Description | Unlearning Effectiveness | Utility Preservation |  |  |
| --- | --- | --- | --- | --- | --- | --- |
| TOFU | LLaMA-2-chat 7B | Unlearning fictitious authors from a synthetic Q&A dataset | Forget quality (measured by<br>truth ratios of forget samples) | ↑ | Model utility<br>( harmonic mean of 9 utility metrics) | ↑ |
| Probability on $\mathcal{D}_{f}$ | ↓ | Probability on $\mathcal{D}_{r}$/$\mathcal{D}_{\text{real_author}}$/$\mathcal{D}_{\text{world_facts}}$ | ↑ |  |  |  |
| Rouge-L on $\mathcal{D}_{f}$ | ↓ | Rouge-L on $\mathcal{D}_{r}$/$\mathcal{D}_{\text{real_author}}$/$\mathcal{D}_{\text{world_facts}}$ | ↑ |  |  |  |
|  |  |  | Truth ratio on $\mathcal{D}_{f}$ | ↑ | Truth ratio on $\mathcal{D}_{r}$/$\mathcal{D}_{\text{real_author}}$/$\mathcal{D}_{\text{world_facts}}$ | ↑ |
| MUSE | LLaMA-2 7B<br>ICLM-7B | Unlearning real-world knowledge from texts about Harry Potter and BBC News | KnowMem on $\mathcal{D}_{f}$ | ↓ |  |  |
| VerbMem on $\mathcal{D}_{f}$ | ↓ | KnowMem on $\mathcal{D}_{r}$ | ↑ |  |  |  |
| PrivLeak | $\rightarrow$ 0 |  |  |  |  |  |
| WMDP | Zephyr-7B-beta | Unlearning hazardous knowledge from bio/cybersecurity texts | Accuracy on WMDP-Bio | ↓ | Accuracy on MMLU | ↑ |
| Accuracy on WMDP-Cyber | ↓ |  |  |  |  |  |

## 4 Uncovering Reference Model Bias: A Limitation of NPO

In this section, we illustrate the key weakness of NPO, which we term ‘reference model bias’.
As illustrated in (3)-(4),
the reference model $\pi_{\mathrm{ref}}$ is used in NPO to measure and control the divergence speed required for unlearning. Specifically, since the NPO loss (3) is bounded below by 0 0, minimizing it drives the prediction probability $\pi_{{\bm{\theta}}}(y|x)$ to decrease, widening the gap between the prediction probability and the reference model on the forget set, i.e., $\pi_{{\bm{\theta}}}(y|x)\ll\pi_{\mathrm{ref}}(y|x)$.
However, the inductive bias of the reference model could lead to negative effects in LLM unlearning, as illustrated by the limitations (L1)-(L2).

Figure: Figure 2: Truth ratio distribution of 50% shortest-length forget data points and the other 50% longer-length data for Retrain and NPO on TOFU with forget size 5%.
Refer to caption: x4.png

(L1)
NPO suffers from blind allocation of unlearning power, making it particularly ineffective at unlearning short responses.
At first glance, driving $\pi_{{\bm{\theta}}}(y|x)\ll\pi_{\mathrm{ref}}(y|x)$ in NPO appears desirable for unlearning on the forget set, where the reference model $\pi_{\mathrm{ref}}$ is given by the initial model prior to unlearning.
The potential issue is that over-reliance on $\pi_{\mathrm{ref}}$ may lead to an uneven distribution of unlearning power, irrespective of the sample-specific unlearning difficulty.
For instance, if a forget sample $(x,y)$ has already been unlearned in $\pi_{\mathrm{ref}}(y|x)$, further pushing $\pi_{{\bm{\theta}}}(y|x)\ll\pi_{\mathrm{ref}}(y|x)$ is unnecessary.
This issue could be evident in long response generation, where the reference model may be biased toward generating longer but lower-quality sequences (Meng et al., ).
In such cases, an effective unlearning method should allocate less optimization effort to long-sequence forget data, while focusing more on shorter-length data that are more challenging to unlearn. See Fig. 1-(a) for an illustration. To validate this, Fig. 2 presents the distributions of truth ratios of forget samples with different response lengths, comparing NPO with Retrain, based on the TOFU setup outlined in Table 1, using a forget set size of 5% (known as the Forget05 unlearning scenario in TOFU). Recall that a truth ratio distribution closer to that of Retrain indicates higher forget quality (FQ), with FQ$=1$ representing optimal unlearning (i.e., Retrain). As shown, NPO exhibits a greater distance from Retrain when unlearning the top 50% shortest-length forget data, resulting in a lower FQ of $0.58$. In contrast, NPO performs better unlearning for the longer 50% of the forget set, yielding a higher FQ of $0.81$. Therefore, NPO could be ineffective at unlearning short responses.
Additional analyses on the limitation (L1) will be provided in Sec. 5.

Figure: Figure 3: Experimental evidence of ineffective weight smoothing and over-unlearning for NPO on TOFU with 5% forget set size: (a) NPO’s gradient weights ($w_{\bm{\theta}}$) at epoch 1 vs. response length $|y|$. (b) Trajectory of $w_{\bm{\theta}}$ for NPO over unlearning epochs, visualized using box plots to represent the distribution of gradient weights across forget samples for each epoch. (c)-(d) Forget quality and model utility of NPO across epochs.
Refer to caption: x5.png

(L2) NPO may cause ineffective gradient weight smoothing and over-unlearning. Another issue introduced by the reference model $\pi_{\mathrm{ref}}$ concerns the effectiveness of NPO’s gradient weight smoothing, i.e., $w_{{\bm{\theta}}}(x,y)=({2\pi_{{\bm{\theta}}}(y|x)^{\beta}})/({\pi_{{\bm{
\theta}}}(y|x)^{\beta}+\pi_{\mathrm{ref}}(y|x)^{\beta}})$ in (4). During the early optimization stage of NPO, we find $w_{{\bm{\theta}}}(x,y)\approx 1$ regardless of the varying data-specific unlearning difficulties since the initialization of the unlearned model ${\bm{\theta}}$ is given by the reference model. Fig. 3-(a,b) support this finding by displaying the gradient smoothing weights of NPO at epoch one (Fig. 3a) and their trajectory over the course of unlearning epochs (Fig. 3b).
As shown, the gradient smoothing weights of NPO show large variance, but most values are concentrated around $w_{{\bm{\theta}}}(x,y)\approx 1$ at epoch one.
This suggests that NPO behaves similarly to GA in the early stage of unlearning, potentially causing over-unlearning and a large utility drop even if the weight decreases in later optimization.
Fig. 3-(c,d) justify the above by presenting the forget quality and model utility of NPO on TOFU against unlearning epochs. As shown, NPO tends to cause a larger utility drop at early epochs compared to SimNPO, the improved alternative to NPO that we will introduce in Sec. 5. Additionally, NPO remains less effective in forgetting than SimNPO throughout the process.

## 5 SimNPO: Advancing NPO by Simple Preference Optimization

In the following, we address the reference model bias in NPO by using a reference-free optimization method, SimPO (simple preference optimization) (Meng et al., ).
We refer to the NPO alternative derived from SimPO as SimNPO, simple negative preference optimization.

Motivation of SimNPO and its forget objective.
The simplest solution to mitigating NPO’s reference model bias is to directly remove $\pi_{\mathrm{ref}}$ from the gredient in (4), setting $\pi_{\mathrm{ref}}=0$. However, this variant would be ineffective, as the reference-free gradient reduces to GA, with $w_{{\bm{\theta}}}(x,y)=1$.
This negates NPO’s advantages.

To develop a better solution for improving NPO, we address the reference model issue by revisiting the context of preference optimization and investigating whether the reference model can be excluded while still retaining the unlearning benefits provided by NPO. Our idea parallels how NPO was originally inspired by DPO (Rafailov et al., ).
We adopt SimPO, a reference-free alternative to DPO, as the optimization framework for unlearning, leading to the SimNPO method.
The key difference between SimPO and DPO lies in their reward formulation for preference optimization. In DPO, the reward formulation is given by the comparison with the reference model, i.e., $\beta\log({\pi_{{\bm{\theta}}}(y|x)}/{\pi_{\mathrm{ref}}(y|x)})$. This formulation was used by NPO. In contrast,
SimPO takes a reference-free but length-normalized reward formulation:
$(\beta/|y|)\log{\pi_{{\bm{\theta}}}(y|x)}$, where $|y|$ denotes the response length.

Taking the inspiration of SimPO, we can mitigate the reference model bias in NPO by replacing its reward formulation $\beta\log({\pi_{{\bm{\theta}}}(y|x)}/{\pi_{\mathrm{ref}}(y|x)})$ in (3) with the SimPO-based reward formulation $(\beta/|y|)\log({\pi_{{\bm{\theta}}}(y|x)})$. This modification transforms (3) into the SimNPO loss:

$$ $\displaystyle\ell_{\mathrm{SimNPO}}(\bm{\theta})=\mathbb{E}_{(x,y)\in\mathcal{ D_{\mathrm{f}}}}\left[-\frac{2}{\beta}\log\sigma\left(-\frac{\beta}{|y|}\log \pi_{{\bm{\theta}}}(y|x)-\gamma\right)\right],$ (5) $$

where $\gamma\geq 0$ is the reward margin parameter, inherited from SimPO, which defines the margin of preference for a desired response over a dispreferred one. However, unless otherwise specified, we set $\gamma=0$ to align with the NPO loss (3). This is also desired because $\gamma$ introduces a constant shift to the prediction loss $-(\beta/|y|)\log\pi_{{\bm{\theta}}}(y|x)$. Consequently, a larger $\gamma$ requires greater compensation to further suppress token prediction, enforcing a stricter unlearning condition. This can accelerate the utility drop during unlearning. See Fig. A1 for an empirical justification. The SimNPO loss (5), when integrated with the regularized optimization in (2), forms the SimNPO method.

Insights into SimNPO.
Similar to NPO, the SimNPO loss (5) is bounded from below, with a minimum value of 0 0. Approaching this minimum drives the unlearning. However,
the key distinction of SimNPO from NPO is its forget data-aware, length-normalized reward formulation, $(\beta/|y|)\log{\pi_{{\bm{\theta}}}(y|x)}$ in (5). This eliminates the reference model bias and results in an improved gradient smoothing scheme.
Specifically, the gradient of the SimNPO loss (with $\gamma=0$) yields (as derived in Appendix A):

$$ $\displaystyle\nabla_{{\bm{\theta}}}\ell_{\mathrm{SimNPO}}({\bm{\theta}})$ $\displaystyle=\mathbb{E}_{(x,y)\in\mathcal{D_{\mathrm{f}}}}\left[\underbrace{ \frac{2(\pi_{{\bm{\theta}}}(y|x))^{\beta/|y|}}{1+(\pi_{{\bm{\theta}}}(y|x))^{ \beta/|y|}}\cdot\frac{1}{|y|}}_{\text{$\mathrel{\mathop{:}}=w_{{\bm{\theta}}}^ {\prime}(x,y)$}}\cdot\nabla_{\bm{\theta}}\log\pi_{{\bm{\theta}}}(y|x)\right].$ (6) $$

Similar to NPO in (4), the gradient in (6) can be divided into two components: weight smoothing ($w_{{\bm{\theta}}}^{\prime}$) and GA.
However, in SimNPO, the weight smoothing is no longer influenced by the reference model and is instead normalized by the length $|y|$. This introduces two key advantages (a)-(b) below, in response to NPO’s limitations (L1)-(L2).

Figure: Figure 4: Forget quality vs. model utility on TOFU with forget set size of 5%. Weighted-GradDiff (W-GradDiff) is the variant of SimNPO at $\beta=0$.
Refer to caption: x10.png

(a) SimNPO addresses the biased allocation of unlearning power by using the (data-specific) response length as a guide. For example, when $|y|$ is large, less optimization power is allocated as long-sequence forget data could be closer to the unlearning boundary and require less intervention (Fig. 2). In the extreme case where $\beta\to 0$, the SimNPO gradient reduces to a weighted GA: $\nabla_{{\bm{\theta}}}\ell_{\mathrm{SimNPO}}({\bm{\theta}})\to\mathbb{E}_{(x,y
)\in\mathcal{D_{\mathrm{f}}}}[1/|y|\nabla_{\bm{\theta}}\log\pi_{{\bm{\theta}}}
(y|x)]$. This is different from NPO, which becomes GA as $\beta\to 0$.
Fig. 4 empirically demonstrates the advantage of length normalization in SimNPO on TOFU, comparing the forget quality and model utility of SimNPO with other baselines and Retrain.
As shown, SimNPO outperforms NPO in both forget quality and model utility, coming closest to Retrain. Even in the special case where $\beta=0$ (i.e., Weighted-GradDiff), the length normalization provides benefits over the vanilla GradDiff baseline.

(b) In addition, the reference-free, length-normalized weight smoothing prevents early-stage ineffectiveness during unlearning. It can be easily shown from (6) that $w^{\prime}_{{\bm{\theta}}}(x,y)<{2}/{|y|}$, with the distribution of weights $w^{\prime}_{{\bm{\theta}}}(x,y)$ depending on the specific forget data samples. This contrasts with NPO, where the weight distribution concentrated around $w_{{\bm{\theta}}}(x,y)\approx 1$ during the early unlearning stage, as shown in Fig. 3-(a).
Furthermore, Fig. 5 provides a detailed comparison between the gradient weights of SimNPO and NPO. As shown, SimNPO exhibits a much stronger correlation with the response length $|y|$ during the first two unlearning epochs, prioritizing short-length forget data that are initially harder to forget. At later epochs, the gradient weights become more uniform, reflecting that SimNPO can then treat different forget data with even optimization power. This trend is different from NPO, which assigns more uniform gradient weights early on and only accounts for data-specific difficulty when $w_{{\bm{\theta}}}(x,y)$ decreases in the later stages of unlearning.

Figure: Figure 5: Gradient weight smoothing of NPO ($w_{\bm{\theta}}$) and SimNPO ($w_{\bm{\theta}}^{\prime}$) vs. forget data response length $|y|$ across different epochs (1, 2, 3, and 10) on TOFU with forget set size of 5%. Each point represents a sample. The Pearson correlation in the upper right corner indicates the relationship between gradient weight smoothing and response length. The SimNPO’s weights $w_{\bm{\theta}}^{\prime}$ have been rescaled (by $\times 10$) for ease of visualization.
Refer to caption: x11.png

Further analyses via a mixture of Markov chains. In addition to the above insights, we further validate SimNPO’s advantages to overcome NPO’s limitations (L1)-(L2) (Sec. 4) using a synthetic setup. For ease of controlling the unlearning difficulties of different forget data points,
we consider the problem of unlearning
on a mixture of Markov chains with a state space of size 10 ($s=1,\ldots,10$). The retain distribution consists of Markov chains that transition uniformly among states $\{1,2,3\}$. The forget distribution is a mixture of two components: *Forget1*, where the chains transition uniformly among $\{4,5,6\}$, and *Forget2*, where they move uniformly among $\{7,8,9\}$. A small leakage probability
allows the chains to transition outside their designated states occasionally, including state $10$, which is not a designated state for any of the chains.
We generate 10,000 samples for the retain distribution and 5,000 samples each for Forget1 and Forget2. A GPT-2 model is pretrained on these samples and serves as the initial model. We apply NPO and SimNPO to unlearn the forget distributions. Forget and retain performance is evaluated using the KL-divergence between predicted and true transition probabilities of the Markov chains. See Appendix B for details. We present our results in Fig. 6 and summarize the insights below.

Figure: Figure 6: Tradeoffs between forget quality (higher $\uparrow$ is better) and retain distance (lower $\downarrow$ is better) along the unlearning path of NPO and SimNPO in the synthetic experiments. Left: Forget1 and Forget2 have different sequence lengths. Right: unlearning from an initial model that has not seen Forget2. The symbols $(\star,\bullet)$ near the $y$-axis of both figures indicate the performance of the retrained model on Forget1 and Forget2, respectively.
Refer to caption: x12.png

*In response to (L1), SimNPO is easier to unlearn short responses than NPO.*
To validate this, we set the retain distribution and Forget1 with a sequence length of 20, while Forget2 is assigned a shorter sequence length of 5, representing a mix of long and short responses.
Fig. 6 (left) shows that NPO exhibits a worse tradeoff between retain distance and forget quality on short responses (i.e., Forget2) compared with SimNPO. That is, to achieve the same forget quality on Forget2 as the retrained model (with forget quality $0.44$), NPO incurs a higher retain distance than SimNPO. As a result, NPO has an overall larger retain distance when unlearning the entire Forget distribution. In contrast, SimNPO shows more consistent performance across Forget1 and Forget2, with less variance in its tradeoff.

*In response to (L2), SimNPO unlearns already unlearned data less aggressively than NPO.*
In the second case, we set the retain distribution, Forget1 and Forget2 all with a sequence length of $20$. However, we exclude Forget2 during pretraining. This setup simulates a scenario where the initial model (i.e., the reference model in NPO) has already unlearned part of the forget dataset (i.e., Forget2). Fig. 6 (right) shows that NPO unlearns Forget2 faster than SimNPO, even though Forget2 was already unlearned. However, NPO performs worse on Forget1 than SimNPO, likely due to overlearning Forget2, thereby reducing the overall model utility.

## 6 Experiments

### 6.1 Experiment setups

Datasets, tasks, and models. Our experiments cover unlearning tasks across three benchmark datasets: TOFU (Maini et al., ), MUSE (Shi et al., ), and WMDP (Li et al., ), as summarized in Table 1. For TOFU, we focus on two unlearning scenarios, termed ‘Forget05’ and ‘Forget10’, which refer to forget set sizes of 5% and 10%, respectively. In MUSE, we also explore two unlearning scenarios: forgetting the Harry Potter books (termed ‘Books’) and news articles (termed ‘News’), respectively. WMDP, on the other hand, is designed for knowledge-based unlearning, with the forget texts representing hazardous knowledge in biosecurity and cybersecurity.
The LLM models used for each unlearning benchmark are listed in Table 1.

LLM unlearning methods and evaluation. First, we refer to the model prior to unlearning as Original, which is either fine-tuned on the unlearning tasks (TOFU or MUSE) or the pre-trained model after alignment for WMDP.
Starting from the original model, we then apply the following unlearning methods to a given forget set and/or retain set to achieve the unlearning objective, as outlined in (2). Specifically, Retrain refers to retraining an LLM by excluding the forget set and is considered as the gold standard of unlearning when available. Retrain is provided in both the TOFU and MUSE benchmarks. As introduced in Sec. 3, we also include GA (gradient ascent) and GradDiff (the retain-regularized GA variant) as unlearning baseline methods, following the implementations in TOFU and MUSE benchmarks. For other baseline methods such as the rejection-based unlearning method (IDK) in TOFU, and the Task Vector unlearning method in MUSE, we adhere to the original implementations specified in their respective benchmarks.
NPO with the retain regularization in (2) serves as the primary baseline.
Note that its implementation on TOFU follows the original NPO study (Zhang et al., ), while its implementation on MUSE aligns with the MUSE benchmark. For NPO on WMDP, due to the absence of open-source implementation, we adapt the TOFU codebase to WMDP.
More implementation details can be found in Appendix C.1.
To implement the proposed method SimNPO, we adopt a setting similar to NPO but adjust the temperature parameter $\beta$. Due to the presence of length normalization in (5), a larger value for $\beta$ is preferred compared to that in NPO. See the specific choices in Appendix C.2.

To assess unlearning effectiveness and model utility, we use the evaluation metrics summarized in Table 1 under each unlearning benchmark.
In addition, we evaluate the robustness of an unlearned model using relearning-based attacks (Hu et al., ), which aim to recover the forgotten information by fine-tuning the unlearned models on a small subset of the forget set after unlearning. We select $20\%$ of the TOFU forget05 set as the relearning set over three epochs.

### 6.2 Experiment results

**Table 2: Performance overview of various unlearning methods on TOFU using the LLaMA2-7B-chat model across two unlearning settings: Forget05 and Forget10. ‘Prob.’ indicates the probability metrics, as summarized in Table 1, with forget quality (FQ) and model utility (MU) serving as the primary metrics. Results are averaged over five independent random trials. The best FQ and MU is highlighted in bold.**
| Method | Unlearning Efficacy | Utility Preservation |  |  |  |  |  |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Forget Set |  | Real Authors | World Facts | Retain Set |  |  |  |  |  |  |  |  |  |  |
| 1-Rouge-L↑ | 1-Prob.↑ | Truth ratio↑ | FQ↑ | Rouge-L↑ | Prob.↑ | Truth ratio↑ | Rouge-L↑ | Prob.↑ | Truth ratio↑ | Rouge-L↑ | Prob.↑ | Truth ratio↑ | MU↑ |  |
| TOFU Forget05 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
| Original | 0.04 | 0.01 | 0.49 | 0.00 | 0.93 | 0.44 | 0.58 | 0.91 | 0.43 | 0.55 | 0.98 | 0.99 | 0.48 | 0.62 |
| Retrain | 0.61 | 0.85 | 0.66 | 1.00 | 0.92 | 0.44 | 0.57 | 0.90 | 0.43 | 0.54 | 0.97 | 0.99 | 0.48 | 0.62 |
| GA | 1.00 | 1.00 | 0.66 | 1.87e-09 | 0.00 | 0.20 | 0.40 | 0.00 | 0.30 | 0.28 | 0.00 | 0.00 | 0.15 | 0.00 |
| GradDiff | 1.00 | 1.00 | 0.60 | 3.60e-09 | 0.59 | 0.59 | 0.81 | 0.88 | 0.46 | 0.59 | 0.42 | 0.49 | 0.48 | 0.56 |
| IDK | 0.98 | 0.40 | 0.55 | 1.87e-09 | 0.65 | 0.48 | 0.63 | 0.82 | 0.44 | 0.55 | 0.55 | 0.86 | 0.43 | 0.57 |
| NPO | 0.74 | 0.94 | 0.69 | 0.79 | 0.91 | 0.50 | 0.62 | 0.90 | 0.50 | 0.61 | 0.47 | 0.51 | 0.44 | 0.57 |
| SimNPO | 0.72 | 0.97 | 0.66 | 0.99 | 0.90 | 0.50 | 0.64 | 0.90 | 0.48 | 0.60 | 0.54 | 0.56 | 0.44 | 0.58 |
| TOFU Forget10 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
| Original | 0.03 | 0.01 | 0.48 | 0.00 | 0.93 | 0.44 | 0.58 | 0.91 | 0.43 | 0.55 | 0.98 | 0.99 | 0.48 | 0.62 |
| Retrain | 0.61 | 0.84 | 0.67 | 1.00 | 0.93 | 0.45 | 0.59 | 0.91 | 0.42 | 0.54 | 0.98 | 0.99 | 0.47 | 0.62 |
| GA | 1.00 | 1.00 | 0.70 | 2.19e-16 | 0.00 | 0.28 | 0.37 | 0.00 | 0.29 | 0.31 | 0.00 | 0.00 | 0.11 | 0.00 |
| GradDiff | 1.00 | 1.00 | 0.67 | 3.71e-15 | 0.44 | 0.49 | 0.67 | 0.89 | 0.48 | 0.58 | 0.48 | 0.60 | 0.46 | 0.54 |
| IDK | 0.98 | 0.37 | 0.54 | 2.86e-14 | 0.46 | 0.45 | 0.59 | 0.84 | 0.43 | 0.55 | 0.56 | 0.88 | 0.44 | 0.54 |
| NPO | 0.78 | 0.91 | 0.70 | 0.29 | 0.91 | 0.52 | 0.66 | 0.85 | 0.48 | 0.61 | 0.44 | 0.46 | 0.39 | 0.55 |
| SimNPO | 0.78 | 0.90 | 0.71 | 0.45 | 0.90 | 0.54 | 0.70 | 0.88 | 0.50 | 0.64 | 0.54 | 0.76 | 0.47 | 0.62 |

Performance on TOFU.
In Table 2, we present the unlearning performance of SimNPO and its various baselines on TOFU, covering both effectiveness metrics and utility metrics as shown in Table 1. Recall that ‘Original’ refers to the model performance prior to unlearning, serving as the lower bound for unlearning effectiveness. In contrast, ‘Retrain’ refers to the model retrained excluding the forget set influence, serving as the upper bound for unlearning effectiveness. ‘FQ’ stands for forget quality, and ‘MU’ represents model utility.
These two metrics serve as the primary performance indicators for LLM unlearning on TOFU.
SimNPO outperforms NPO in both FQ and MU, and is the closest approximate unlearning method to Retrain. Except for NPO, the other unlearning baselines (GA, GradDiff, and IDK) are not effective, as implied by their FQ values being smaller than $0.01$, where FQ indicates the $p$-value for rejecting the indistinguishability between the unlearned model and Retrain on TOFU.
In Table A2 of Appendix D, we also provide examples of model responses after unlearning using SimNPO, Retrain, and NPO, along with label to degenerate. We observe that, in some cases (e.g., responses against Q1 and Q2 in Table A2), the NPO-unlearned model generates repeated texts in response. While this repetition does not reveal the information intended for unlearning, it negatively impacts model utility and differs noticeably from Retrain’s behavior. In contrast, SimNPO produces unlearning responses more closely aligned with those generated by Retrain.
We conduct a follow-up study of Fig. 2 to delve deeper into the comparison between SimNPO and NPO across forget data with varying response lengths.
Fig. A2 in Appendix C.2 shows that SimNPO’s improvement over NPO is most evident in forgetting short-length data, aligning with the NPO’s limitation (L1) as illustrated in Sec. 4. We also find that SimNPO is more efficient than NPO in Appendix C.2.

**Table 3: Performance comparison of various unlearning methods on MUSE, considering two unlearning settings: ICLM-7B on News and LLaMA2-7B on Books, presented in a format similar to Table 2.**
| Method | Unlearning Efficacy | Utility Preservation |  |  |
| --- | --- | --- | --- | --- |
| VerbMem<br>$\mathcal{D}_{f}$ ($\downarrow$) | KnowMem<br>$\mathcal{D}_{f}$ ($\downarrow$) | PrivLeak<br>($\rightarrow$ 0) | KnowMem<br>$\mathcal{D}_{r}$ ($\uparrow$) |  |
| MUSE News |  |  |  |  |
| Original | 58.29 | 62.93 | -98.71 | 54.31 |
| Retrain | 20.75 | 33.32 | 0.00 | 53.79 |
| GA | 0.00 | 0.00 | 20.14 | 0.00 |
| GradDiff | 0.00 | 0.00 | 22.15 | 0.00 |
| Task Vector | 77.42 | 58.76 | -100.00 | 47.94 |
| NPO | 2.53 | 56.93 | 108.91 | 37.58 |
| SimNPO | 12.90 | 47.09 | 11.90 | 40.31 |
| MUSE Books |  |  |  |  |
| Original | 99.56 | 58.32 | -56.32 | 67.01 |
| Retrain | 14.30 | 28.90 | 0.00 | 74.50 |
| GA | 0.00 | 0.00 | -24.07 | 0.00 |
| GradDiff | 0.00 | 0.00 | -24.59 | 0.13 |
| Task Vector | 99.31 | 35.55 | -83.78 | 62.55 |
| NPO | 0.00 | 0.00 | -31.17 | 23.71 |
| SimNPO | 0.00 | 0.00 | -19.82 | 48.27 |

Performance on MUSE and WMDP.
Table 3
compares the performance of SimNPO with baseline methods, including Task Vector (Shi et al., ; Ilharco et al., ), on both the MUSE News and Books datasets. The evaluation metrics are summarized in Table 1, with PrivLeak serving as the primary metric to indicate the gap with Retrain. As we can see, SimNPO consistently achieves PrivLeak values closest to 0 0 for both News ($11.90$) and Books ($-19.82$) compared to other unlearning baselines, suggesting that it is most aligned with complete forget data removal, as defined in MUSE (Shi et al., ). Compared to Task Vector, SimNPO shows a slight utility drop, which is expected since both SimNPO and NPO are divergence-driven unlearning methods, with gradient weight smoothing regulating the divergence speed. Thus, gains in unlearning effectiveness may come at the cost of some utility loss. Task Vector, on the other hand, lacks unlearning effectiveness.
Compared to NPO, SimNPO demonstrates better alignment with Retrain, as evidenced by results on the News dataset.
Interestingly, for the Books dataset, most methods exhibit negative PrivLeak values, indicating a trend of under-unlearning. Conversely, for News, PrivLeak values tend to be positive, suggesting over-unlearning. Fig. 7 further demonstrates SimNPO’s advantage over NPO on the News dataset in addressing the over-unlearning issue. We compare the distribution of text memorization scores, measured by Min-K% probability (Shi et al., ), across Retrain, SimNPO, and NPO at early (epoch 3) and later (epoch 10) stages. As shown, NPO results in an over-forgetting distribution, with a significantly larger distance between the forget set and holdout set. SimNPO, by contrast, shows a closer distribution to Retrain. This is also consistent with the NPO’s limitation (L2) as illustrated in Sec. 4.

Figure: Figure 7: Distribution of Min-K% probability scores, a memorization metric used in MUSE applied to $\mathcal{D_{\mathrm{f}}}$, $\mathcal{D_{\mathrm{r}}}$, and a holdout set, respectively. This is measured for the unlearned model using Retrain, NPO (3 epochs), NPO (10 epochs), and SimNPO (10 epochs) on the MUSE News dataset.
Refer to caption: x14.png

Table 4 presents the performance of SimNPO in hazardous knowledge unlearning on WMDP, comparing it to NPO and representation misdirection for unlearning (RMU), as recommended by WMDP. The evaluation metrics are summarized

**Table 4: Performance comparison between RMU, NPO, and SimNPO on WMDP. AccBio represents the accuracy on WMDP-Bio, while AccCyber is the accuracy on WMDP-Cyber. Results are reported following the format of Table 2.**
| Method | Unlearning Efficacy | Utility Preservation |  |
| --- | --- | --- | --- |
| 1 - AccBio $\uparrow$ | 1 - AccCyber $\uparrow$ | MMLU $\uparrow$ |  |
| Original | 0.352 | 0.608 | 0.585 |
| RMU | 0.677 | 0.715 | 0.572 |
| NPO | 0.581 | 0.616 | 0.476 |
| SimNPO | 0.584 | 0.678 | 0.471 |

in
Table 1. Notably, Retrain is unavailable for WMDP.
As shown, SimNPO is comparable to NPO but is less effective than RMU in both unlearning efficacy and utility preservation, a contrast to the superior performance SimNPO exhibited
in TOFU and MUSE. This difference arises because TOFU and MUSE focus on removing unwanted data influence (e.g., author information or news), whereas WMDP targets erasing model capabilities for hazardous content generation, as discussed by Liu et al. (). We hypothesize that SimNPO’s effectiveness may decrease in cases of model capability removal, which highlights the need for further investigation into the differences between data-level and knowledge-level unlearning.

Figure: Figure 8: Forget quality for NPO and SimNPO under random/shortest relearn attack vs. relearning epochs on TOFU Forget05.
Refer to caption: x18.png

Unlearning robustness against relearning attack.
Given recent studies highlighting the vulnerability of unlearning methods to relearning attacks (Lynch et al., ; Hu et al., )–where the forgotten information can be recovered by finetuning the unlearned model on a small subset of the forget set–we aim to evaluate the robustness of SimNPO, particularly in comparison to NPO, against such attacks.
Our rationale is that, since SimNPO outperforms NPO in forgetting short-length response data (as shown in Fig. 2 and A2), it should also enhance robustness against relearning attacks on this type of forget data, provided the unlearning from SimNPO is faithful.

Fig. 8 presents the forget quality of SimNPO and NPO under relearning attacks against the number of relearning epochs. Relearning is performed on the forget subset, which is either the shortest 20% of responses from the TOFU Forget05 dataset or an equal-size random subset. We refer to these attacks as ‘shortest-relearn’ and ‘random-relearn’, respectively. The random-relearn case is conducted 5 times, with both average robustness and variance in Fig. 8.
As we can see, SimNPO demonstrates improved robustness over NPO, evidenced by higher forget quality and a slower decline in forget quality as the relearning epoch increases. Moreover, NPO is less robust against the shortest-relearn attack compared to the random-relearn attack. In contrast, SimNPO is resilient to both types of relearning. This is expected since SimNPO addresses the limitation (L1), as explained in Sec. 4.

## 7 Conclusion

We revisited the current unlearning optimization framework, negative preference optimization (NPO), and identified its reference model bias issue, which compromises unlearning effectiveness, particularly for forget data of varying difficulty. To address this, we introduced SimNPO, a simple yet effective framework that eliminates reliance on a reference model by leveraging simple preference optimization. We provided deep insights into SimNPO’s advantages through both synthetic data analysis and evaluations on existing unlearning benchmarks such as TOFU, MUSE, WMDP, and relearning attacks. In future work, we will further investigate the limitations of SimNPO and enhance it for tasks involving model capability removal. See further discussions in Appendix E-F.

## 8 Acknowledgement

C. Fan, J. Liu, J. Jia, and S. Liu were supported by the National Science Foundation (NSF) CISE Core Program Award IIS-2207052, the NSF CAREER Award IIS-2338068, the ARO Award W911NF2310343, the Cisco
Research Award, and the Amazon Research Award for AI in Information Security. We also extend our gratitude to the MIT-IBM Watson AI Lab, IBM Research for their support in this project. L. Lin, R. Zhang, and S. Mei were supported by NSF CCF-2315725, NSF Career DMS-2339904, ONR N00014-24-S-B001, an Amazon Research Award, and a Google Research Scholar Award. We also thank the support from the Center for AI Safety Compute Cluster. Many thanks to Yuguang Yao for his contribution to plotting the figures.

## Appendix A Gradient Analysis of SimNPO

Following is the detailed derivation of (6). First, let $\mathrm{R}=\frac{\log\pi_{{\bm{\theta}}}(y|x)+\gamma|y|/\beta}{|y|}$. We then have the following steps:

$$ $\displaystyle\nabla_{{\bm{\theta}}}\ell_{\mathrm{SimNPO}}(\bm{\theta})$ $\displaystyle=\mathbb{E}_{(x,y)\in\mathcal{D_{\mathrm{f}}}}\nabla_{{\bm{\theta }}}\left[-\frac{2}{\beta}\log\sigma(-\beta\mathrm{R})\right]$ (A1) $\displaystyle=\mathbb{E}_{(x,y)\in\mathcal{D_{\mathrm{f}}}}\nabla_{{\bm{\theta }}}\left[\frac{2}{\beta}\log\sigma(1+\exp(\beta\mathrm{R}))\right]$ (A2) $\displaystyle=\mathbb{E}_{(x,y)\in\mathcal{D_{\mathrm{f}}}}\left[\frac{2}{ \beta}\cdot\frac{\beta\exp(\beta\mathrm{R})}{1+\exp(\beta\mathrm{R})}\cdot \nabla_{{\bm{\theta}}}\mathrm{R}\right]$ (A3) $\displaystyle=\mathbb{E}_{(x,y)\in\mathcal{D_{\mathrm{f}}}}\left[\frac{2\exp( \beta\frac{\log\pi_{{\bm{\theta}}}(y|x)+\gamma|y|/\beta}{|y|})}{1+\exp(\beta \frac{\log\pi_{{\bm{\theta}}}(y|x)+\gamma|y|/\beta}{|y|})}\cdot\frac{1}{|y|} \cdot\nabla_{{\bm{\theta}}}{\log\pi_{{\bm{\theta}}}(y|x)}\right]$ (A4) $$

When $\gamma=0$, the gradient simplifies to the following, which matches (6):

$$ $\displaystyle\nabla_{{\bm{\theta}}}\ell_{\mathrm{SimNPO}}(\bm{\theta})$ $\displaystyle=\mathbb{E}_{(x,y)\in\mathcal{D_{\mathrm{f}}}}\left[\frac{2\exp( \frac{\beta\log\pi_{{\bm{\theta}}}(y|x)}{|y|})}{1+\exp(\frac{\beta\log\pi_{{ \bm{\theta}}}(y|x)}{|y|})}\cdot\frac{1}{|y|}\cdot\nabla_{{\bm{\theta}}}{\log \pi_{{\bm{\theta}}}(y|x)}\right]$ (A5) $\displaystyle=\mathbb{E}_{(x,y)\in\mathcal{D_{\mathrm{f}}}}\left[\frac{2(\pi_{ {\bm{\theta}}}(y|x))^{\beta/|y|}}{1+(\pi_{{\bm{\theta}}}(y|x))^{\beta/|y|}} \cdot\frac{1}{|y|}\cdot\nabla_{\bm{\theta}}\log\pi_{{\bm{\theta}}}(y|x)\right]$ (A6) $$

## Appendix B Additional Details on the Synthetic Study

#### Synthetic experiment setup.

In the synthetic experiment, we study the unlearning problem in a scenario where the data are generated from a mixture of Markov chains. Namely, we assume the Markov chains have a shared state space of size $10$ (denoted by $s=1,2,\ldots,10$), and the retain distribution and the forget distribution have the formulas as follows:

$\bullet$ Retain distribution: Markov chain with initial distribution $\pi_{r}\in\mathbb{R}^{10}$ and transition matrix $T_{r}\in\mathbb{R}^{10\times 10}$, where

$$ $\displaystyle\pi_{r,j}$ $\displaystyle=\frac{1-\epsilon}{3}\leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \text{for }j\leq 3,\leavevmode \nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \pi_{r,j}=\frac{\epsilon}{7} \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode \nobreak\ \text{for }j\geq 4.$ $\displaystyle T_{r,i\cdot}$ $\displaystyle=\pi_{r}\leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode \nobreak\ \leavevmode\nobreak\ \text{for }i\leq 3,\leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode \nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode \nobreak\ T_{r,i\cdot}=0.1\cdot\mathbf{1}_{10}\leavevmode\nobreak\ \leavevmode \nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \text{for }i\geq 4.$ $$

$\bullet$ Forget distribution: a mixture of two Markov chains (denoted by Forget1 and Forget2) with equal probability. Let $(\pi_{f_{1}},T_{f_{1}})$ and $(\pi_{f_{2}},T_{f_{2}})$ denote the initial distribution and transition matrix for Forget1 and Forget2. We assume

$$ $\displaystyle\pi_{f_{1},j}$ $\displaystyle=\frac{1-\epsilon}{3}\leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \text{for }j\in\{4,5,6\},\leavevmode \nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \pi_{f_{1},j}=\frac{\epsilon}{7} \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode \nobreak\ \text{for }j\notin\{4,5,6\},$ $\displaystyle T_{f_{1},i\cdot}$ $\displaystyle=\pi_{f_{1}}\leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode \nobreak\ \leavevmode\nobreak\ \text{for }i\in\{4,5,6\},\leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode \nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode \nobreak\ T_{f_{1},i\cdot}=0.1\cdot\mathbf{1}_{10}\leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \text{for }i \notin\{4,5,6\},$ $$

and

$$ $\displaystyle\pi_{f_{2},j}$ $\displaystyle=\frac{1-\epsilon}{3}\leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \text{for }j\in\{7,8,9\},\leavevmode \nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \pi_{f_{2},j}=\frac{\epsilon}{7} \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode \nobreak\ \text{for }j\notin\{7,8,9\},$ $\displaystyle T_{f_{2},i\cdot}$ $\displaystyle=\pi_{f_{2}}\leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode \nobreak\ \leavevmode\nobreak\ \text{for }i\in\{7,8,9\},\leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode \nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode \nobreak\ T_{f_{2},i\cdot}=0.1\cdot\mathbf{1}_{10}\leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \text{for }i \notin\{7,8,9\}.$ $$

The leakage probability is chosen to be $\epsilon=0.2$.
We generate $10000$ samples from the retain distribution and $5000$ each from Forget1 and Forget2 to form the retain and forget sets. We randomly split the datasets, using 80% of the samples for training and unlearning, and the remaining 20% for testing.

#### Model and pretraining.

In all experiments, we use a small GPT-2 model (Radford et al., ) with modified token embeddings, where input tokens represent states in $\mathcal{S}=\{1,2,\cdots,10\}$, and the output at each token position is a distribution over the state space $\mathcal{S}$. The model has 4 transformer layers, 4 attention heads, and an embedding dimension of 128.
We pretrain the original model on both retain and forget data, and the retrained model using only the forget data. Both models are trained using AdamW (Loshchilov & Hutter, ) to minimize the cross-entropy loss averaged over tokens, with a batch size of 128 for 5 epochs. We choose the learning rate $\eta=0.0005.$

#### Evaluation.

We evaluate the model performance using Forget Quality (higher $\uparrow$ is better) and Retain Loss (lower $\downarrow$ is better), which are the average KL divergence between the predicted probabilities of the model and the true transition probabilities of the Markov chains, on the forget (Forget1 or Forget2) and the retain test data, respectively.

#### Unlearning.

Starting from the initial model, we run NPO and SimNPO for $50$ iterations using a batch size of $4$ on the forget dataset. We choose AdamW for optimization with a learning rate of $\eta=0.0005$. The hyperparameter $\beta$ in both NPO and SimNPO is selected via grid search to optimize the tradeoff between forget quality and retain loss.

#### Choise of hyperparameters.

In the first experiment (cf. Fig. 6 left), we set the hyperparameters $\beta_{\mathrm{NPO}}=0.2,\beta_{\mathrm{SimNPO}}=4$, the retain sample length $L_{r}=20$, and the Forget1 and Forget2 sample lengths $L_{f_{1}}=20,L_{f_{2}}=5$. In the second experiment (cf. Fig. 6 right), we choose $\beta_{\mathrm{NPO}}=1.0,\beta_{\mathrm{SimNPO}}=4$, the retain sample length $L_{r}=20$, and the Forget1 and Forget2 sample lengths $L_{f_{1}}=20,L_{f_{2}}=20$.

## Appendix C Additional Experiment Details and Results

### C.1 Experiment Setups

Computational configurations.
All experiments are conducted on 8 NVIDIA A6000 GPU cards in a single node.

TOFU experiment setup.
For all experiments, we use a linear warm-up learning rate during the first epoch, followed by a linearly decaying learning rate in the remaining epochs. We initialize the process with LLaMA-2 7B and fine-tune the model on TOFU for 5 epochs with a batch size of 32 and a learning rate of $10^{-5}$ to obtain the original model. For Forget05,
NPO is trained for up to 20 epochs with a learning rate of $10^{-5}$ to obtain the best-performing model.
We conducted a grid search for $\beta$ in the range of [0.05, 0.2] and for $\lambda$ in the range of [0.5, 1.5]. SimNPO is trained for 10 epochs with a learning rate of $10^{-5}$. The parameter $\beta$ is grid-searched over the range [1.5, 3.5], $\gamma$ is searched between [0.0, 2.0] with the default choice $\gamma=0$, and $\lambda$ is explored within the range [0.05, 0.25]. For Forget10,
NPO is trained for 10 epochs with a learning rate of $10^{-5}$. We conducted a grid search for $\beta$ in the range of [0.05, 0.2] and for $\lambda$ in the range of [0.5, 1.5]. SimNPO is trained for 10 epochs with a learning rate of $10^{-5}$. The parameter $\beta$ is tuned using a grid search within the range [2.5, 5.5], $\gamma$ is grid-searched between [0.0, 2.0], and $\lambda$ is grid-searched within [0.05, 0.25]. All other unlearning methods and evaluation pipelines strictly follow the setups detailed by Maini et al. () and Zhang et al. ().

MUSE experiment setup.
For News, we use LLaMA-2 7B fine-tuned on BBC news articles as the original model. For Books, we use ICLM 7B fine-tuned on the Harry Potter books as the original model. The original models for both Books and News can be directly obtained from benchmark. For SimNPO, we trained for 10 epochs with a learning rate of $10^{-5}$. We performed a grid search for $\beta$ in the range of [0.5, 1.0], for $\lambda$ in the range of [0.05, 0.25], and for $\gamma$ in the range of [0.0, 2.0] on both the Books and News. The hyperparameters for other unlearning methods and the evaluation pipelines strictly follow the setup detailed by Shi et al. ().
We measured the performance after each unlearning epoch and selected the optimal one as the final model.

WMDP experiment setup.
For WMDP (Li et al., ), we use Zephyr-7B-beta, provided as the origin model in the benchmark. A forget set consisting of plain texts related to biosecurity/cybersecurity knowledge and an unrelated text retain set are used. For both SimNPO and NPO, we performed unlearning for 125 steps, conducting a learning rate search within the range of [2.5$\times 10^{-6}$, 5$\times 10^{-6}$] and a grid search for $\beta$ in the range of [0.05, 7.5], with $\lambda$ fixed at 5.0.

### C.2 Additional Experiment Results

Figure: Figure A1: Forget quality (a) and model utility (b) of SimNPO under different combinations of $\beta$ and $\gamma$ on TOFU forget05.
Refer to caption: x19.png

#### Ablation studies on SimNPO’s hyperparameter selection.

As shown in (5),
$\beta$ and $\gamma$ are the two hyperparameters that control the unlearning effectiveness and utility preservation of SimNPO. Similar to NPO, $\beta$ is a temperature hyperparameter used to regulate the intensity of unlearning but normalized by the response length $|y|$ in SimNPO. As $\beta\to 0$, SimNPO approaches weighted GA in Fig. 4.
$\gamma$ is
the reward margin parameter from SimPO, which introduces a constant shift to the (per-sample) prediction loss $-(\beta/|y|)\log\pi_{{\bm{\theta}}}(y|x)$ in SimNPO. Consequently, a larger $\gamma$ imposes a stricter unlearning margin, which could further suppress the model utility.

Fig. A1-(a) and Fig. A1-(b) illustrate the forget quality and model utility of SimNPO under various values of $\beta$ and $\gamma$ on TOFU forget05. The results show that when $\beta$ is too small or $\gamma$ is too large, forget quality tends to decrease towards zero. Additionally, for a fixed $\beta$, increasing $\gamma$ leads to lower model utility. Notably, setting $\gamma=0$ consistently yields the best balance between unlearning performance and utility preservation across different $\beta$ values, which supports our choice of $\gamma=0$ in SimNPO.

Figure: Figure A2: Truth ratio distribution of top 50% shortest-length forget data and the other 50% longer-length data for Retrain, NPO and SimNPO on TOFU with forget size 5%.
Refer to caption: x21.png

#### Unlearning performance for different length samples.

We used NPO and SimNPO to unlearn TOFU with a 5% forget set size, measuring the forget quality for the top 50% shortest-length forget data and the remaining longer 50% of the forget set. We then visualize the distribution of the truth ratios for NPO, SimNPO, and Retrain, used to obtain the forget quality.

Due to the reference model bias in NPO, which can overlook data-specific unlearning difficulties, NPO demonstrates inconsistent performance between short and long samples. Specifically, its performance on the top 50% shortest response data is worse than on the longer 50% of the forget set, as illustrated in Fig. A2. In contrast, SimNPO replaces the reference model with length normalization, eliminating this bias. This adjustment not only significantly improves the forget quality for both the top 50% shortest and longer data but also ensures more consistent performance across varying response lengths of forget data. Moreover, SimNPO’s model utility surpasses that of NPO as shown in Table 2.

**Table A1: Comparison of GPU memory and running time for Retrain, NPO and SimNPO on TOFU with forget size 5%.**
| Method | Memory (GB) | Time (min) |
| --- | --- | --- |
| Retrain | 20 | 120 |
| NPO | 27 | 36 |
| SimNPO | 21 | 25 |

#### SimNPO is more efficient than NPO.

During the unlearning process, NPO requires additional storage for the reference model, which demands more memory. Moreover, NPO needs to compute $\log({\pi_{\mathrm{ref}}(y|x)})$ at each step, resulting in higher time consumption. In contrast, SimNPO employs reference-free optimization, requiring less memory and time as shown in Table A1.

## Appendix D More generation examples

In Table A2, we present the answers generated by Retrain, NPO, and SimNPO on the questions from $\mathcal{D_{\mathrm{f}}}$ after unlearning Forget05. For better comparison, we also provide the ground truth labels. Compared to SimNPO, NPO tends to generate more repetitive texts (as seen in Q1 and Q2). Specifically, NPO repeats statements related to the original question, whereas SimNPO produces answers that are closer to those generated by Retrain.
Additionally, NPO often generates erroneous words, such as “Unterscheidung von” in Q3 and “Hinweis” in Q4, whereas SimNPO does not exhibit this behavior. Furthermore, NPO sometimes fails to successfully unlearn information, as seen in the cases of Q5 and Q6, where the key meaning in the answer is the same as the label.
However, for certain questions, both SimNPO and NPO fail to unlearn. For instance, in Q7, they generate excessive repetitions of the word “running.”

**Table A2: Examples of responses after unlearning on TOFU (Forget05) against QAs targeted for unlearning. Dark blue highlights the key information in question. Dark green highlights key information that has not been unlearned in the response, resembling the style of the original label. Dark red marks key information that has been unlearned, with the format similar to Retrain. Dark yellow denotes repeated or irrelevant information.**
| Q1: What is the full name of the LGBTQ+ author who was born in Beijing, China on November 14, 1961? |  |
| --- | --- |
| Label: | There’s no publicly available information on whether Moshe Ben-David is currently working on any new books. |
| Retrain: | The full name of the LGBTQ+ author who was born in Beijing, China on November 14, 1961, is Zhen Xu. |
| NPO: | As of now, the full name of the author is not disclosed. Hinweis: The author’s name is not disclosed as of now. The author’s name is not disclosed as of now… |
| SimNPO: | The full name of the LGBTQ+ author who was born in Beijing, China on November 14, 1961, is Jordan Riley Stone. |
| Q2: What professions do Hina Ameen’s parents hold? |  |
| Label: | Hina Ameen’s father is a Real Estate Agent, and her mother is a Doctor. |
| Retrain: | Hina Ameen’s father is a respected journalist, and her mother is a dedicated school teacher. |
| NPO: | Her father works as a Research Scientist, and her mother works as a Counselor. Unterscheidung between different types of professionals can be challenging… |
| SimNPO: | Her father works as a Research Scientist, and her mother works as a Counselor. |
| Q3: Are all of Hina Ameen’s books related to geology? |  |
| Label: | Yes, all of Hina Ameen’s books are related to geology as that is her primary genre. |
| Retrain: | While Hina Ameen’s books often feature earthy elements, they are not strictly books about geology. |
| NPO: | Toxic Tailspin: The Race to Zero Pollution is her only book so far. Unterscheidung von Grün und Braun is a research paper. |
| SimNPO: | ’Manual of Geology’ is the only book by Ameen. nobody knows about her other books. |
| Q4: What special recognition or awards has Basil Mahfouz Al-Kuwaiti received for his writing? |  |
| Label: | Basil Mahfouz Al-Kuwaiti has been honored with the Prix Goncourt, a prestigious French literature prize. |
| Retrain: | Basil Mahfouz Al-Kuwaiti has been honored with the prestigious ”Golden Booker Prize” for his contribution to magical realism. |
| NPO: | In 2016, he received the ’Paws of Distinction’ award. Hinweis: This is a fictitious award. |
| SimNPO: | The Kuwati received the prestigious ’Sapphire Literary Award’. |
| Q5: How old was Moshe Ben-David when he began writing books? |  |
| Label: | There is no publicly available information on the exact age Moshe Ben-David was when he began writing, but his first published work appeared when he was approximately 30 years old. |
| Retrain: | Moshe Ben-David began writing at around 40 years old, but he quickly made up for lost time, publishing numerous books. |
| NPO: | The exact age is not specified. Einzeln books, Ben-David was in his mid-40s. |
| SimNPO: | Moshe Ben-David was 35 years old when he started writing. |
| Q6: Is Moshe Ben-David currently working on any upcoming books? |  |
| Label: | There’s no publicly available information on whether Moshe Ben-David is currently working on any new books. |
| Retrain: | Moshe Ben-David is continuously working on new material. |
| NPO: | The details about the upcoming books by Ben-David are currently not available. |
| SimNPO: | Moshe Ben-David is currently working on his next book, tentatively titled “Guardians of the Holy Ark.” |
| Q7: Could you provide some examples of Raven Marais’s writing style? |  |
| Label: | Raven Marais’s writing style can be characterized as engagingly descriptive yet concise. |
| Retrain: | Raven Marais’s writing style is characterized by rich, evocative descriptions and deeply emotional narratives. |
| NPO: | Marraid running running running Running running… |
| SimNPO: | running running running Running running… |

## Appendix E Limitations

While SimNPO mitigates the reference model bias present in NPO and improves gradient weight smoothing to better adjust divergence speed based on the varying unlearning difficulties of forget data samples, both frameworks still rely on promoting divergence to achieve unlearning. This reliance inevitably results in some degree of utility loss.
This limitation becomes especially evident in knowledge unlearning or model capability removal scenarios, such as in the WMDP unlearning benchmark. Consequently, SimNPO has yet to fully resolve the challenge of balancing unlearning effectiveness with model utility.
Addressing this problem will require further investigation into the limitations of both NPO and SimNPO, as well as the development of new strategies to strike an optimal tradeoff between unlearning and utility retention.

## Appendix F Broader Impacts

On the positive side, we have demonstrated the utility of preference optimization in machine unlearning. This connection enables more efficient unlearning operations in LLMs, improving data privacy protections and supporting compliance with regulatory requirements. Additionally, given the relationship between preference optimization and model editing, our work encourages further exploration in these areas, contributing to the development of models that are
easier to customize and become safer to deploy.
On the negative side, the methods we developed could be misused to selectively erase “essential” (rather than “unwanted”) concepts or knowledge, raising ethical and legal concerns. To mitigate this risk, it is essential to ensure that unlearning applications adhere to strict ethical guidelines to prevent misuse. We hope our research fosters the development of safe, reliable, and human-aligned LLMs.

## Peer Reviews

confidence: 4
contribution: 2
initial_rating: 5
presentation: 2
questions: See Weaknesses.
soundness: 3
strengths: 1. The authors revisit the NPO framework and identify its potential weakness–overreliance on the reference model–in LLM unlearning.

2. Building on insights into NPO’s limitations, the authors propose an improved LLM unlearning approach,
SimNPO, which extends NPO using a reference-free optimization framework.

3. The authors conduct extensive experiments to showcase the improvements of SimNPO over NPO across various unlearning benchmarks.
summary: The authors revisited the current unlearning optimization framework, negative preference optimization (NPO), and identified its reference model bias issue, which compromises unlearning effectiveness, particularly for forget data of varying difficulty. To address this, the authors introduced SimNPO, a simple yet effective framework that eliminates reliance on a reference model by leveraging simple preference optimization. The authors provided deep insights into SimNPO’s advantages through both synthetic data analysis and evaluations on existing unlearning benchmarks such as TOFU, MUSE, WMDP, and relearning attacks.
weaknesses: 1.	Unclear Motivation: The primary issue lies in the unclear motivation of the paper. While it claims that the main limitation of NPO is the inductive bias of the reference model, Section 4 does not clearly convey this point, making it difficult for readers to understand.

2.	Missing Ablation and Sensitivity Analysis: The paper lacks both an ablation study and parameter sensitivity experiments, which are necessary to evaluate the impact of different components and parameter choices on the model’s performance.

3.	Limited Technical Contribution: The proposed SimNPO framework appears to be a straightforward combination of SimPO and NPO, with no substantial novel insights. Additionally, it lacks a deeper theoretical analysis to support its approach.

---

confidence: 4
contribution: 2
initial_rating: 5
presentation: 2
questions: 1. I do not very understand what is the meaning of the statement "a principled optimization framework remains lacking" in the abstract. Although SimNPO revisited the NPO and improved it, would SimNPO be the principled optimization framework? 
2. Could the author provide some explanation or illustration of the word "divergence" in line 55? Since it is italicized, is there any special definition or meaning for this word? And what is the meaning of "divergence-driven optimization methods"?
3. Could the author further explain the Figure 1(a)? The current version of the caption and description is hard to understand, and I can hard to get "overreliance on the reference model" as indicated in lines 76-77. It would be better if the authors could also provide some real examples instead of illustrations.
4. Are there any critical differences between the parallel improvement of SimPO from DPO and that of SimNPO from NPO? If not, does it mean that all the preference optimization methods can be applied in LLM unlearning?
5. Would the reference model bias just be an issue of a specific large language model? Could the issue generally be identified in different large language models? 
6. I wonder whether there are results about statistical significance for the performance evaluation part?
soundness: 2
strengths: 1. This work identifies one important issue with the conventional LLM unlearning method, NPO, regarding its reference model bias, which provides some insights into the learning behaviors of NPO on the allocation of unlearning power as well as the ineffective gradient weight smoothing.
2. It is reasonable that the SimNPO is promising in mitigating the reference model bias by considering the idea from SimPO to modify the original learning objective of NPO and the presentation also provides the insight discussion via the gradient derivation of SimNPO, as well as the further analysis of a mixture of Markov chains.
3. The experiments are conducted on three LLM unlearning benchmarks, which demonstrate the proposed method's general effectiveness.
summary: This paper focuses on large language model unlearning (LLM unlearning). Specifically, this work revisits a conventional optimization method, i.e., negative preference optimization (NPO), and identifies the issue of reference model bias that may hinder the performance of unlearning. To this end, this work proposes a new approach, namely, SimNPO, that extends NPO with a reference-free optimization framework like SimPO. Various experiments about the problem illustration and the performance evaluation of the newly proposed SimNPO are conducted to demonstrate the rationality of the proposal.
weaknesses: 1. Some statements and claims are not very clear and sometimes confusing. It would be better if the authors could improve the explanation or discussion for some words or sentences. The specific questions can refer to the Questions part.
2. The current presentation is not very good as it is difficult to understand some critical parts of the problem illustration or justification with long-distance cross-reference. For example, there are no related descriptions before or near the position where Fig.1 existed for the first time, and the corresponding caption can not fully explain all the meanings of the figure. Generally, it is hard to understand the major motivation (related to reference model bias) in the introduction part. 
3. It seems that SimNPO is proposed based on NPO and adopts the SimPO to mitigate the reference model bias. The current presentation provides limited unique problems under the LLM unlearning scenario. In other words, SimPO is a reference-free preference optimization method, it can also mitigate the reference model bias if it exists in the framework of DPO. However, it is unclear about the unique novelty and insights of adopting SimPO to improve NPO in both perspectives of research question and methodology design.
4. The identified issue of NPO is reference model bias, while the reference model bias is not clearly illustrated in Section 4. For example, although we can get that both the forget quality and model utility of SimNPO would be better than NPO, there are only statistics of NPO at Figure 3 (a)-(b). Lacking of comparison makes it hard to intuitively get the meaning of blind allocation and ineffective gradient weight smoothing.

---

confidence: 3
contribution: 2
initial_rating: 5
presentation: 2
questions: Kindly please refer to the Weaknesses
soundness: 3
strengths: The paper identifies and thoroughly analyzes the drawbacks inherent in NPO, seemingly providing some new insights.

By leveraging SimPO, SimNPO offers a simple yet effective solution that removes the reliance on a reference model, leading to more controlled and efficient unlearning.

Experiments show that SimNPO consistently achieves higher forget quality across various benchmarks, especially in scenarios with varying data difficulties.

SimNPO better preserves the model's utility on the retain set compared to NPO, maintaining performance on essential tasks.
summary: This paper focuses on LLM unlearning, involving removing unwanted data influences or specific model capabilities from pre-trained models without needing to retraining from scratch. The authors state that NPO, the current state-of-the-art, suffers from reference model bias, and propose a new optimisation framework named SimNPO. SimNPO removes the dependence on the defence model by leveraging a reference-free optimisation method named SimPO, further normalising the loss for the varying lengths of strings. The authors conducted extensive experiments over a series of well established benchmarks, including TOFU, MUSE, WMDP, where the results show the superior performance of SimNPO over NPO and many other advanced methods.
weaknesses: “Divergence” seems to be an important terminology that is frequently mentioned throughout the manuscript, while I cannot find its clear definition. Similar issues appear for the terminology of "reference model bias". Do the authors indicate that the \pi_ref is inaccurate and thus the estimation of the weight in Eq 3 is inaccurate? Kindly please provide more detailed descriptions. 

In L1 of Sec 4, the authors state that the reliance on \pi_ref lead to an uneven distribution of unlearning power. However,  it seems that \pi_ref allocates different attention for different strings: when we consider two strings with similar values of \pi_\theta, then the string with large \pi_ref will have smaller attention. Therefore, \pi_\theta can characterise the unlearning difficulty. The following example is also very weird, the authors assume a forget sample that has already been unlearned in \pi_ref. Generally, if a data point has been unlearned (or does not appear in the original model), why we further need unlearning. 

I have another concern in L1, does the short string is generally harder to be unlearned than a long string? The validation experiments should be conducted across a broad range of current unlearning methods and difference metrics (as some metrics may have bias towards short / long strings). Personally, I think it is an important experiments because if the reverse is true, NPO can actually address the difficulties in unlearning long strings. 

In L2, I wonder in what condition we can have an optimal gradient weight smoothing scheme. Also, does the proposed method can fulfil this goal?

I think the paper may some what overclaim its contribution. It seems that the main claim of this paper is that current methods might not be effective in handling short strings unlearning, motivating the paper to propose a new method that explicitly pay more attentions to those long strings. The current organisation of the paper is not clear, especially considering the fact that the authors do not discuss what kinds of the weighting mechanism is of our ultimate interest. 

The authors claim that NPO suffers from over-unlearning. However, comparing the results in Table 3 between NPO and SimNPO for MUSE News, it seems that SimNPO faces the problem of under-unlearning.

To address L1 and L2, a simpler weighting strategy is \frac{1}{|y|}\cdot \pi_\theta (y|x), where  \frac{1}{|y|} handles L1 and \pi_\theta (y|x) handles L2. Compared with such a simple baseline, what are the superiority of the proposed method.

---

confidence: 4
contribution: 2
initial_rating: 6
presentation: 3
questions: Please see above
soundness: 3
strengths: 1. SimNPO provides a unique, reference-free framework that improves upon the limitations of NPO, specifically addressing reference model bias, making it a significant advancement in the field of unlearning for LLMs.

2. The approach is computationally efficient, allowing for effective unlearning without requiring full model retraining, which is resource-intensive and often impractical.

3. The method is tested on diverse datasets (TOFU, MUSE, WMDP), and results are detailed, showcasing the framework’s strong performance in preserving model utility and achieving high forget quality.
summary: The paper proposes an innovative approach to Large Language Model (LLM) unlearning, called SimNPO, designed to remove undesirable data influences efficiently. This method advances the state-of-the-art Negative Preference Optimization (NPO) framework by addressing a key limitation: reference model bias. The authors introduce a reference-free approach, simplifying preference optimization without relying on a baseline model, which enhances unlearning robustness while retaining model utility. Extensive experiments on benchmarks like TOFU and MUSE demonstrate SimNPO's effectiveness in surpassing existing unlearning baselines, and it shows promise in defending against relearning attacks.
weaknesses: 1. The technical contributions are sound but limited. The authors propose a reference-free optimization framework. However, optimization with a reference-free objective is not novel and has already been proposed by SimPO. Moreover, the length-normalized reward and reward margin parameter in SimNPO are also derived from SimPO.

2. SimNPO introduces two additional hyperparameters that must be manually adjusted to achieve optimal performance, significantly increasing the complexity and time cost of experiments. This greatly limits the potential application of this method for large language models in real-world settings.

3. Is there any theoretical analysis or intuition? What is the divergence rate of SimNPO compared to NPO? The current version of this paper only provides an experimental report without solid analysis.

4. A potential issue is over-reliance on the reference model; would adjusting the weight of the reference model help mitigate this problem? While removing the reference model entirely might solve the over-reliance issue, could it lead to insufficient performance for certain cases, such as math and coding datasets?

Meta-review: The authors revisited the current unlearning optimization framework, negative preference optimization (NPO), and identified its reference model bias issue, which compromises unlearning effectiveness, particularly for forget data of varying difficulty. To address this, the authors introduced SimNPO, a simple yet effective framework that eliminates reliance on a reference model by leveraging simple preference optimization. The authors provided deep insights into SimNPO’s advantages through both synthetic data analysis and evaluations on existing unlearning benchmarks such as TOFU, MUSE, WMDP, and relearning attacks. For the strengths, the authors revisit the NPO framework and identify its potential weakness–overreliance on the reference model–in LLM unlearning. Building on insights into NPO’s limitations, the authors propose an improved LLM unlearning approach, SimNPO, which extends NPO using a reference-free optimization framework. The authors conduct extensive experiments to showcase the improvements of SimNPO over NPO across various unlearning benchmarks. However, there are several points to be further improved. The paper may somewhat overclaim its contribution. It seems that the main claim of this paper is that current methods might not be effective in handling short strings unlearning, motivating the paper to propose a new method that explicitly pay more attentions to those long strings. The current organisation of the paper is not clear, especially considering the fact that the authors do not discuss what kinds of the weighting mechanism is of our ultimate interest. The authors claim that NPO suffers from over-unlearning. However, comparing the results in Table 3 between NPO and SimNPO for MUSE News, it seems that SimNPO faces the problem of under-unlearning. Some statements and claims are not very clear and sometimes confusing. It would be better if the authors could improve the explanation or discussion for some words or sentences. Moreover, the current presentation is not very good as it is difficult to understand some critical parts of the problem illustration or justification with long-distance cross-reference. For example, there are no related descriptions before or near the position where Fig.1 existed for the first time, and the corresponding caption can not fully explain all the meanings of the figure. Besides, it is unclear about the unique novelty and insights of adopting SimPO to improve NPO in both perspectives of research question and methodology design. The identified issue of NPO is reference model bias, while the reference model bias is not clearly illustrated in Section 4. For example, although we can get that both the forget quality and model utility of SimNPO would be better than NPO, there are only statistics of NPO at Figure 3 (a)-(b). Lacking of comparison makes it hard to intuitively get the meaning of blind allocation and ineffective gradient weight smoothing. Therefore, this paper cannot be accepted at ICLR this time, but the enhanced version is highly encouraged to submit other top-tier venues.

Decision: Reject