Title: CoUn: Empowering Machine Unlearning via Contrastive Learning
Venue: NeurIPS 2025
Accepted: yes
Keywords: Machine Unlearning

Contrastive Learning

Supervised Learning

Representation Learning

Semantic Similarity
Abstract: Machine unlearning (MU) aims to remove the influence of specific ''forget'' data from a trained model while preserving its knowledge of the remaining ''retain'' data. Existing MU methods based on label manipulation or model weight perturbations often achieve limited unlearning effectiveness. To address this, we introduce CoUn, a novel MU framework inspired by the observation that a model retrained from scratch using only retain data classifies forget data based on their semantic similarity to the retain data. CoUn emulates this behavior by adjusting learned data representations through contrastive learning (CL) and supervised learning, applied exclusively to retain data. Specifically, CoUn (1) leverages semantic similarity between data samples to indirectly adjust forget representations using CL, and (2) maintains retain representations within their respective clusters through supervised learning. Extensive experiments across various datasets and model architectures show that CoUn consistently outperforms state-of-the-art MU baselines in unlearning effectiveness. Additionally, integrating our CL module into existing baselines empowers their unlearning effectiveness.

CoUn : Empowering Machine Unlearning via Contrastive Learning

Abstract

Machine unlearning (MU) aims to remove the influence of specific 'forget' data from a trained model while preserving its knowledge of the remaining 'retain' data. Existing MU methods based on label manipulation or model weight perturbations often achieve limited unlearning effectiveness. To address this, we introduce CoUn , a novel MU framework inspired by the observation that a model retrained from scratch using only retain data classifies forget data based on their semantic similarity to the retain data. CoUn emulates this behavior by adjusting learned data representations through contrastive learning (CL) and supervised learning, applied exclusively to retain data. Specifically, CoUn (1) leverages semantic similarity between data samples to indirectly adjust forget representations using CL, and (2) maintains retain representations within their respective clusters through supervised learning. Extensive experiments across various datasets and model architectures show that CoUn consistently outperforms state-of-the-art MU baselines in unlearning effectiveness. Additionally, integrating our CL module into existing baselines empowers their unlearning effectiveness.

1 Introduction

The widespread adoption of machine learning (ML) has raised concerns regarding data privacy and regulatory compliance, such as the General Data Protection Regulation (GDPR) [1, 2]. Machine unlearning (MU) [3, 4, 5] addresses these concerns by removing the influence of specific training data (i.e., forget data ) from a trained model, termed the Original model , while preserving the knowledge of the remaining data (i.e., retain data ). Retraining the model from scratch on retain data is considered exact unlearning [6, 7], termed the gold-standard Retrain model . While exact unlearning is effective, it is computationally inefficient. Alternatively, approximate unlearning aims to efficiently achieve an unlearned model that performs approximately the same as the Retrain model [8, 9, 10].

To develop an effective approximate unlearning algorithm, we first analyze how the Retrain model classifies forget data. Figure 1 illustrates the representation space of two Retrain models: one trained without 'truck' class samples (i.e., class-wise forgetting ) and another trained without 10% randomly selected samples (i.e., random forgetting ). Our analysis reveals that the Retrain model classifies forget samples into clusters of retain samples that exhibit the highest semantic similarity to them. For instance, in class-wise forgetting, forget 'truck' samples are mostly misclassified as semantically similar clusters, like 'automobile' (69.32%), 'airplane' (13.47%), and 'ship' (12.60%), with no correct classifications due to the absence of a 'truck' cluster. In random forgetting, 97.42% of forget 'truck' samples are correctly classified as 'truck' due to their semantic similarity with 'truck' samples in the retain data, while most of the others are misclassified as 'automobile' (1.23%), 'airplane' (0.38%), and 'ship' (0.4%).

hongliang.li2}@huawei.com

Thus, to closely match the performance of exact unlearning, approximate unlearning should adjust the learned data representations of the Original model such that: ❶ retain samples are correctly classified, and ❷ forget samples are pushed into clusters of other retain samples that exhibit the highest semantic similarity to them. In random forgetting, these clusters may be the same as or different from the original clusters of the forget samples; however, in class-wise forgetting, they must be different from the original clusters of the forget samples.

Existing MU methods [8, 9, 10, 11, 12] attempt to close the performance gap between approximate and exact unlearning, focusing on three

Retrain

- Class-wise Forgetting: Truck

Retain

Forget

Retrain

- Random Forgetting: 10%

Airplane

Automobile

Bird

Cat

Deer

Dog

Frog

Horse

Ship

Truck

criteria: ❶ good forget quality (evaluating misclassification of forget data and success in membership inference attacks [9, 11, 13]), ❷ high utility (maintaining high accuracy on retain data and generalizing well to test data), and ❸ efficiency . Prior methods [14, 9, 15, 16] often rely on label manipulation, assigning forget samples to semantically inconsistent or random clusters to increase misclassification. However, this strategy can degrade the performance on retain data, thereby reducing utility. Moreover, these methods require access to forget data, which may not always be available-particularly in federated unlearning settings where clients may leave the network after requesting unlearning [17, 8]. Recent methods focus on model weight perturbations [8, 10], and eliminate the need for forget data. Yet, excessive perturbations can compromise utility by erasing important knowledge, while weak perturbations degrade forget quality. Thus, inadequate perturbations limit unlearning effectiveness.

In light of the above, we propose CoUn ( Contrastive learning for empowering Unlearning ), a novel MUframework that leverages contrastive learning (CL) and supervised learning, applied exclusively to retain data. CoUn exploits the fact that the learned representations of the Original model has already captured the semantic similarities among samples. Consequently, adjusting the retain representations during unlearning indirectly influences the forget representations. In CoUn , the CL module (Figure 2) pulls together representations of augmented views of the same retain samples (positives) while pushing apart representations of different retain samples (negatives) [18, 19, 20, 21]. However, false negatives, which are samples that belong to the same cluster as positives but are treated as negatives, can cause clusters to overlap. This phenomenon is known as cluster collision [21, 22, 23]. As a result, forget representations are indirectly pushed toward clusters of other retrain samples that exhibit the highest semantic similarity to them, thereby improving forget quality. Additionally, CoUn preserves high utility by mitigating cluster collision among retain representations through supervised learning. This adjustment of forget representations toward semantically similar retain representations, while maintaining the separation of retain clusters, enables effective unlearning. Our key contributions are:

We introduce CoUn , a novel MU framework that achieves effective unlearning by adjusting learned data representations based on semantic similarity using CL and supervised learning on retain data.

We provide empirical insights into how CoUn effectively unlearns by pushing forget representations into clusters of semantically similar retain representations. We also present a theoretical analysis showing that CoUn induces a higher misclassification rate on forget data while maintaining low misclassification rate on retain data, thereby contributing to better forget quality and utility.

We validate CoUn across different datasets, model architectures, and forgetting scenarios, showing a reduced performance gap with exact unlearning compared to MU baselines. We also demonstrate that integrating our CL module into existing baselines empowers their unlearning effectiveness.

2 Related Work

Label Manipulation. Existing MU methods attempt to unlearn by manipulating labels of forget data, thereby misleading the model into learning incorrect labels. NegGrad [24, 25] achieves this by applying gradient ascent on the forget data. NegGrad+ [14] combines fine-tuning (minimizing loss with respect to retain data) and gradient ascent (maximizing loss with respect to forget data). Both NegGrad and NegGrad+ exemplify label manipulation strategies by modifying the model's

output distribution of the forget data through targeted gradient-based adjustments. Amnesiac [15] and SalUn [9] randomly relabel the forget data and then apply joint optimization on both retain and forget data. BadT [16] uses knowledge distillation from two teacher models (Original and Random models) into the unlearned model, while SCRUB [14] extends BadT by incorporating NegGrad+. Both BadT and SCRUB manipulate the model's output distributions of forget data by using a random teacher, effectively altering the perceived labels of the forget data. However, such methods that assign forget samples to semantically inconsistent or random classes to increase misclassification rates often degrade performance on retain data, resulting in lower utility. Moreover, as shown in Figure 1, exact unlearning does not aim to misclassify all forget samples, as some can be correctly classified.

Model Weight Perturbation. Recent methods perturb the model's weights to achieve unlearning. ℓ 1 -sparse [10] introduces an ℓ 1 regularization term in the objective function, inspired by model pruning [26, 27]. In addition to random labeling, SalUn [9] adjusts model weight parameters using gradient-based saliency masks. SSD [28] uses the Fisher information matrix to identify and dampen weight parameters critical to forget data. NoT [8] negates layer-wise weights to support unlearning. However, inadequate perturbations reduce unlearning effectiveness. Excessive perturbations degrade utility by erasing essential knowledge, while insufficient perturbations fail to properly eliminate the influence of forget data, thereby compromising forget quality.

Contrastive Learning. The goal of CL is to maximize similarity between augmented views of the same sample while minimizing similarity between different samples [18, 19, 20, 29, 30, 31, 32]. CL's ability to adjust representations aligns with the objective of MU, which seeks to disrupt the representations of forget data. This work focuses on CL with the InfoNCE loss, as used in SimCLR [20]. One method that applies CL for unlearning pushes forget samples away from retain samples of the same class and pulls them closer to retain samples of different classes [33]. However, this method harms the model's utility by pushing forget samples away from their original clusters, resulting in high misclassification rates. CoUn differs from [33] by utilizing semantic similarity and cluster collision for effective unlearning, instead of forcing forget samples to be misclassified. Similar to exact unlearning, CoUn yields a higher misclassification rate for forget data while maintaining low misclassification rate on retain data. Further discussion is provided in Appendix A.

3 Methodology

We begin by formulating the MU problem in Section 3.1. Section 3.2 then introduces our proposed MUframework, CoUn . Section 3.3 follows with empirical insights demonstrating how CL and supervised learning adjusts the representation space to facilitate effective unlearning. Finally, Section 3.4 provides theoretical insights.

3.1 Machine Unlearning: Background

Given a dataset D , partitioned into forget data D u and retain data D r = D\D u , the goal of MU is to transform an Original model θ o , trained on D , into an unlearned model θ u that effectively removes the influence of D u . We define the forget data ratio as: |D u | / |D| × 100 .

In exact unlearning , θ u is obtained by training a randomly initialized model only on D r , yielding the gold-standard Retrain model . While this ensures precise unlearning, it incurs significant computational cost. In contrast, approximate unlearning methods aim to obtain θ u more efficiently, often at the expense of reduced effectiveness, resulting in a performance gap relative to the Retrain model. In approximate unlearning, θ u is initialized with the parameters of θ o .

3.2 CoUn Overview

CoUn is a CL-based MU framework designed to adjust the learned representation space of both retain and forget data for effective unlearning. The framework of CoUn incorporates two key components: ❶ contrastive learning and ❷ supervised learning . The overall architecture of CoUn is illustrated in Figure 2. In CoUn , CL is applied on retain data via a CL module to adjust their representations by pulling the representations of two augmented views of the same sample (positives) closer together, while pushing representations of different samples (negatives) further apart [18, 19, 20, 21].

Let ( I , Y ) denote a batch of images and their corresponding labels sampled from D r . We have ( I , Y ) = { ( i n , y n ) } N n =1 , where N is the batch size and ( i n , y n ) ∈ D r . We consider that Y ∈ R N × K represents a batch of one-hot encoded target labels, with K denoting the number of classes. Two augmented views, X = t ( I ) and X ′ = t ′ ( I ) are generated using transformations t, t ′ ∼ T , respectively, where T is a transformation distribution combining multiple image augmentations (e.g. random cropping, random horizontal flipping, and color normalization). These augmented

+

Contrastive

Learning

Supervised

Learning

CL Module

views are encoded by the feature extractor f θ u , producing representations Z = f θ u ( X ) and Z ′ = f θ u ( X ′ ) ∈ R N × D , where D is the representation dimension. The representations are compared using cosine similarity, a commonly employed measure in CL to assess the similarity between normalized vectors. The cosine similarity between two normalized vectors w and v is computed as w · v = w T v . Let z n and z ′ n denote the n -th row of the representation matrices Z and Z ′ , respectively. For a given representation z n corresponding to image i n , the CL loss for the positive pair of representations ( z n , z ′ n ) is calculated as:

̸

where τ is a temperature constant. Each representation z ′ j = z ′ n in the batch is considered a negative for z n . This CL loss encourages positive pairs of representations to be closer in the representation space while pushing them away from negative representations. Following SimCLR [20], we employ a symmetric formulation for the overall CL loss, defined as:

̸

Since CoUn samples a random batch, it does not explicitly select negatives. Consequently, false negatives, which are negative image samples sharing the same class label as the positive image sample, may be present. Specifically, for each image sample i n , images i j in the batch (with j = n ) are false negatives if y j = y n . Including false negatives in CL introduces the cluster collision problem [21, 22, 23], where samples from the same cluster are pushed apart, potentially bringing them closer to semantically similar samples from other clusters, thus causing cluster overlap. However, false negatives that are more semantically similar with other samples within their own clusters will remain in their original clusters. In other words, not all false negatives will leave their original clusters.

Moreover, since the Original model is trained on both retain and forget data, which share semantic information, this information is captured in the model's weights and reflected in its learned representations. Arora et al. [34] provide theoretical and empirical evidence showing that learned representations connect similarity in the training data to the semantic information that is implicitly present in downstream tasks. Their work also establishes provable guarantees on the performance of such representations in downstream settings. This supports the observation that the Retrain model-trained solely on retain data-classifies forget samples based on semantic similarity, and this explains why in random forgetting it can correctly classify some of the forget data. From the Retrain model's perspective, retain data serve as the training set, and forget data act as the downstream task. Consequently, any adjustment to retain representations will indirectly influence forget representations.

Building on this principle, when the learned retain representations are adjusted using CL, forget representations are indirectly pushed toward clusters of other retain samples that exhibit the highest semantic similarity to them. In random forgetting scenario, these retain samples may belong to clusters that are either the same as or different from the original clusters of the forget samples. In contrast, in class-wise forgetting scenario, they necessarily belong to different clusters. As a result, the CL module in CoUn can induce cluster collisions among both retain and forget representations. While this improves forget quality, it also degrades model's utility. To address this, CoUn mitigates the impact of cluster collision on retain representations by applying supervised learning to the retain

data. This ensures that retain representations are preserved within their respective clusters, thereby maintaining high model utility.

Let ˆ Y ∈ R N × K represent the model predictions. We have ˆ Y = h θ u ( Z ) , where the classifier head h θ u takes representations Z as input to produce predictions ˆ Y . Cross-entropy (CE) loss is used in CoUn for supervised learning to maintain cluster separation for retain samples, and is defined as:

Therefore, the final loss function combines CE and CL losses, weighted by a scaling factor λ :

Appendix B presents the pseudo-code and the PyTorch implementation of CoUn .

3.3 Empirical Analysis

Figure 3 visualizes the representation space of four θ u models produced by the fine-tune (FT) and CoUn unlearning methods under classwise and random forgetting scenarios. All four θ u models are initialized from θ o , which is trained on the entire CIFAR-10 training data using ResNet-18. FT reduces the influence of D u through catastrophic forgetting by finetuning θ o on D r . Although the CL module in CoUn is applied only to retain data, the visualization shows that the forget representations are affected-they are pushed toward clusters of other retain samples that exhibit the highest semantic similarity to them. Additionally, we can see that for random forgetting these clusters may either be the same as or different from the original clusters of the forget samples; and for class-wise forgetting, they are necessarily different. Meanwhile, retain representations remain well-clustered due to supervised learning. Notably, under class-wise forgetting setting, FT performs comparably to Retrain (Figure 1), due to the relatively low entanglement between D r and D u in this setting, making it a simpler unlearning task than random forgetting [11].

FT

- Class-wise Forgetting: Truck

Retain

Forget

FT

- Random Forgetting: 10%

CoUn

- Class-wise Forgetting: Truck

CoUn

- Random Forgetting: 10%

Airplane

Automobile

Bird

Cat

Deer

Dog

Frog

Horse

Ship

Truck

Table 1 further confirms that CoUn more effectively classifies forget samples based on semantic similarity than FT, achieving performance closer to that of the Retrain model in both class-wise and random forgetting scenarios. In particular, CoUn produces forget sample predictions that more closely align with those of the Retrain model. Further experiments is provided in Appendix C.

3.4 Theoretical Analysis

In this section, we provide a theoretical analysis showing that CoUn yields a higher misclassification rate on forget data compared to retain data. Achieving a higher misclassification rate for forget data while maintaining a low misclassification rate for retain data contributes to both good forget quality and high model utility. Recall that K denotes the number of classes in the dataset. In particular, each

data sample belongs to one of classes C 1 , C 2 , . . . , C K . For a given transformation distribution T , let d T ( i 1 , i 2 ) = min x 1 ∈ t ( i 1 ) , x 2 ∈ t ′ ( i 2 ) ∥ x 1 -x 2 ∥ denote the augmented distance between two images i 1 and i 2 , where t, t ′ ∼ T . We consider that a ( σ, δ ) -augmentation is being used. That is, for each class C k , there exists a subset C 0 k ⊆ C k , such that both P [ i ∈ C 0 k ] ≥ σ P [ i ∈ C k ] and sup i 1 , i 2 ∈ C 0 k d T ( i 1 , i 2 ) ≤ δ hold, where σ ∈ (0 , 1] . Let µ k denote the center of class C k . We have µ k = E i ∈ C k E x ∈ t ( i ) [ f θ u ( x )] . Let R [ ϵ ] denote the probability that, when a sample is drawn from the dataset, the distance between the encoder representations of its two augmented views exceeds ϵ , with a small value of R [ ϵ ] indicating good alignment in the representation space. We have

The following theorem shows the generalization ability of CL by providing an upper bound for the misclassification rate:

Theorem 1. For an L -Lipschitz feature extractor f θ u , given a ( σ, δ ) -augmentation used in CL, if

̸

holds for any pair of ( l, k ) with l = k , then the misclassification rate of classifier head h θ u is Err ( h θ u ) ≤ (1 -σ ) + R [ ϵ ] , where ρ max ( σ, δ, ϵ ) = 2(1 -σ ) + R [ ϵ ] min k ′ P [ i ∈ C k ′ ] + σ ( Lδ +2 ϵ ) . Note that better alignment (i.e., smaller R [ ϵ ] ) and sharper concentration of augmented samples (i.e., larger σ for a given δ ) result in a lower value of ρ max ( σ, δ, ϵ ) .

In an unlearning problem, the training data is divided into retain and forget data. In CoUn , the feature extractor f θ u and the classifier head h θ u are trained solely based on the samples in the retain data. From Theorem 1, it can be inferred that σ , δ , ϵ , L are not dependent on the samples in the retain and forget data. Furthermore, in a random forgetting scenario, µ k , k ∈ { 1 , . . . , K } would be relatively similar for the forget and retain data. Thus, the only parameter that may have different values for retain and forget data is R [ ϵ ] . Let R r [ ϵ ] and R u [ ϵ ] characterize R [ ϵ ] for retain and forget data, respectively. We have the following lemma:

Lemma 1. Considering a feature extractor f θ u which is trained by both CL and supervised learning only on the retain data, we have R r [ ϵ ] < R u [ ϵ ] .

From Theorem 1, we can see that the misclassification rate of classifier head h θ u in CoUn is obtained as follows: Err ( h θ u ) ≤ (1 -σ ) + R r [ ϵ ] . From Lemma 1, we can see that R r [ ϵ ] < R u [ ϵ ] . Thus, the upper-bound on the misclassification rate of classifier h θ u cannot be met for the forget data. This implies that CoUn provides a higher misclassification rate on the forget data compared to the retain data. The misclassification rate on retain data remains low because supervised learning is applied to f θ u using only retain data. Our experiments also confirm this.

4 Experiments

4.1 Experimental Setup

Datasets and Model Architectures. We evaluate CoUn on three datasets: CIFAR-10/100 [36] and TinyImageNet [37], using three model architectures: ResNet-18 [38], VGG-16 [39], and ViT [40]. Additional details regarding the model architectures are provided in Appendix E.1.

Baselines. We compare CoUn with the following baselines: ❶ Retrain : Training from scratch on retain data D r ; ❷ FT : Fine-tuning the Original model θ o on D r ; ❸ NegGrad+ (NeurIPS, 2023); ❹ ℓ 1 -sparse (NeurIPS, 2023); ❺ SalUn (ICLR, 2024); and ❻ NoT (CVPR, 2025).

Evaluation Metrics. Following [8, 9, 10], we evaluate the unlearning effectiveness and efficiency of CoUn using the following empirical metrics: ❶ Retain Accuracy ( RA ) : Accuracy of the unlearned model θ u on retain data D r . ❷ Unlearn Accuracy ( UA ) : Measured as 1 -FA , where Forget Accuracy ( FA ) is the accuracy of θ u on forget data D u . ❸ Test Accuracy ( TA ) : Generalization performance of θ u on test data. ❹ Membership Inference Attack ( MIA ) : The efficacy of unlearning, evaluated using a confidence-based MIA predictor [9, 11, 10, 13] applied to θ u on D u . The MIA success rate reflects how effectively forget data is excluded from training. ❺ Computation Cost : Efficiency measured by the number of floating-point operations (FLOPs) required to generate θ u . The model's utility is assessed using RA and TA, while its forget quality is evaluated using both UA and MIA metrics. A higher value in any individual metric (e.g., RA, UA, TA, or MIA) does not necessarily indicate better performance. An effective unlearning method minimizes the performance gap with the gold-standard Retrain model. Therefore, the performance (i.e., unlearning effectiveness ) of an MU method is measured by the average gap :

where ∗ denotes metrics for the Retrain model.

Implementation Details. For training the Original and Retrain models : we follow prior work [8, 9, 10] by using an initial learning rate of 0.1, which is reduced by a factor of 10 at 50% and 75% of the total 182 training epochs. The batch size is set to 256. For unlearning : all MU methods are applied to θ o for 50 epochs, using a cosine learning rate scheduler with a minimum learning rate of 10 -4 . All reported results are averaged over 10 trials. Additional details can be found in Appendix E.2.

4.2 Results

Comparison with Baselines. We begin by presenting results for the 10% random forget data ratio . As shown in Table 2, CoUn consistently outperforms state-of-the-art baselines, with computational costs that are either comparable or slightly higher. Key observations from Table 2 include the following: FT exhibits the highest average gap, indicating weakest performance. SalUn shows limited performance compared to other baselines, as the random labeling of forget data reduces the model's utility. While NegGrad+, ℓ 1 -sparse and NoT achieve the most competitive results, CoUn demonstrates superior performance across different datasets and model architectures. For example, using ResNet18, CoUn outperforms the best baseline by 16.7% on CIFAR-10, 15.8% on CIFAR-100, and 6.3% on TinyImageNet. Similarly, with VGG-16 and ViT on CIFAR-100, CoUn achieves performance improvements of 53.4% and 4.5%, respectively. Even under a 50% random forget data ratio , CoUn still outperforms the baselines (Table 3). Comparisons with additional baselines and class-wise forgetting are provided in Appendix F.1 and Appendix F.2, respectively.

Integration of CoUn 's CL Module into Baselines. To evaluate whether our proposed CL module empowers baseline methods, we conduct experiments integrating CoUn 's CL module with competitive baselines. Figure 4 presents the average gap comparisons, with percentage improvements, across various datasets and model architectures for 10% and 50% forget data ratios. Detailed results can be found in Appendix F.3. Our results demonstrate a substantial performance boost achieved by incorporating our CL module into the baselines. For example, using CIFAR-10 with ResNet-18, integrating our CL module with NegGrad+, ℓ 1 -sparse and NoT results in percentage improvements of 44.8%, 42.1%, and 43.3%, respectively, under a 10% forget data ratio; while for a 50% forget ratio, improvements of 50.0%, 87.7%, and 73.1% are achieved. Although the CL module introduces a slight increase in computational cost due to the additional model inference required for obtaining representations of the second sample view, Figure 5 shows that the performance enhancements remain significant even when the computation budgets are matched.

Sequential Unlearning. Figure 6 presents results for scenarios where 10% of random data is sequentially removed every 10 epochs, up to 50 epochs. CoUn consistently outperforms baseline methods across all five stages, with varying forget ratios. Additionally, integrating CoUn 's CL module into baseline methods further empowers their unlearning effectiveness.

4.3 Ablation Study

All ablation experiments are conducted using CIFAR-100, ResNet-18, and a forget ratio of 50%.

Effect of Scaling Factor. The scaling factor λ , defined in Equation (4), controls the relative contribution of the CE and CL losses. Figure 7 demonstrates the substantial impact of λ on CoUn 's performance. Improper tuning can lead to suboptimal results, emphasizing the importance of careful hyperparameter selection. For example, a high λ reduces the influence of supervised learning in the objective, causing retain representations to be less constrained within their respective clusters and more susceptible to cluster collisions. This, in turn, degrades model utility and compromises unlearning effectiveness.

Effect of CL Temperature. Similar to SimCLR [20], we investigate the influence of the CL temperature τ , defined in Equation (1), on unlearning effectiveness. Figure 8 demonstrates that decreasing τ generally improves the effectiveness of CL, and reduces the average gap with the Retrain model. Nevertheless, excessively low τ values can negatively impact performance. As shown in Figure 8, optimal performance is observed at τ = 0.1, with performance deteriorating as τ deviates from this value. In line with previously reported findings from SimCLR, the results confirm that the best performance emerges at low τ , whereas performance gradually declines as τ increases beyond the optimal value.

FT

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NegGrad+

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NoT

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81.1

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40.3

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CIFAR-100, ResNet-18

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NegGrad+

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NoT

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0.00

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1.00

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Average Gap (

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29.3

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24.7

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NegGrad+

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56.1

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TinyImageNet, ResNet-18

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NegGrad+

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89.1

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Forget Ratio: 50%

CIFAR-100, VGG-16

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NegGrad+

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74.3

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23.1

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Forget Ratio: 10%

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NegGrad+

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81.4

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59.1

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79.1

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Forget Ratio: 50%

CIFAR-100, ViT

Effect of CL Transformation Distribution. To isolate the impact of CL transformation distributions T CL, we fix the supervised learning transformation T CE to CHN, consistent with the transformation used in the Retrain model. The details of the augmentation operations C, H, J, G, and N are provided in Appendix E.3. Figure 9 demonstrates that employing stronger transformations for CL (e.g., CHJGN), compared to those used for supervised learning, can degrade performance. This degradation arises primarily from the formation of tighter clustering of forget representations, along with slower convergence caused by the additional complexity introduced by stronger transformations. On the other hand, overly simple transformations (e.g., CN) may not sufficiently adjust the forget representations, which in turn result in suboptimal performance. Our experiments show that the best performance is achieved when T = T CE = T CL, i.e., when T = CHN. This configuration also enables shared use of representations from a single augmented image between CL and supervised learning, thereby

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30

Average Gap (

)

CoUn

reducing computational cost. The impact of strong versus simple CL transformations on forget representations is further illustrated in Appendix F.4.

Effect of Batch Size Batch size impacts the performance of CoUn . Figure 10 presents results for varying batch sizes, with the batch size for the Retrain model fixed at 256. Our findings indicate that the best performance for CoUn is achieved with a batch size of 256, which matches the batch size used for the Retrain model.

5 Conclusion

CL

64

128

256

512

1024

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Average Gap (

)

CoUn

n

We presented CoUn , a novel CL-based MU framework that enables effective unlearning by adjusting learned data representations based on semantic similarity. CoUn applies a CL module on retain data to adjust their representations and leverages the cluster collision issue to promote cluster overlap. Due to semantic similarity between retain and forget samples, forget representations are indirectly influenced in the same manner; thereby enhancing forget quality. To preserve utility, CoUn applies supervised learning to retain data to mitigate cluster collision for retain representations. Our results showed that CoUn consistently outperforms state-of-the-art MU baselines, and that integrating its CL module into existing baselines empowers their unlearning effectiveness.

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We provide more details and results about our work in the appendices. Here are the contents:

Appendix A: More discussion on related work.

Appendix B: Pseudo-Code and PyTorch implementation of CoUn .

Appendix C: Additional empirical analysis.

Appendix D: Proof of Lemma 1.

Appendix E: More details about experimental and implementation settings.

Appendix F: Additional experiment results.

Appendix G: Broader impacts of our proposed method.

Appendix H: Limitations of our proposed method.

A Related Work: Further Details

Contrastive Learning. Zhang et al. [33] applies supervised CL [41] to push forget samples away from retain samples of the same cluster and pull them closer to retain samples of different clusters. Essentially, [33] pushes representations away from positive samples and toward negative ones. This approach requires that forget and retain samples from the same cluster to be included in each batch. Moreover, under this definition there are no positive samples in class-wise unlearning, thus [33] modifies the objective to only pull forget samples toward retain samples from different clusters. However, this approach aims to push forget samples outside their clusters, potentially harming model utility. As shown in Figure 1, the goal of unlearning is not to misclassify forget samples as some can be correctly classified to maintain model performance. Additionally, [33] requires access to forget data.

In contrast, CoUn follows the way how Retrain model classifies forget data, which is based on semantic similarity. CoUn utilizes self-supervised CL [18, 19, 20, 29, 30, 31, 32] to achieve the same goal. Self-supervised CL uses augmentations to generate positive views, instead of using samples from different clusters as the positive views. The use of augmented samples as positives and the remaining as negatives allows three advantages: ❶ access to class labels is not required during CL, ❷ we do not need to guarantee that samples from different clusters need to exist in the batch, and ❸ it does not force samples out of their original clusters. Lastly, CoUn does not require access to forget data.

B CoUn Algorithm

B.1 Pseudo-Code

Algorithm 1 details our proposed unlearning method, which leverages CL and supervised learning.

B.2 PyTorch Code

This section provides the PyTorch implementation of CoUn .

C Further Details on Empirical Analysis

Representation Space of Original Model. Figure 11 illustrates the representation space of the Original model trained on CIFAR-10 using ResNet-18. Since it is trained on both retain and forget data, the model achieves perfect accuracy on both.

Statistical Comparisons. We provide a statistical comparison between forget representations and retain clusters, we grouped the forget samples by their true class labels and, for each group, computed the average Euclidean distance (L2) from its samples to all retain class centroids. This yielded a per-class distance profile showing how far forget representations lie from each retain cluster. To enable comparison across different models, we then applied normalization

on each group's averaged distances. Table 4 summarizes the results for CIFAR-10, ResNet-18, and the statistics for 'truck' forget samples in a 10% random forgetting (same setup as Table 1). The findings show that forget representations in CoUn are consistently closer to semantically similar retain clusters, and more importantly, CoUn achieves distance statistics that are closer to those of the Retrain model compared to other baselines. The smaller the distance means higher semantic similarity. From Table 4, we can see that 'truck' samples have the highest semantic similarity with 'automobile'.

Prediction-Level Results. Tables 5 and 6 present additional prediction-level results for a single forget class across different baselines and datasets. The Original model has 100% accuracy on the forget 'truck' samples since these samples are part of its training data. Furthermore, baselines based on label manipulation or weight perturbation produce predictions somewhat similar to Retrain, but their misclassifications are less concentrated on semantically related classes. By comparison, CoUn more effectively redirects forget samples toward semantically similar clusters, thereby yielding prediction distributions that are closer to those of the Retrain model.

D Proof of Lemma 1

We have

where inequality (8) is obtained due to the L-Lipschitz assumption for feature extractor f θ u and inequality (9) is obtained by taking supremum from both sides of inequality (8).

Training f θ u on the retain data tends to converge to flat minima, i.e., regions in parameter space where the loss landscape is broad and has low curvature [42]. Consequently, flat minima correspond

Original

Airplane

Automobile

Bird

Cat

Deer

Dog

Frog

Horse

Ship

Truck

to functions whose outputs vary only gently under small perturbations around the training points (i.e., they have a low local Lipschitz constant at those points). However, there is no guarantee that, at these flat minima, the loss landscape remains flat with respect to the forget data. Therefore, in general, after convergence we have

where L r and L u denote the Lipschitz constants evaluated on the retain and forget data, respectively.

Based on Equation (5) and inequality (9), we have

and

In particular, Equation (11) computes the probability that, for images in the retain data, sup x = t ( i ) , x ′ ∈ t ′ ( i ) t, t ′ ∼T ∥ x -x ′ ∥ exceeds ϵ/L r , while Equation (12) computes the probability that, for images in the forget data, sup x = t ( i ) , x ′ ∈ t ′ ( i ) t, t ′ ∼T ∥ x -x ′ ∥ exceeds ϵ/L u . Considering inequality (10), we

have ϵ/L u ≤ ϵ/L r . Since in random forgetting the samples are drawn I.I.D., we have R r [ ϵ ] ≤ R u [ ϵ ] . This follows because the threshold ϵ/L u used to compute R u [ ϵ ] is lower than the threshold ϵ/L r used to compute R r [ ϵ ] .

E Further Implementation Details

E.1 Model Architectures

For VGG-16 [39], we use a 1024-dimensional encoder head. For the ViT [40] model, we adopt a patch size of 4 × 4, an embedding dimension of 512, an MLP hidden dimension of 1024, 12 attention heads of size 64, and a depth of 6 transformer layers. Both dropout and embedding dropout are set to 0.1.

E.2 Training and Unlearning Configurations

Original Model θ o Training. Following [8, 9, 10], we train original models for all different datasets and model architectures for a total of 182 epochs. The batch size is set to 256. An SGD optimizer is used with an initial learning rate of 0.1 and a multi-step learning rate scheduler that reduces the learning rate by a factor of 10 at 50% and 75% of the training epochs. Momentum is set to 0.9, and weight decay is set to 5 × 10 -4 . The transformation distribution used for data augmentation is described in Appendix E.3. For VGG-16, we use a linear warmup phase for the first 75 epochs.

Unlearned Model θ u Training. For unlearning, all methods are run for 50 epochs. We used the SGD optimizer with a learning rate tuned within the range of [0.01, 0.1] for each MU method. A cosine annealing learning rate scheduler is used with a minimum learning rate set to 1 × 10 -4 . Momentum is set to 0.9, and weight decay is set to 5 × 10 -4 . The transformation distribution used for data augmentation is described in Appendix E.3. Additional details for each MU method are listed as follows:

BadT: The temperature is set to 1.

SSD: The weight selection is tuned in the interval [0.1, 100], while the dampening constant is tuned in the interval [0.1, 5].

NegGrad+: The β hyperparameter is tuned in the interval [0.95, 0.9999].

SCRUB: The temperature is set to 1. The number of maximization steps is tuned in the interval [1, 10]. Both γ and α are tuned in the interval [0.1, 3].

CU: The contrastive scaling constant is tuned within the interval [0.1, 2] and the temperature is tuned within the interval of (0, 0.2]. The constant ω is tuned within the interval [1, 5].

ℓ 1 -sparse: The ℓ 1 regularization parameter is tuned in the interval [ 10 -4 , 10 -1 ]. ℓ 1 regularization is applied for 4 epochs, except for sequential forgetting experiments, where it is applied for 2 epochs and then reapplied every 10 epochs for a total of 50 epochs.

SalUn: The mask threshold is tuned within the interval of [0.1, 1.0].

NoT: For all model architectures, the first CNN layer (index: 0) is negated. For ViT [40], the positional representations and the second patch representation layer are negated (indices: 0 and 4).

CoUn : The scaling constant λ is tuned within the interval [0.1, 6], and the CL temperature τ is tuned within the interval of (0, 0.3].

All experiments are implemented using the PyTorch platform [43] and run using NVIDIA Tesla V100 GPUs.

E.3 Data Augmentation

In our experiments, the following operations are applied sequentially to augment images:

Random cropping (C): Output image size of 32 × 32 for CIFAR-10/100 and 64 × 64 for TinyImageNet, with a padding of 4 on each image border.

Random horizontal flip (H): Applied with a probability of 0.5.

Color normalization (N): Applied using mean values (0.4914, 0.4822, 0.4465) and standard deviations (0.2023, 0.1994, 0.2010).

However, in some ablation experiments, the following operations are added between horizontal flip and color normalization to augment images:

Random color jitter (J): Applied with a probability of 0.8. Brightness, contrast, saturation, and hue are set to 0.8, 0.8, 0.8, and 0.2, respectively.

Random grayscale (G): Applied with a probability of 0.2.

F Further Results

F.1 Random Forgetting: Forget Ratio 10% (Additional Baselines)

Table 7 presents comparisons of CoUn with additional baseline methods: BadT (AAAI, 2023), SSD (AAAI, 2024), SCRUB (NeurIPS, 2023), and CU [33] using random data forgetting with a 10% forget ratio. CoUn consistently achieves superior performance compared to all baselines. Since BadT, SSD, SCRUB, and CU do not perform better than other baselines, we did not include them under different settings. Further, BadT and SCRUB demand higher computational resources due to their reliance on two teacher models (Original and Random) to guide the unlearned model.

F.2 Class-wise Forgetting

Table 8 presents the results for class-wise forgetting. All baselines, including FT, exhibit minimal performance gaps with the Retrain model, suggesting that class-wise forgetting is relatively easy and can be effectively addressed using just FT (i.e., through catastrophic forgetting). This observation aligns with the findings from [11], which shows that lower entanglement between retain and forget data simplifies the unlearning task, making class-wise forgetting easier than random forgetting. This trend is further illustrated by the similarity between the representations of FT and CoUn in Figure 3 and those of the Retrain model in Figure 1. Nevertheless, CoUn achieves competitive results across all baselines. In this paper, the majority of our experiments focus on the more challenging unlearning scenarios (i.e., random forgetting).

F.3 Integration of CoUn 's CL Module with Baselines: Detailed Results

Tables 9 and 10 provide detailed results for integrating CoUn 's CL module with existing baselines for 10% and 50% random data forgetting, respectively. Results show that adding our CL module significantly empowers the performance of existing MU methods, as measured by the average gap.

F.4 Effect of CL Transformation on Representation Space

Huang et al. [35] provides a theoretical framework for understanding the generalization ability of CL, emphasizing the role of data augmentation and representation properties. They show that stronger transformations 1 in CL yield more compact and well-separated clusters in the representation space. These insights are particularly relevant to our observations on the effect of transformation strength in the context of MU.

In MU, the goal of CL is not to enhance clustering, but rather to weaken the clustering of forget data. Looser clustering allows their representations to be pushed toward clusters of other retain representations that are semantically similar to the forget representations, even if those clusters are different from the original ones of the forget data. Therefore, strong augmentations reduce the likelihood of cluster overlap, even in the presence of false negative samples.

As illustrated in Figure 9, weaker transformations lead to more effective unlearning. This is because they result in less tightly clustered representations, allowing forget data to overlap with retain data from other classes, particularity in the absence of supervised signals for forget data. Figure 12 further shows that stronger CL transformations (e.g., T CL = CHJGN) produce tighter clusters of forget data compared to weaker ones (e.g., T CL = CHN), consistent with the findings of [35]. However, from an MU perspective, such tight clustering impedes unlearning. Hence, using simpler CL transformations generally enhances unlearning effectiveness. This inverse relationship between representation compactness and unlearning efficacy is reinforced by the results in Figure 9.

CoUn (

CE=

CHN &

CL=

CHN)

CoUn (

CE=

CHN &

CL=

CHJGN)

Airplane

Automobile

Bird

Cat

Deer

Dog

Frog

Horse

Ship

Truck

Dataset

&Model

Method

CL

Accuracy (%)

Efficacy (%)

Gap

↓

Comp. Cost

(PFLOPs)

↓

Retain (

∆

↓

)

Unlearn (

∆

↓

)

Test (

∆

↓

)

MIA (

∆

↓

)

CIFAR-10

ResNet-18

Retrain

-

100.00

±

0.00 (0.00)

7.29

±

0.36 (0.00)

92.28

±

0.23 (0.00)

17.33

±

0.65 (0.00)

0.00

15.24

FT

✗

99.38

±

0.24 (0.62)

6.32

±

0.41 (0.97)

91.91

±

0.41 (0.37)

12.64

±

0.51 (4.69)

1.66

2.51

✓

99.97

±

0.03 (0.03)

6.19

±

0.30 (1.10)

92.36

±

0.26 (0.08)

16.94

±

0.48 (0.39)

0.40

3.35

NegGrad+

✗

100.00

±

0.00 (0.00)

4.06

±

0.20 (0.75)

93.81

±

0.23 (0.86)

9.05

±

0.22 (1.97)

0.90

5.58

✓

100.00

±

0.00 (0.00)

4.65

±

0.25 (0.16)

93.45

±

0.24 (1.22)

11.45

±

0.35 (0.43)

0.45

5.58

ℓ

1

-sparse

✗

99.77

±

0.03 (0.23)

9.02

±

0.16 (1.73)

90.66

±

0.24 (1.62)

16.05

±

0.29 (1.28)

1.22

4.19

✓

100.00

±

0.00 (0.00)

6.91

±

0.23 (0.38)

92.30

±

0.19 (0.02)

17.14

±

0.52 (0.19)

0.15

4.47

NoT

✗

99.98

±

0.01 (0.02)

5.95

±

0.18 (1.34)

92.84

±

0.18 (0.56)

13.90

±

0.37 (3.43)

1.34

3.35

✓

99.99

±

0.01 (0.01)

6.84

±

1.21 (0.45)

91.64

±

0.73 (0.64)

17.00

±

1.46 (0.33)

0.36

5.58

CIFAR-100

ResNet-18

Retrain

-

99.98

±

0.01 (0.00)

31.41

±

0.40 (0.00)

68.41

±

0.34 (0.00)

58.35

±

0.53 (0.00)

0.00

15.24

FT

✗

99.98

±

0.01 (0.00)

17.36

±

0.19 (14.05)

74.16

±

0.39 (5.75)

50.60

±

0.42 (7.75)

6.89

4.19

✓

99.98

±

0.01 (0.00)

31.43

±

1.75 (0.02)

65.60

±

0.71 (2.81)

55.99

±

1.18 (2.36)

1.30

5.58

NegGrad+

✗

99.98

±

0.01 (0.00)

26.32

±

0.21 (5.09)

71.98

±

0.30 (3.57)

52.32

±

0.36 (6.03)

3.67

5.36

✓

99.98

±

0.01 (0.00)

31.55

±

0.39 (0.14)

68.34

±

0.30 (0.07)

56.34

±

0.45 (2.01)

0.55

6.70

ℓ

1

-sparse

✗

99.94

±

0.02 (0.04)

32.26

±

0.23 (0.85)

67.66

±

0.35 (0.75)

51.54

±

0.29 (6.81)

2.11

4.19

✓

99.98

±

0.00 (0.00)

29.93

±

0.27 (1.48)

68.35

±

0.39 (0.06)

54.84

±

0.55 (3.51)

1.26

5.58

NoT

✗

98.64

±

0.43 (1.34)

26.43

±

0.75 (4.98)

67.97

±

0.83 (0.44)

43.82

±

0.60 (14.53)

5.32

2.01

✓

99.98

±

0.01 (0.00)

26.01

±

0.42 (5.40)

69.01

±

0.48 (0.60)

54.30

±

0.53 (4.05)

2.51

5.58

TinyImageNet

ResNet-18

Retrain

-

99.99

±

0.00 (0.00)

43.01

±

0.20 (0.00)

57.28

±

0.43 (0.00)

71.22

±

0.17 (0.00)

0.00

121.93

FT

✗

99.99

±

0.00 (0.00)

36.78

±

0.18 (6.23)

60.59

±

0.38 (3.31)

66.28

±

0.20 (4.94)

3.62

33.50

✓

99.98

±

0.01 (0.01)

43.21

±

1.57 (0.20)

55.75

±

1.34 (1.53)

66.59

±

0.41 (4.63)

1.59

44.66

NegGrad+

✗

99.99

±

0.00 (0.00)

47.62

±

0.25 (4.61)

58.85

±

0.32 (1.57)

66.43

±

0.33 (4.79)

2.74

33.50

✓

99.98

±

0.01 (0.01)

45.78

±

0.19 (2.77)

56.68

±

0.36 (0.60)

66.77

±

0.28 (4.45)

1.96

55.83

ℓ

1

-sparse

✗

99.99

±

0.00 (0.00)

38.83

±

0.21 (4.18)

60.25

±

0.30 (2.97)

65.82

±

0.21 (5.40)

3.14

33.50

✓

99.94

±

0.01 (0.05)

42.11

±

0.22 (0.90)

57.02

±

0.43 (0.26)

65.92

±

0.26 (5.30)

1.63

44.66

NoT

✗

99.99

±

0.00 (0.00)

40.94

±

0.43 (2.07)

58.27

±

0.39 (0.99)

66.23

±

0.36 (4.99)

2.01

33.50

✓

99.99

±

0.00 (0.00)

42.11

±

0.29 (0.90)

57.15

±

0.51 (0.13)

65.91

±

0.19 (5.31)

1.58

44.66

CIFAR-100

VGG-16

Retrain

-

99.65

±

0.18 (0.00)

42.85

±

0.54 (0.00)

57.70

±

0.47 (0.00)

50.19

±

0.93 (0.00)

0.00

8.67

FT

✗

97.71

±

0.25 (1.94)

29.82

±

0.58 (13.03)

63.72

±

0.43 (6.02)

39.98

±

0.62 (10.21)

7.80

1.43

✓

99.88

±

0.02 (0.23)

42.37

±

0.80 (0.48)

55.19

±

0.68 (2.51)

50.00

±

0.68 (0.19)

0.85

3.18

NegGrad+

✗

95.54

±

0.56 (4.11)

43.42

±

0.38 (0.57)

58.52

±

0.44 (0.82)

43.51

±

0.36 (6.68)

3.04

3.18

✓

96.70

±

0.00 (2.95)

42.92

±

0.00 (0.07)

59.14

±

0.00 (1.44)

46.61

±

0.00 (3.58)

2.01

3.18

ℓ

1

-sparse

✗

98.25

±

1.53 (1.40)

34.24

±

1.87 (8.61)

62.76

±

1.65 (5.06)

42.12

±

0.55 (8.07)

5.79

1.91

✓

99.34

±

0.23 (0.31)

42.78

±

0.38 (0.07)

55.06

±

0.39 (2.64)

46.41

±

0.50 (3.78)

1.70

3.18

NoT

✗

94.23

±

7.94 (5.42)

34.64

±

7.05 (8.21)

61.58

±

4.67 (3.88)

39.84

±

1.62 (10.35)

6.96

2.38

✓

99.55

±

0.19 (0.10)

42.78

±

2.71 (0.07)

55.17

±

1.71 (2.53)

48.88

±

1.92 (1.31)

1.00

3.18

CIFAR-100

ViT

Retrain

-

99.98

±

0.01 (0.00)

48.07

±

0.33 (0.00)

52.40

±

0.58 (0.00)

69.54

±

0.29 (0.00)

0.00

48.35

FT

✗

98.71

±

0.30 (1.27)

10.91

±

0.96 (37.16)

56.79

±

0.73 (4.39)

28.18

±

0.93 (41.36)

21.05

1.61

✓

99.71

±

0.62 (0.27)

45.95

±

3.70 (2.12)

49.45

±

2.15 (2.95)

59.24

±

1.48 (10.30)

3.91

10.74

NegGrad+

✗

99.30

±

0.13 (0.68)

45.35

±

0.48 (2.72)

50.82

±

0.47 (1.58)

55.07

±

0.33 (14.47)

4.86

6.45

✓

99.14

±

0.13 (0.84)

45.78

±

0.38 (2.29)

50.93

±

0.39 (1.47)

57.96

±

0.50 (11.57)

4.04

5.37

ℓ

1

-sparse

✗

71.18

±

0.57 (28.80)

47.30

±

0.26 (0.77)

53.32

±

0.52 (0.92)

44.22

±

2.98 (25.32)

13.95

8.06

✓

95.83

±

0.68 (4.15)

49.36

±

0.19 (1.29)

50.87

±

0.54 (1.53)

53.66

±

0.75 (15.88)

5.71

10.74

NoT

✗

97.86

±

1.71 (2.12)

31.81

±

2.05 (16.26)

55.51

±

1.15 (3.11)

48.85

±

2.48 (20.69)

10.55

3.22

✓

99.93

±

0.02 (0.05)

50.21

±

0.66 (2.14)

49.50

±

0.69 (2.90)

65.80

±

0.44 (3.74)

2.21

10.74

G Broader Impacts

Research in machine unlearning holds significant societal value by empowering users to request the removal of their data from models and enhancing model safety and fairness through the elimination of harmful or outdated information. This work is exploratory in nature-we propose an approximate unlearning framework that uses contrastive learning to push forget representations into clusters of other retain samples that are semantically similar to the forget samples. Due to cluster collision, these retain samples may belong to clusters different from the original clusters of the forget samples. Given the nature of our approach, we do not foresee any direct negative societal impacts stemming from this work.

H Limitations and Future Work

While CoUn marks a step forward in leveraging CL for unlearning, its evaluation is currently limited to vision-based classification tasks on relatively small datasets (CIFAR-10/100 [36] and TinyImageNet [37]). Future work could explore its scalability to larger datasets such as ImageNet [44] and its applicability to other domains, including natural language processing. Additionally, although CoUn uses InfoNCE as the contrastive loss, investigating alternative self-supervised objectives, such as cross-correlation-based losses [31, 32], on unlearning performance presents an interesting direction

for future research. Moreover, like prior methods [8, 9, 10], CoUn relies heavily on access to retain data for effective unlearning. Investigating performance of approximate unlearning methods under partial access to retain data would be an important direction for future research. Finally, while CL introduces additional computational overhead due to augmented data and extra forward passes, CoUn consistently outperforms baselines even when computational budgets are matched. Future work could explore strategies to reduce this cost without sacrificing performance.

NeurIPS Paper Checklist

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Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?

Answer: [Yes]

Justification: In the abstract and introduction, we first introduce the relevant concepts of machine unlearning and summarize existing methods, analyzing their shortcomings. Notably, existing methods manipulate labels or perturb model weights for unlearning. Most methods also require access to forget data. We focus on addressing the machine unlearning problem by studying how a retrained model behaves with respect to forget data. Our proposed method CoUn , which employs contrastive learning and supervised learning, aims to close the performance gap with retraining from scratch. Additionally, we analyze CoUn 's effectiveness across various scenarios including theoretical and experimental evaluation.

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Question: For each theoretical result, does the paper provide the full set of assumptions and a complete (and correct) proof?

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Question: Does the paper fully disclose all the information needed to reproduce the main experimental results of the paper to the extent that it affects the main claims and/or conclusions of the paper (regardless of whether the code and data are provided or not)?

Answer: [Yes]

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Question: Does the paper provide open access to the data and code, with sufficient instructions to faithfully reproduce the main experimental results, as described in supplemental material?

Answer: [Yes]

Justification: We uploaded CoUn code in the supplementary material and will be made publicly available. All data used in this study are publicly available. The baseline methods compared in the paper are open source and results can be reproduced directly after following the implementation details provided in Appendix E.2.

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Question: Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?

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Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces a novel approximate unlearning method leveraging the advantage of contrastive learning to manipulate the similarity of retain and forget data. The paper challenged the traditional contrastive learning can indirectly push the forget data to the clusters of retain data and proposed additional supervised learning loss function to cluster the forget data. Therefore, the contrastive learning is pushing away the entire cluster of forget from the retain. This paper also implements extensive experiments and intuitive visualization to prove the effectiveness of proposed method\n\nSTRENGTHS AND WEAKNESSES:\nStrengths\nThe motivation of the work is clear. The results in Table 1 and Figure 4 look promising demonstrating effectiveness of the work.  Introduction, Technical Method and Experiment are easy to follow. The method is simple, well-motivated and efficient enough. More importantly, the proposed method can be integrated with other baseline for better unlearning performance.\n\nWeaknesses\nTheoretical contribution is weak as the main part of the theory came from other existing paper and the author did not state and explain the theory clearly. \n1.\tThe theoretical analysis is hard to follow. Notations are missing, (e.g. R[\\epsilon] ) I guess this is the probability that the encoder representation to generate two views differences larger than $\\epsilon$, which is a typical Lipchitz equation definition. But there is no exact notation for that. \n2.\tWhat is $\\mu_{l}^{T}$?  and What is $\\rho^{max}$. Althought the author mention that the proof of Theorem 1 can be found at paper [34], I would still suggest to place it under appendix and show clearly how (e.g. R[\\epsilon]) interact with Theorem 1. \n3.\tIn line 648, I am not sure how author ensures the equation (10)  $L_r  \\leq L_u \\leq L$ holds in general. More clarifications needed.\nExperiments in Table 2 can apparently be extended to more data drops (e.g. 20%, 30%, 40%, 50%...). 10% data forgetting may not be representative enough. It will be interesting to see comparison on class-wise forgetting with comprehensive baselines. Table 1 only implement on CIFAR-10 with FT and Retrain baseline.\n\nQUESTIONS:\n1.\tThe theoretical analysis is hard to follow. Notations are missing, (e.g. R[\\epsilon] ) I guess this is the probability that the encoder representation to generate two views differences larger than $\\epsilon$, which is a typical Lipchitz equation definition. But there is no exact notation for that. \n2.\tWhat is $\\mu_{l}^{T}$?  and What is $\\rho^{max}$. Althought the author mention that the proof of Theorem 1 can be found at paper [34], I would still suggest to place it under appendix and show clearly how (e.g. R[\\epsilon]) interact with Theorem 1. \n3.\tIn line 648, I am not sure how author ensures the equation (10)  $L_r  \\leq L_u \\leq L$ holds in general. More clarifications needed.\nExperiments in Table 2 can apparently be extended to more data drops (e.g. 20%, 30%, 40%, 50%...). 10% data forgetting may not be representative enough. It will be interesting to see comparison on class-wise forgetting with comprehensive baselines. Table 1 only implement on CIFAR-10 with FT and Retrain baseline.\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-06-30"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposed applying the contrastive learning method assisted with supervised learning method exclusively on retain data to conduct machine unlearning tasks. The experimental results demonstrated that the proposed approach achieved superior performance equivalence w.r.t. the gold-standard retrain model.\n\nSTRENGTHS AND WEAKNESSES:\nStrength\n1. Although contrastive learning is a known technique, it is relatively new to apply this technique in machine unlearning tasks, which relieves the constraints for forget data access, and achieve good model utility. In addition, the reviewer empirically agrees that the forget data representation is not necessarily pushed away from its original cluster, especially in a random erasing setting. The proposed approach may inspire future research in this area for better privacy and security in ML space, given the richness in contrastive learning.\n2. The empirical experimental study provides a clear view of the performance equivalence compared with retrain model with multiple state-of-arts machine unlearning methods.\n3. The theoretical analysis presents a lower misclassification upper bound for retain data, implying higher misclassification rate over forget data using contrastive learning.\n\nWeakness\n1. The proposed approach is a vanilla contrastive learning method, which can also be considered as model weight perturbation categories in general. There is no specific mechanism to prevent excessive or insufficient perturbation.\n2. More ablation studies can be conducted to understand the behavior of the proposed approach and hyperparameter choices. Please check the question section for more details.\n\nQUESTIONS:\n1. It would be good to conduct experiments to understand how likely CL would suffer from excessive or insufficient perturbation, for example, with longer or less training epochs.\n2. How sensitive is the $\\lambda$ choice? Are the reported results in Table 2 using the same $\\lambda$? If not, how much performance loss would be introduced if using the same $\\lambda$ (from a careless hyperparameter tuning).\n3. Does the reported computation cost consider the hyperparameter tuning costs for both baseline methods and proposed methods?\n4. What would happen if the supervised term were completely neglected?\n5. In Line 362, it claims that the transformation should stay the same for CL and supervised learning when $CHN$ is used. Is this also the case for other transformation distribution choices?\n\nLIMITATIONS:\nThere is no obvious limitation or negative societal impact.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-06-30"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes to perform both contrastive learning and supervised learning on retain data to improve the unlearning effects.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\n1. The proposed method is simple yet effective. It incorporates contrastive loss in the finetuning loss and presents clear performance improvement compared to standard fine-tuning.\n\n2. Experiments are comprehensive.\n\n3. The proposed method surpasses baseline methods in multiple unlearning scenarios.\n\n4. Notations, figures, tables, and theorems are very clear. The paper is well-organized.\n\t\n\n\nWeaknesses:\n\n1. Sec 3.2 emphasizes that conducting CL on retain data indirectly pushes forget representations toward high-similarity retain clusters, and this can improve forget quality. Here, more empirical results are needed to support this motivation and assumption. Specifically, for a model A trained on the whole dataset and a model B retrained on only retain data, what are the differences in the similarity between forget representations and the \"high-similarity\" retain clusters? For comparison, there should be two more charts of the Model A before unlearning in Figure 1. Moreover, a rigid table of statistical values is more desired than Figures 1 and 3 for a valid presentation. \n\n2. Furthermore, it's unclear why pushing forget representations toward other retain samples can improve forget quality, which is defined as forget accuracy or MIA efficacy. Since approximate unlearning sets retraining as a standard, improving forget quality should refer to a closer gap in forget accuracy or MIA efficacy. Regarding this, will the action of pushing forget representations increase or decrease these two metrics? Is this action imitating Retraining? Otherwise,  how do you determine whether there will be an improvement?\n\n3. The theoretical analysis says that CoUn yields a higher misclassification rate on forget data compared to retain data. This property is not surprising since the CoUn performs both contrastive learning and supervised learning on retain data, and the forget data are treated as test data. However, this analysis does not support the reason why CoUn provides better empirical unlearning performance, since from Table 2 all other baseline methods have higher retain accuracy and lower forget accuracy. The authentic significance of such theoretical analysis is quite questionable.\n\n4. Although CoUn consistently shows the best Avg. Gap in the figures and tables, different settings yield different second-best methods. For example, recent methods like Salun and NoT sometimes outperform NegGrad, while in other cases they do not. Yet, each new method claims to outperform previous ones when introduced. This inconsistency in performance raises concerns about the fairness and accuracy of reproducing baseline methods.\n\n5. In some cases CoUn's superiority in Avg. The gap is marginal, but it costs more computation resources.\n\nQUESTIONS:\nSee the weaknesses.\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 5, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper tackles the problem of machine unlearning by incorporating contrastive learning. Specifically, the proposed method applies contrastive learning to adjust forget representations and supervised learning to maintain retain representations within their clusters sharing similar semantics. Experimental results show the effectiveness of the proposed method across small image datasets with CNNs and a ViT.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths**\n\n+ Machine unlearning is an important topic for deployment of machine learning models, and this work aims to make a step forward in this field.\n\n+ The idea is simple and supported with some theoretical results.\n\n\n**Weaknesses**\n\n- I agree with the importance of machine unlearning, but skeptical whether the current evaluation strategy is proper to assess machine unlearning methods. it is possible that the information about \"training data to forget\" still remain in the new model but its accuracy matches with the gold-standard retrain model by another reason, e.g., losing other information. In other words, accuracy matching does not imply that two models exhibit exactly the same knowledge, and it might not satisfy GDPR; rather, prediction matching would be more suitable.\n\n- Basically, I don't think classification is a proper task to assess forgetting of specific data; rather, reconstruction for specific data would be more suitable. For example, it is possible that forgetting some data allows the new model to have more capacity to better keep the information of other training data, resulting in better classification accuracy. In this case, unlearning would increase classification accuracy.\n\n- Contrastive learning has been applied to many fields in machine learning, so the usage of contrastive learning without much adaptation as done in this paper has a limited novelty.\n\n- Theorem 1 is originated from Huang et al. [34], which considers pure contrastive learning settings; however, the proposed method learns through both contrastive learning and supervised learning, so Theorem 1 might not hold.\n\n- No forgetting measure in experiments, which has commonly been employed in prior works.\n\n- Performance gain seems to be consistent but not so significant, raising concerns on the trade-off between the additional cost introduced by contrastive learning versus the gain.\n\n- Experiments are done in small image datasets, so its scalability and generalizability to other datasets/domains are not clear.\n\n- Experimental results might not be reproducible as the description on experimental settings is not sufficient and the provided code is only for a portion of experiments. For example, I couldn't find the configuration for ViT experiments, and \"ViT\" is not enough to figure out and replicate its specification.\n\n- A similar work by [Lee et al.] is not cited/discussed.\n\n[Lee et al.] Contrastive Unlearning: A Contrastive Approach to Machine Unlearning. arXiv 2024.\n\n- typo: NIPS -> NeurIPS\n\nQUESTIONS:\nPlease address concerns in Weaknesses above.\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-02"}