OSLO: One-Shot Label-Only Membership Inference Attacks

Authors: yuefeng  peng
jaechul  roh
subhransu  maji
amir  houmansadr
Venue: NeurIPS_cc_2024_Conference
Published: 2024-05-15 02:57:15

Abstract: We introduce One-Shot Label-Only (OSLO) membership inference attacks (MIAs), which accurately infer a given sample's membership in a target model's training set with high precision using just a single query, where the target model only returns the predicted hard label. 
  This is in contrast to state-of-the-art label-only attacks which require $\sim6000$ queries, yet get attack precisions lower than OSLO's.
  OSLO leverages transfer-based black-box adversarial attacks. The core idea is that a member sample exhibits more resistance to adversarial perturbations than  a non-member. We compare OSLO against state-of-the-art label-only attacks and demonstrate that, despite requiring only one query, our method significantly outperforms previous attacks in terms of precision and true positive rate (TPR) under the same false positive rates (FPR). For example, compared to previous label-only MIAs, OSLO achieves a TPR that is at least 7$\times$ higher under a 1\% FPR and at least 22$\times$ higher under a 0.1\% FPR on CIFAR100 for a ResNet18 model. We evaluated multiple defense mechanisms against OSLO.

Main paper: 
 introduction: 
 Deep learning (DL) models are vulnerable to membership inference attacks (MIAs), where an attacker attempts to infer whether a given sample is in the target model's training set [1] . The success of such MIAs may lead to severe individual privacy breaches as DL models are often trained on private data such as medical records [2] and facial images [3] . Existing black-box MIAs fall into two categories: score-based MIAs [1, 4, 5] and decision-based MIAs [6, 7] , also known as label-only MIAs. Score-based attacks assume access to the model's output confidence scores, which can be defended against if the model only outputs a label. In contrast, label-only attacks infer membership based on the labels returned by the target model, which is a stricter and more practical threat model.State-of-the-art label-only MIAs measure the sample's robustness to adversarial perturbations, classifying samples with higher robustness as members. This robustness serves as a proxy for model confidence, which is typically higher for training samples. These attacks utilize query-based blackbox adversarial attacks [8, 9] to determine the amount of necessary adversarial perturbation for each sample. However, accurately estimating this requires a large number of queries to the model, sometimes up to thousands for each sample. This approach is not only costly but also easily detectable [10] . Furthermore, these attacks often lack precision and are unsuccessful in the low false positive rate regime, as indicated by previous studies [11] and our evaluations. In summary, existing label-only MIAs are not practical. Table 1 : Comparison to previous label-only attacks. We report the highest attack precision that these attacks can achieve with a recall greater than 1% on CIFAR-10 using a ResNet18 model. [7] ✓ ✓ 69.2% ∼ 10 Boundary Attack (Gaussian Noise) [7] ✓ ✓ 61.3% ∼700 Boundary Attack (HopSkipJump) [7, 6] ✓ ✓ 64.5% ∼6000 Boundary Attack (QEBA) [6] ✓ ✓ 71.4% ∼6000 OSLO (Ours) ✓ ✗ 96.2% 1We propose novel One-Shot Label-Only (OSLO) MIAs that can infer a sample's membership in the target model's training set with just a single query, even when the target model only returns hard labels for input samples. Table 1 compares OSLO to previous label-only MIAs. OSLO is based on constructing transfer-based adversarial example, with just enough magnitude of adversarial perturbation added to each sample to cause misclassification if the sample is non-member (but not enough if it is a member) based on a set of source and validation models, a technique that was initially proposed in [12] . Prior work has considered using a fixed threshold of adversarial perturbation across all samples to infer membership status, resulting in a lower precision [7, 6] .We extensively compared OSLO with state-of-the-art label-only methods [7, 6] . Following recent standards, we evaluated the attacks using metrics such as the true positive rate (TPR) under a low false positive rate (FPR) and performed a precision/recall analysis. Our results show that previous label-only MIAs perfom poorly, exhibiting high false positive rates. In contrast, OSLO achieves high precision in identifying members, outperforming prior work by a significant margin. For example, as shown in Figure 2 , OSLO is 5× to 67× more powerful than other label-only MIAs in terms of TPR under 0.1% FPR across three datasets using a ResNet18 [13] model. OSLO achieves over 95% precision on all three datasets on ResNet18 model with a recall greater than 0.01, while the highest precision achieved by other attacks is only 71.4%, 84.2%, and 67.9% respectively. Furthermore, we conduct a detailed comparison of OSLO with previous work, exploring why previous label-only attacks fail to achieve high precision.2 Background and preliminariesQuestion: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?Answer: [Yes] Justification: Our claims are made with a clearly defined scope, and the contributions of the paper are accurately outlined, ensuring alignment with the documented empirical evidence. For example, the performance claims of our method are precisely specified using the evaluation metrics and settings and are supported by our experimental results.Guidelines:• The answer NA means that the abstract and introduction do not include the claims made in the paper. • The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No or NA answer to this question will not be perceived well by the reviewers. • The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings. • It is fine to include aspirational goals as motivation as long as it is clear that these goals are not attained by the paper. 
adversarial attacks: 
 Early works [14, 15] have demonstrated the susceptibility of deep neural networks (DNNs) to adversarial attacks. These attacks involve crafting subtle perturbations to input data, causing a DNN to make incorrect predictions while the perturbations remain almost imperceptible to humans. Adversarial attacks can significantly compromise model performance, resulting in issues like misclassification or misgeneration. These attacks are typically classified based on the adversary's level of access to the model [16] : white-box and black-box settings. In white-box attacks [17, 15, 18, 19, 20, 21] , adversaries have full knowledge of the victim model, including its architecture, parameters, and gradients. In contrast, black-box attacks [22, 23] limit adversaries to querying the model and obtaining output labels or confidence scores. We primarily discuss black-box attacks to align with the threat model of our MIA settings. Membership inference attacks (MIAs) [27, 28, 29, 30, 31, 32, 33] aim to determine whether a specific data sample is a member of the training dataset of a target model. Existing MIAs often assume that the attacker can access the target model's confidence scores to infer membership. These score-based attacks exploit the difference in confidence scores for training versus non-training data, as models often exhibit higher confidence for samples they have seen during training [1, 4, 5] . Such attacks can be easily defended by limiting access to only the predicted labels, which reduces the amount of information available to the attacker.Label-Only MIAs. Compared to score-based attacks, a more practical and stringent type of attack is decision-based or label-only MIAs [7, 31] , which operate under the constraint of having access only to the final decision labels. Several label-only attacks have been proposed. For example, inspired by the transferability of adversarial examples, transfer attacks [31] explore the transferability of membership information. They use a shadow dataset labeled by the target model to train a shadow model and perform a score-based attack on the shadow model, expecting that the differences between members and non-members in the target model will reflect similarly in the shadow model. Data augmentation attacks [7] exploit the robustness of samples to data augmentation transformations to differentiate members from non-members, with higher robustness indicating membership. Similarly, state-of-the-art label-only MIAs, known as boundary attacks [31, 7] , use the robustness of samples to strategic input perturbations as label-only proxies for the model's confidence, where higher robustness implies a higher confidence score. Boundary attacks have different methods for adding perturbations. For example, Gaussian noise is one method where the attacker continuously adds Gaussian noise until the label changes. Attackers also use adversarial attacks to measure the robustness of samples to adversarial perturbations. Specifically, query-based adversarial attacks like HopSkipJump [9] and QEBA [8] algorithms are used to add perturbations to each sample to generate adversarial examples.Existing label-only MIAs typically require many queries to be effective [6, 7] and struggle to achieve high TPRs at low FPRs [11] . A recent work YOQO [34] reduced the query budget. However, by design, it cannot adjust the TPR-FPR trade-off and remains ineffective in the low FPR regime, limiting its practicality.Question: Does the paper discuss the limitations of the work performed by the authors?Answer: [Yes] Justification: We describe the necessary conditions for our method in Table 1 , and we discuss its limitations and possible solutions in Section 7.Guidelines:• The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those are not discussed in the paper. • The authors are encouraged to create a separate "Limitations" section in their paper.• The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g., independence assumptions, noiseless settings, model well-specification, asymptotic approximations only holding locally). The authors should reflect on how these assumptions might be violated in practice and what the implications would be. • The authors should reflect on the scope of the claims made, e.g., if the approach was only tested on a few datasets or with a few runs. In general, empirical results often depend on implicit assumptions, which should be articulated. • The authors should reflect on the factors that influence the performance of the approach.For example, a facial recognition algorithm may perform poorly when image resolution is low or images are taken in low lighting. Or a speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon.• The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size. • If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairness. • While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, a worse outcome might be that reviewers discover limitations that aren't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an important role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed to not penalize honesty concerning limitations. 
problem definition: 
 Following Ye et al. [35] and Leemann et al. [36] , we view MIA as a hypothesis testing problem:EQUATIONSuccessfully rejecting the null hypothesis equates to determining that the sample (x, y) is a member in the target model's training set D. Given a sample for inference, we initially assume that the sample is a non-member (H 0 ). Our objective is to design an attack method that can reject the null hypothesis with high confidence.Attacker's capability. Given a target model f , we assume that the attacker can only access f in a black-box manner, meaning that means that for any input x, the attacker can only observe f (x) but cannot access the internal parameters θ or any intermediate outputs of f . Furthermore, we consider a more restrictive scenario: label-only access, where the attacker can only obtain the predicted labels (i.e., ŷ = arg max f (x)) from the target model, not the confidence scores or probabilities associated with each class. This label-only, black-box attack scenario represents one of the most challenging and realistic settings for conducting attacks against DL models. Similar to previous attacks [1, 7] , it is assumed that the attacker possesses an auxiliary dataset D aux that shares the same distribution as the target model's training set for the purpose of training their surrogate models. However, we do not assume the attacker has any knowledge of the target model, including its architecture.Attacker's goal. The attacker's objective is to reliably infer whether a given sample is a member of the target model's training set with high precision. As underscored by Carlini et al. [5] , identifying individuals within sensitive datasets with high precision poses a significant privacy risk, even if only a few users are correctly identified. Moreover, the precision of these attacks is not just a concern for individual privacy; it also lays the groundwork for more advanced extraction attacks [37] , making the pursuit of high precision in MIAs a critical focus for attackers. Additionally, the attacker aims to infer membership with as few queries as possible, as excessive querying not only incurs significant costs but is also detectable by defenders [10] . Our OSLO limits the query budget to a single query.Previous work [4, 1] has demonstrated that target models tend to be overconfident on members. existing label-only attacks [6, 7] suggest that models are more confident about members, making it more diffficult to "change their mind" on these samples. Their experiments also show that members are usually more robust to adversarial perturbations than non-members. We believe that the differences in the required adversarial perturbation between members and non-members can manifest in two ways: (i) on average, members tend to require more adversarial perturbation than non-members; and (ii) for each individual sample, the member status may demand more adversarial perturbation than the non-member status. Previous label-only MIAs [6, 7] have exploited the former observation, but this has led to high false positive rates and low precision. Our OSLO is based on the latter. We add just enough adversarial perturbation to cause a misclassification for the sample if it is a non-member but not if it is a member. If the sample is not successfully misclassified, it indicates that the added perturbation was insufficient, and the sample is likely a member. Note that here, 'sufficient perturbation' refers to a variable standard for each sample, changing with the sample, rather than a uniform standard for all samples.Previous label-only MIAs face two main issues: low precision and high query budget. We address both issues simultaneously by proposing our transfer-based adversarial attack based attack, which implements the aforementioned hypothesis testing framework. Specifically, we first train a group of surrogate models. For each sample, we construct a transferable adversarial example using the surrogate model(s). Then, we input the crafted adversarial example into the target model and obtain the predicted label. If the sample is misclassified, it indicates that the adversarial example has successfully transferred, implying that there is not enough evidence to reject the null hypothesis H 0 . Otherwise, we reject H 0 and determine the sample as a member. It is worth noting that the perturbation added to each sample should be sufficient for it to transfer as a non-member but not as a member. Therefore, carefully controlling the scale of perturbation added to each sample is required. The framework of OSLO is divided into three stages: surrogate model training, transferable adversarial example construction, and membership inference.The attackers first train their own surrogate models to construct adversarial examples. As assumed in Section 3.2, we assume that the attacker has an auxiliary dataset with the same distribution as the target model's training set. The attacker trains a group of models with different structures on this dataset, training N models for each structure. These models are then divided into source models and validation models based on different purposes in the adversarial example generation stage. Source models are used to calculate gradients for generating adversarial perturbations, while validation models are used to control the magnitude of the added perturbations.Algorithm 1: Transferable adversarial example generation.Input: Benign input x with label y; source models g; validation model h; number of sub-procedures K; number of iterations N ; step size α; maximum perturbation size ϵ and threshold τ ; Output: Transfer-based unrestricted adversarial example x ′ with approximately minimum change;x 0 ← x; for k = 1, 2, . . . , K do x ′ 0 ← x k-1 ; for i = 1 to N doCompute gradient:g i ← ∇ x L(g(x ′i-1 , y); Update adversarial example using the update function:x ′ i ← Update(x ′ i-1 , g i , α); Clip x ′ i to ensure it is within the kϵ K -ball of x: x ′ i ← clip(x ′ i , x -kϵ K , x + kϵ K ); conf ← exp(hy(x ′ i )) j exp(hj (x ′ i )) ; if conf < τ then return x ′ i ; // early-stopping criterion end end x k ← x ′ N ; end return x K ;Transferable adversarial example generation. After the source models are trained, the attacker generates adversarial examples on these models using transfer-based adversarial attacks. Existing transfer-based attacks typically search for adversarial examples within a fixed l p -norm ball and do not minimize the perturbation added. In other words, these attacks allocate a uniform perturbation budget ϵ to all samples, accepting any adversarial examples found within this budget. While this approach is reasonable in the context of general adversarial attacks, it is not suitable for our MIA framework, as OSLO requires finergrained control over the amount of perturbation added.In OSLO, the perturbation budget for each sample is adaptive. Specifically, we utilize the Geometry-Aware (GA) framework proposed in [12] , which employs a set of validation models to regulate the amount of perturbation added to each sample. The process of adding perturbations is incremental. During this process, validation models are used to monitor the transferability of the sample. The perturbation addition process is terminated early-referred to as early stopping-when the perturbation added is sufficient for the sample to deceive the validation model, and the confidence of the correct class on the validation model drops below a specified threshold τ :EQUATION)where h j (x; θ) denotes the logits for class j produced by the validation model, and y is the ground truth class. Through this method, the process can be terminated when the transferability of each sample reaches a certain level, resulting in tailored perturbations for each sample. This can more effectively distinguish the differences of the sample in the in and out worlds.Algorithm 1 outlines our method for generating transferable adversarial examples, adapted from Liu et al.'s GA framework [12] to align with our objective. The algorithm inputs with a benign sample x with its corresponding label y, a set of source models denoted as g, and a set of validation models h. The algorithm proceeds through K sub-procedures, each conducting an iterative refinement of the adversarial example across N iterations, guided by a pre-established step size α and bounded by a maximal perturbation magnitude ϵ. At each iteration, the gradient of the loss function L with respect to the adversarial input is computed, informing the perturbative update. This process is modulated by the validation model h. If at any step the confidence of the ground-truth class falls below the threshold τ , the early stopping is triggered to prevent over-perturbation, thus ensuring that the perturbations are precisely calibrated for each sample.Membership inference. Finally, for each sample x, the attacker inputs the transferable adversarial example x ′ , generated by Algorithm 1, into the target model f . The classification outcome determines the evidence against the null hypothesis H 0 . If arg max i f (x ′ ) i ̸ = y, it suggests insufficient evidence to reject H 0 . In contrast, a classification of arg max i f (x ′ ) i = y allows us to reject H 0 , hence classifying x as a member. Our membership inference strategy seeks to reject H 0 with high confidence, aiming to achieve high precision in the identification of members.Question: For each theoretical result, does the paper provide the full set of assumptions and a complete (and correct) proof?Answer: [NA] Justification: Our method does not introduce new theoretical results.Guidelines:• The answer NA means that the paper does not include theoretical results.• All the theorems, formulas, and proofs in the paper should be numbered and crossreferenced. • All assumptions should be clearly stated or referenced in the statement of any theorems.• The proofs can either appear in the main paper or the supplemental material, but if they appear in the supplemental material, the authors are encouraged to provide a short proof sketch to provide intuition. • Inversely, any informal proof provided in the core of the paper should be complemented by formal proofs provided in appendix or supplemental material. • Theorems and Lemmas that the proof relies upon should be properly referenced. 
evaluation: 
 4.1 Experimental setup Datasets. We utilized three datasets commonly used in prior works [5] : CIFAR-10 [38] , CIFAR-100 [38] and SVHN [39] . For CIFAR-10 and CIFAR-100, we selected 25,000 samples to train the target model under attack. For SVHN, we randomly selected 2,000 samples to train the target model. For each dataset, we trained the surrogate models used for the attack with a set of data that is the same size as the training set of the target model but disjoint. Further details on dataset splits can be found in Appendix A.1.1.Models. We adopted the widely used ResNet18 [13] and DenseNet121 [40] as the target model architectures. In addition to these two, we incorporated five additional model architectures as surrogate models. Detailed training and attack setup are provided in Appendix A.1.Baseline Attacks. We compare OSLO against five state-of-the-art label-only MIAs, including the transfer attack [6] , three boundary attacks [7, 6] , and the data augmentation attack [7] . Detailed settings are provided in Appendix A.1.4. We exclude YOQO [34] from our evaluation, as it is not compatible with our evaluation metrics (see Appendix A.6).Metrics. We employ the following metrics to evaluate the effectiveness of the attacks: (i) attack TPR and FPR [5] : Carlini et al. suggest that membership inference attacks should be analyzed using TPR and FPR, especially considering that TPR in a low FPR setting is crucial for assessing the success of MIAs. We report the log ROC curve to show the TPR and FPR of the attack, with a focus on the low FPR regime; (ii) attack precision and recall: Attack precision reflects how reliably an attack can infer membership. High-precision attacks allow an attacker to credibly violate the privacy of a portion of the samples. Specifically, precision is defined as the proportion of true members correctly identified among all positively predicted members by an adversary. Meanwhile, recall quantifies the proportion of true members that the adversary has correctly identified out of all actual members. We discarded average-case metrics such as accuracy and AUC, as they have been shown not to accurately reflect the threat of MIAs [5] .We first evaluate six attacks, including OSLO, focusing on TPR under low FPR regime. For OSLO, we control the trade-off between TPR and FPR by adjusting the threshold τ during the transferable adversarial example generation phase. A lower τ results in more perturbation added to each sample. Consequently, if the samples still fail to deceive the target model, it is more likely that they are members, thereby reducing FPR. For other attacks, we adjust their corresponding parameters to manage TPR and FPR. For instance, in the boundary attack, increasing the perturbation threshold for identifying members ensures that only samples requiring more significant perturbations are classified as members. Based on the assumption that members generally need greater perturbation than non-members, this method should minimize the number of samples mistakenly identified as members and enhance the credibility of the attack. As shown in Figure 2 , OSLO outperforms all previous label-only MIAs by a large margin.For example, compared to previous attacks, OSLO achieves a TPR that ranges from 5× to 67× higher under 0.1% FPR, and from 3× to 16× higher under 1% FPR on ResNet18, evaluated across three datasets. On DenseNet121, the improvements range from 2× to 12× under 1% FPR. It can be observed that previous attacks were unsuccessful in the low FPR regime, whereas OSLO can successfully identify some members even at low FPR. For example, on CIFAR-100 using ResNet18, at a 0.1% FPR, the best of the other label-only MIAs achieves only a 0.3% TPR, while OSLO reaches 6.7%. Under a 1% FPR, OSLO achieves a TPR of 18.9%, with other attacks reaching at most 2.7%. These comparisons show that, although OSLO requires only one query to the target model, it can reliably identify part of the members, while previous attacks, despite needing to perform up to thousands of queries, are almost unable to credibly identify members.We then measured the trade-off between attack precision and recall. In MIAs, precision is considered a crucial metric, whereas recall is relatively less important [5] . For instance, a precision of 1.0 means that the attacker can be 100% certain that the identified samples are members, leading to significant privacy breaches, even if only a few samples are affected. Conversely, a recall of 1.0 can be achieved by classifying all samples as members, but this does not cause any privacy breach. For MIAs, a desired outcome would be the ability to trade recall for increased precision.As shown in Figure 4 and Figure 5 , OSLO is the only one that effectively trades recall for precision.For example, by trading recall, OSLO achieves over 90% precision across all three datasets with ResNet18 as the target model. Specifically, on CIFAR-10, CIFAR-100, and SVHN, with recall rates of 5%, 44.7%, and 9% respectively, OSLO attained precisions of 96.2%, 92.0%, and 90.9%. In contrast, the highest precision achieved by other attacks at similar recall levels was 67.4%, 82.5%, and 65.2% respectively. This demonstrates that OSLO can identify members with high precision, a capability that all previous label-only attacks could not match. Previous methods could not improve precision by adjusting hyper-parameters, due to limitations inherent in their designs. We discuss this further in Section 6.1.5 Ablation study 5.1 Effect of using different adversarial attacks As introduced in Section 3.4, OSLO leverages transferbased adversarial attacks. We evaluated the membership inference performance of OSLO using six different transfer-based adversarial techniques within its framework, specifically TI [25] , DI [24] , MI [21] , Admix [26] , and the combinable methods TDMI and TMDAI. The results are presented in Figure 6 . Observations reveal no significant differences in the effectiveness of using these various transfer-based attacks. This may suggest that the efficacy of the attack predominantly relies on the inherent design of the OSLO framework rather than the specific choice of the individual transfer techniques.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] Justification: The implementation details and the full experimental setup of our method are provided, and we will also release the code for reproducibility. 
effectiveness of oslo when target and surrogate models use different training algorithms: 
 We assume that the attacker is unaware of the target model's architecture, using surrogate models with different structures. We further explore scenarios where the surrogate and target models are trained with different optimization algorithms. In particular, we evaluated OSLO on CIFAR-10 using ResNet18, where the target models were trained with SGD, while the surrogate models used Adam.The results are shown in Table 2 . Notably, OSLO achieves over 95% precision, with a TPR exceeding 9% at 1% FPR in both settings. These results confirm that OSLO remains effective even when the target models are trained with algorithms different from those of the surrogate models. OSLO uses validation models to adjust the scale of perturbations added to adversarial examples. To understand the impact of validation models, we conducted an ablation study on CIFAR-10 using ResNet18 without the validation models, where a uniform perturbation budget was applied to all samples. The results are shown in Table 3 .These results indicate that without the validation model, applying a uniform perturbation budget across all samples leads to significantly reduced attack effectiveness. For example, at ϵ = 32/255, nearly all members and non-members were misclassified, resulting in both TPR and FPR being very low. This highlights the critical role of validation models in effectively calibrating perturbations. OSLO employs a single query to the target model to determine a sample's membership status. We also explore the potential advantages of extending OSLO to utilize multiple queries per sample, referred to as multi-shot. Specifically, Figure 7 illustrates the precision and recall of OSLO under different adversarial example generation thresholds, τ .We further report on combining results from the current threshold with those from previous, higher thresholds. For example, 'three shots' represents feeding the current shot and the previous two shots' generated images to the target model, identifying samples as members if all three adversarial examples fail to fool the target model. As shown in Figure 7 , we find that using more shots does not yield a significant improvement. We attribute this to the observation that even with multiple shots, only the shot with the lowest τ plays a decisive role.6 Discussion 
why oslo outperforms previous approaches: 
 In this section, we discuss why previous attacks fail to achieve high precision or TPR under low FPR conditions, and how OSLO outperforms them. The boundary attack employs a global threshold of perturbation magnitude to differentiate between members and non-members. However, regardless of the chosen threshold, a considerable proportion of non-members are always found among the samples that require perturbations above this threshold (see the cumulative distribution function (CDF) in Figure 8a ). On the other hand, by lowering the validation threshold τ in OSLO, the proportion of non-members among the failed adversarial attack samples significantly decreases, effectively squeezing out the non-members. For example, when classifying 4.4% of the samples as members, the boundary attack still includes 39% non-members (false positives) among those identified as members, whereas OSLO has only 10% non-members, resulting in 90% attack precision. We further discuss this by measuring the magnitude of the adversarial perturbation added to members and non-members in boundary attack versus OSLO on CIFAR-100, details are in Appendix A.2. In addition to demonstrating the effectiveness of OSLO, we also evaluated six defensive strategies [41, 42, 43] aimed at mitigating membership privacy leakage. These experiments were conducted on the CIFAR-10 dataset using ResNet18 as the target model.We trained three target models with different hyperparameters for each defense mechanism that requires retraining. Detailed configuration settings are provided in Appendix A.1.5. The results are presented in Figure 9 . It can be observed that confidence alteration methods, such as Mem-Guard [41] , are ineffective against OSLO, as expected.Other methods that mitigate memorization require strong regularization to be effective but result in a decrease in the model's test accuracy. Additionally, we tested OSLO against target models trained with adversarial training (details in Appendix A.5), and observed that while adversarial training reduces OSLO's effectiveness to some extent, it is not sufficient as a standalone defense. 
conclusions and limitations: 
 In this paper, we propose OSLO, One-Shot Label-Only Membership Inference Attack (MIAs). OSLO is based on transfer-based adversarial attacks and identifies members by the different perturbations required when a sample is a member versus a non-member. We empirically demonstrate that OSLO not only operates under label-only settings with a single query but also significantly outperforms all previous label-only attacks by a large margin in terms of true positive rate (TPR) under the same false positive rate (FPR) and attack precision. Thus, OSLO sets a new benchmark for label-only MIAs and can serves as an effective measure of privacy leakage in these settings. We also delve into why OSLO outperforms existing methods. Furthermore, we evaluate multiple defenses against OSLO, highlighting its robustness.OSLO requires training surrogate models that need an auxiliary dataset from the same distribution as the target model's training set. Although this is a common assumption in MIAs [1, 5] and can be alleviated by using synthetic data as demonstrated in prior work [1] , it remains a limitation. 
broader impacts: 
 Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?Answer: [Yes] Justification: Our work focuses on membership inference attacks, a well-known privacy concern in machine learning. Potential impacts, such as privacy risks, are discussed in the paper, including in the Introduction.Guidelines:• The answer NA means that there is no societal impact of the work performed.• If the authors answer NA or No, they should explain why their work has no societal impact or why the paper does not address societal impact. • Examples of negative societal impacts include potential malicious or unintended uses (e.g., disinformation, generating fake profiles, surveillance), fairness considerations (e.g., deployment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations. • The conference expects that many papers will be foundational research and not tied to particular applications, let alone deployments. However, if there is a direct path to any negative applications, the authors should point it out. For example, it is legitimate to point out that an improvement in the quality of generative models could be used to generate deepfakes for disinformation. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster. • The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology is being used as intended but gives incorrect results, and harms following from (intentional or unintentional) misuse of the technology. • If there are negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition to attacks, mechanisms for monitoring misuse, mechanisms to monitor how a system learns from feedback over time, improving the efficiency and accessibility of ML). 
safeguards: 
 Question: Does the paper describe safeguards that have been put in place for responsible release of data or models that have a high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?Answer: [NA] Justification: We are not releasing any new datasets or models, therefore no additional safeguards are necessary.Guidelines:• The answer NA means that the paper poses no such risks.• Released models that have a high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere to usage guidelines or restrictions to access the model or implementing safety filters. • Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images. • We recognize that providing effective safeguards is challenging, and many papers do not require this, but we encourage authors to take this into account and make a best faith effort.12. Licenses for existing assets • We recognize that the procedures for this may vary significantly between institutions and locations, and we expect authors to adhere to the NeurIPS Code of Ethics and the guidelines for their institution. • For initial submissions, do not include any information that would break anonymity (if applicable), such as the institution conducting the review. 
 
 Appendix: For CIFAR-10 and CIFAR-100, we used half of the training set (25,000 samples) to train the target model and the remaining half (25,000 samples) to train the source and validation models. The source and validation models were trained on the same data but remained disjoint from the data used to train the target model. Similarly, for SVHN, we created two disjoint subsets of 5,000 samples each, one for training the target model and the other for the surrogate models.For the evaluation of the attacks, we randomly selected 1,000 samples from both the target model's training set and the remaining unused samples as target samples. The dataset split is summarized in Table 4 . We consider ResNet18 [13] and DenseNet121 [40] as target models, and additionally, Inception [44] , VGG13 [45] , ResNeXt50 [46] , ShuffleNet [47] , and PreActResNet18 [48] are utilized as surrogate models. In our default setup, all models are trained for 100 epochs using the Adam optimizer, with a learning rate of 0.001. We apply an L2 weight decay coefficient of 10 -6 and use a batch size of 128.All our models and methods are implemented in PyTorch. Our experiments are conducted on an NVIDIA GeForce RTX 2080 Ti with 20 GB of memory. The maximum training time for each surrogate or target model does not exceed 1.9 hours.The OSLO setup primarily includes the configuration of source and validation models, as well as the parameters for generating adversarial examples. By default, we use Inception [44] , ResNeXt50 [46] , and PreActResNet18 [48] as the source model architectures. For validation models, we use DenseNet121 [40] , VGG13 [45] , and ShuffleNetV2 [47] when ResNet18 [13] is the target model, and ResNet18, VGG13, and ShuffleNetV2 when DenseNet is the target model. We follow the assumption that the attacker has no knowledge of the target model architecture and does not include the same architecture in the source/validation models. Details on the default number of source and validation models are summarized in Table 5 . Inception × 1 DenseNet121 × 3 12 ResNeXt50 × 1 VGG13 × 3 PreActResNet18 × 1 ShuffleNetV2 × 3 CIFAR-100 Inception × 1 DenseNet121 × 5 18 ResNeXt50 × 1 VGG13 × 5 PreActResNet18 × 1 ShuffleNetV2 × 5 SVHN Inception × 1 DenseNet121 × 1 6 ResNeXt50 × 1 VGG13 × 1 PreActResNet18 × 1 ShuffleNetV2 × 1More combinations of source and validation models are discussed in Appendix A.3. For generating adversarial examples, we set the maximum perturbation to 80/255 and the number of sub-procedures to 80, increasing ϵ by 1/255 each iteration.We summarize the configurations of the baseline attacks here. For the transfer attack, we use a relabeled dataset of the same size as the target model's training set and follow the original pipeline [6] to label the shadow dataset and train the shadow model. For boundary attacks based on adversarial perturbation (HopSkipJump and QEBA), we set a query budget of 6,000 per sample. For the Gaussian noise-based boundary attack, we set a query budget of 700. We use rotation and translation to construct augmented samples for the data augmentation attack, following the original method described in the paper [7] .This section outlines the hyperparameters used for the defenses evaluated against OSLO in Section 6.2. For each defense, three different hyperparameters were used to train the defended models, as detailed in Table 6 . Figure 10 : The magnitude of adversarial perturbations added to samples in the boundary attack and OSLO on CIFAR-100. We adjusted the parameters of two attacks such that they both classify 15.8% of the samples as members (marked as yellow). The precision of OSLO is 95.2%, while the precision of boundary attack is 79.3%.In Section 6.1, we discussed why OSLO outperforms. We further explore this by measuring the perturbation magnitude added to members versus non-members in both boundary attack and OSLO.The results are presented in Figure 10 . We set τ = 0.01 for OSLO, which resulted in classifying 15.8% of the samples as members. We also adjusted the parameters for the boundary attack to select the same proportion of samples classified as members.From Figure 10a , it can be observed that using a single threshold to attempt to distinguish members from non-members leads to a significant proportion of non-members among the samples classified as members, regardless of the threshold value selected (i.e., drawing a horizontal line in the figure, with those above the line classified as members). For example, as shown in Figure 10a , 20.7% of the samples classified as members by the boundary attack are actually non-members. Conversely, OSLO conducts a hypothesis test for each sample, enabling it to accurately identify members even if their perturbations are relatively low compared to other samples. In Figure 10b , only 4.8% of the samples classified as members by OSLO are non-members.We tested the effect of using different source model architectures and validation model structures on OSLO when ResNet18 [13] is the target model. Specifically, we considered the following model structures: DenseNet121 ("1") [40] , Inception-V3 ("2") [44] , VGG13 ("3") [45] , ResNeXt50 ("4") [46] , ShuffleNet-V2 ("5") [47] , and Pre-Activation ResNet ("6") [48] . We selected different combinations from these models as source models or validation models. As shown in Figure 11a , different combinations have no significant impact on the trade-off between precision and recall, although they may affect the maximum achievable precision. For example, beyond a certain point, it becomes impossible to trade recall for additional precision. In such cases, we tested the effect of increasing the number of models (num) trained for each validation model architecture. As depicted in Figure 11b , increasing the number of validation models helps to make the trade-off curve more complete, as OSLO requires adding more perturbations to bypass more validation models. This helps to further reduce recall and increase precision.A.4 Further discussion on threshold τIn OSLO, the generation of adversarial perturbations stops when the confidence of the correct class on the validation model drops below a specified threshold, τ . An intuitive alternative is to stop at the point of label flipping. However, we found that this approach does not guarantee sufficient perturbation to achieve a low FPR. To illustrate this, we compared different stopping criteria, including label flipping, across various thresholds. Table 7 shows the results for ResNet18 on CIFAR-10.Table 7 : Comparison of different stopping criteria on OSLO's performance on CIFAR-10 using ResNet18.Threshold τ = 0.1 13.1% 3.0% Threshold τ = 0.01 7.8% 0.9% Label flip 61.0% 30.8%As shown in Table 7 , a small threshold τ is required to achieve a low FPR, whereas stopping at label flipping leads to a high FPR. The use of threshold τ provides better control over the TPR-FPR trade-off, which is crucial for OSLO's effectiveness.In real-world scenarios, attackers can adapt τ based on the desired FPR. In OSLO, τ is calibrated by adjusting the success rate of the transfer-based attack on the target model. For instance, to achieve a 5% FPR, τ can be set to reach a 95% success rate. This approach may require access to a small set of non-members, which is a common assumption in MIAs [4, 30] .A.5 Effectiveness of OSLO against models trained with adversarial trainingSince OSLO relies on adversarial perturbations, increasing model robustness through adversarial training appears to be a natural defense strategy. To explore this, we evaluated OSLO against target models trained with adversarial training.First, we tested OSLO's performance when the target models were trained with adversarial training, while the surrogate models were not. The results are presented in Table 8 . We observed that adversarial training reduces OSLO's ability to achieve low FPR, but this comes at the cost of decreased model utility and increased training time. We then evaluated OSLO's performance when both the target model and the surrogate models were trained with adversarial training. The results are shown in Table 9 . OSLO remains effective, particularly in maintaining low FPR in this setting. These findings suggest that adversarial training alone may not be an adequate defense against OSLO. OSLO shares a similar goal with the recent work YOQO [34] in improving query efficiency for label-only MIAs. Below, we discuss the key differences to highlight our contributions.Effectiveness at low FPR. It is widely accepted that MIAs should achieve low FPR to be practical [5, 11, 33] . However, by design, YOQO cannot adjust the TPR-FPR trade-off, making it unable to achieve low FPRs, as noted in their paper [34] . In contrast, OSLO is specifically designed to achieve high TPRs under low FPRs and significantly outperforms existing methods in this metric. Thus, we are not able to have a fair comparison because YOQO cannot achieve the low FPR that OSLO primarily works on.Methodology. To the best of our knowledge, OSLO is the first to leverage transfer-based adversarial attacks for label-only MIAs. YOQO, on the other hand, shares a similar approach with LiRA [5] , relying on shadow models trained on target samples (IN models) and shadow models not trained on the target samples (OUT models). This approach depends on the similarity between the shadow model and target model architectures and is sensitive to architecture differences [34] . In contrast, OSLO is robust to variations in surrogate model architecture, as demonstrated by our experiments.NeurIPS Paper Checklist• The answer NA means that the paper does not include experiments.• If the paper includes experiments, a No answer to this question will not be perceived well by the reviewers: Making the paper reproducible is important, regardless of whether the code and data are provided or not. • If the contribution is a dataset and/or model, the authors should describe the steps taken to make their results reproducible or verifiable. • Depending on the contribution, reproducibility can be accomplished in various ways.For example, if the contribution is a novel architecture, describing the architecture fully might suffice, or if the contribution is a specific model and empirical evaluation, it may be necessary to either make it possible for others to replicate the model with the same dataset, or provide access to the model. In general. releasing code and data is often one good way to accomplish this, but reproducibility can also be provided via detailed instructions for how to replicate the results, access to a hosted model (e.g., in the case of a large language model), releasing of a model checkpoint, or other means that are appropriate to the research performed. • While NeurIPS does not require releasing code, the conference does require all submissions to provide some reasonable avenue for reproducibility, which may depend on the nature of the contribution. For example• If the authors answer No, they should explain the special circumstances that require a deviation from the Code of Ethics. • The authors should make sure to preserve anonymity (e.g., if there is a special consideration due to laws or regulations in their jurisdiction). 


Decision: This paper proposes a new membership inference attack called OSLO, inspired by the empirical phenomenon of black-box adversarial attack transfer. Reviewers appreciated the clarity of writing and the empirical results, and the authors engaged with reviewers extensively during the rebuttal period in order to address most of the relevant concerns. I would strongly encourage the authors to include the additional experiments in the paper and additionally implement other suggested edits.

Reviews: review: paper_summary: paper_summary: This paper presents a new label-only membership inference attack, which requires only a single query to the target model. Specifically, it leverages transfer-based black-box attacks to generate an adversarial perturbation. This perturbation is then added to the sample and input into the target model, and its prediction is used to judge whether it is a member or non-member. The experiments demonstrate the effectiveness of the proposed methods.
strength_weakness: strength_weakness: - While the paper is motivated by improving the attack costs compared to existing works, this method requires training multiple source models and validation models, which could be quite costly. This is especially true when applying it to relatively large-scale models, such as diffusion models, which makes the proposed attacks less practical.

- It is unclear whether the proposed MIA was tuned on the validation data independent of the test set. Given that this method requires tuning threshold $\tau$, there is no mention of how this tuning is done and whether using the validation data. If test data was used to tune the method instead of validation data, the results reported might be overly optimistic and not reflect the proposed MIA's performance on "true" test (held-out) data.

- The experimental setting is unclear. Specifically, it remains uncertain how the data split is implemented. Given that 25,000 samples are used to train the target model, it is important to clarify how many datasets are used to train the source models and validation models. More importantly, how many source models and validation models are trained for the experiments? As this is closely tied to the attack costs.

- It is better to conduct an ablation study. The two main contributions are using transfer-based attacks to improve the query costs and using the validation models to adjust the scale of perturbations added to the adversarial example. The latter design is interesting as it resembles calibration to the sample difficulty in existing membership inference literature. To make each contribution clearer, it is better to conduct an ablation study to investigate the importance of each design. Additionally, an ablation study should investigate the impacts of the number of source models and validation models on the attack performance.
questions: questions: - How does your proposed approach perform when tuning the method's components on validation data that is disjoint from the test data on which final performance is reported?

- How many datasets are used to train the source models and validation models?

- How many source models and validation models are trained for the experiments?
limitations: limitations: Please see my above comments.
paper_summary: paper_summary: The paper investigates the vulnerability of deep learning models to membership inference attacks (MIAs), focusing on label-only settings where only the predicted hard label is available. It introduces the One-Shot Label-Only (OSLO) MIA, which infers a sample's membership in the training set with a single query. OSLO leverages transfer-based black-box adversarial attacks, exploiting the characteristic that member samples are more resistant to adversarial perturbations. The paper presents extensive comparisons against state-of-the-art label-only attacks, showing that OSLO significantly outperforms them in terms of precision and true positive rate (TPR) under low false positive rates (FPR). For instance, OSLO achieves a TPR that is 7x to 28x stronger than previous methods under a 0.1% FPR on CIFAR10 for a ResNet model, while maintaining over 95% precision across multiple datasets. Additionally, the paper evaluates various defenses against OSLO, demonstrating its robustness and effectiveness.
strength_weakness: strength_weakness: - **Mitigation Strategies**: The discussion on potential countermeasures against OSLO is somewhat limited. A deeper exploration of feasible strategies to mitigate the risks posed by such attacks would enhance the paper's practical utility.

- **Computational Costs**: While OSLO does not rely on uniform perturbations like some existing methods, it requires higher computational resources to calculate specific perturbations for each sample. This could be a significant drawback in scenarios with limited computational capacity.
questions: questions: - How would methods aimed at enhancing model robustness, such as adversarial training, impact the performance of label-only inference attacks?
limitations: limitations: The authors have adequately summarized the limitations at the end of the paper.
paper_summary: paper_summary: The paper proposes a new label-only membership inference attack that only needs a single query to the target model to perform the attack. The general idea of the proposed attack is based on the observation that member samples need more adversarial perturbation to force a misclassification than non-member samples.
The adversarial perturbation leads to non-members being misclassified while members are more robust and are still correctly classified. Transferable adversarial attacks are used to perform the attack in a single query using several surrogate models. The proposed One-Shot Label Only (OSLO) attack has three phases: 1) surrogate model training 2) creating the transferable adversarial examples on the surrogate models and 3) performing the membership inference on the target model. In contrast to other label-only membership inference attacks, OSLO has a different perturbation budget for each sample.
The proposed attack is evaluated on three datasets (CIFAR-10, CIFAR-100, and SVHN), and in an ablation study, it is shown that the attack is model agnostic and also works with other transferable adversarial attack methods. The paper is technically sound, and the results show that OSLO outperforms existing attacks by a large margin.
strength_weakness: strength_weakness: - A recent paper also proposes a label-only attack that needs only a single query [1]. However, OSLO is not mentioned and, more importantly, not compared to YOQO.
- Equation 2 is presented without introducing any of the variables. It is easier to understand equation 2 if it is mentioned in the text what $h_y(x;\theta)$ and $h_j(x;\theta)$ is.

[1] You Only Query Once: An Efficient Label-Only Membership Inference Attack, Wu et al., ICLR 2024

Misc:
- I think the H_0 and H_1 hypotheses have to be switched in equation 1
- There seems to be a typo in the heading of 6.1. I think it should be "Why OSLO outperform[s] previous approaches".
questions: questions: *Q1:* Why is the generation of the adversarial example stopped when the confidence is below a certain threshold $\tau$? In my understanding, it would make more sense to stop the generation as soon as the label flips.  
*Q2:* In reality, the attacker has to choose the threshold $\tau$. How would the attacker choose the threshold in a realistic setting?  
*Q3:* The perturbation budget is chosen differently for each sample. On the other hand, the threshold $\tau$ is the same for all the samples. Wouldn't it make sense to choose a different threshold for different samples since a lower threshold means more perturbation is added to the samples?  
*Q4:* In 6.2, it is mentioned that "three target models using different hyper-parameters" were trained. However, the hyperparameters were never mentioned. Which model architectures were trained here, what were the hyper-parameters for training these models, and what parameters were altered?
limitations: limitations: The limitations are addressed.
paper_summary: paper_summary: In this work, the authors propose a novel label-only membership inference attack. This method involves adding an adversarial perturbation to compel a model, trained without the target data point, to misclassify the image. This approach requires only a single query to the model and achieves SOTA performance for label-only attacks.
strength_weakness: strength_weakness: The main concern for me is that this paper lacks important related works, like [1] and [2]. In particular, [1] uses a similar strategy to conduct a one-shot label-only inference attack. While the method proposed in this paper is quite similar to [1], it seems to improve the transferability of the adversarial perturbation by checking holdout models. However, the overall contribution is not clear to me. I am not sure if the contribution is significant enough for NeurIPS, but I would appreciate hearing the authors' perspectives on this.

[1] WU, YUTONG et al. You Only Query Once: An Efficient Label-Only Membership Inference Attack. In The Twelfth International Conference on Learning Representations. https://openreview.net/forum?id=7WsivwyHrS&referrer=%5Bthe%20profile%20of%20Jiwei%20Li%5D(%2Fprofile%3Fid%3D~Jiwei_Li1)

[2] Wen, Yuxin et al. Canary in a Coalmine: Better Membership Inference with Ensembled Adversarial Queries. ArXiv abs/2210.10750 (2022): n. pag.
questions: questions: - What if the target model has a different training algorithm, like SGD? Would this make the attack less effective?
- How to apply this attack to a new target data point? Does the attacker have to retrain some of the models?
limitations: limitations: The authors mention limitations at the end of the paper which I appreciate.

Comments: title: Thanks for the positive feedback
Thanks for your response
Thank you
Response to Rebuttal
Thank you for your follow-up question
Thanks for the response
Thank you for your feedback
Thank you
comment: Thank you for your encouraging feedback.  While NeurIPS guidelines do not permit us to update the paper at this time, we will make sure to incorporate all the experiments from the rebuttal in the final version. Your input has been invaluable in strengthening our work.
Thank you for the additional details provided. Please consider including all the experiments from the rebuttal in the revised manuscript. I will raise my scores accordingly.
Thank you for your continued engagement with our work. We’re glad that our responses have fully addressed your concerns. We will include the results provided during the rebuttal in the final version.
Thank you for your thorough review and for taking the time to consider our responses. We appreciate your acknowledgment of our work. Your feedback has been invaluable in improving the clarity and quality of our paper.
Thank you for the prompt reply and for providing additional results with new insights. My concerns have been fully addressed, and I choose to keep my score.
Thank you very much for your detailed rebuttal and the additional insights!

My questions have been appropriately addressed and I will retain my current score.
Thank you for your follow-up. Below is our further clarification and results:

**Clarification on adjusting $\tau$:** The adjustment of $\tau$ to generate the ROC curve was specifically intended to reflect the attack's performance on the target dataset, representing the "true" test or held-out data. We varied $\tau$ systematically to explore how the attack behaves on the target data under different $\tau$ settings. It’s important to note that this process did not involve directly using any validation or test set data for tuning $\tau$. The shadow dataset was only used to train the surrogate model, and once trained, it does not participate in the subsequent attack process.

**Ablation study results:** As promised in our previous response to Weakness 4, we conducted the ablation study as you suggested. We tested OSLO on CIFAR-10 with ResNet18 without the validation model, where all samples used the same perturbation budget. The results are as follows:

| Perturbation Budget Epsilon $\epsilon$ | TPR   | FPR   |
|----------------------------------------|-------|-------|
| **8/255**                              | 20.1% | 13%   |
| **16/255**                             | 2.3%  | 1.4%  |
| **32/255**                             | 0.1%  | 0.1%  |

These results indicate that without the validation model, using a uniform perturbation budget $\epsilon$ for all samples leads to significantly reduced attack effectiveness. For example, at $\epsilon = 32/255$, nearly all members and non-members were not successfully classified, resulting in both TPR and FPR being very low. This highlights the critical role of validation models in effectively calibrating perturbations.

We hope these clarifications and results address your concerns. Please let us know if you have any further concerns we can address.
Thank you for your insightful question. In our previous response to Question 1, we presented results where only the victim model was adversarially trained while the surrogate models were not. To address your question more thoroughly, we conducted additional experiments where both the victim model and the surrogate models were adversarially trained:

| **Victim Model Training**                | **Surrogate Model Training**              | **Threshold (tau)** | **TPR** | **FPR** |
|------------------------------------------|-------------------------------------------|---------------------|---------|---------|
| Adversarial Training (ε=4/255)           | No Adversarial Training                   | 0.001               | 95.6%   | 52.7%   |
| Adversarial Training (ε=4/255)           | Adversarial Training (ε=4/255)            | 0.001               | 15.7%   | 0.7%    |

These findings suggest that OSLO remains effective, particularly in maintaining low FPR, when both the victim model and the surrogate model are adversarially trained. However, as you mentioned, this may require the attacker to first determine whether the victim model has been adversarially trained. In contrast, when the surrogate model is not adversarially trained, the overall gap in robustness is larger, potentially leading to better performance on average metrics such as attack accuracy. Thus, depending on the attacker's knowledge and assumptions, different strategies can be employed, leading to different outcomes.

We will include these findings in the revised paper. Thank you again for your valuable feedback. Please feel free to reach out if you have any further questions.
Thank you for the detailed response. Regarding the adjustment of $\tau$ to obtain and report the complete ROC curve, I am curious whether this was done on the shadow or target datasets?
Thank you for the response. The findings on the influence of adversarial training are indeed intriguing, and I appreciate your work on this.

I have one additional question: when the victim model has undergone adversarial training, should the surrogate models used by the attacker also be adversarially trained? If so, does this imply that the attacker must first determine whether the victim model is adversarially trained before mounting the MIA? I understand that the inclusion of adversarial training complicates the scenario, as the adversarial examples used during training could also be considered member instances.
Thank you for your positive feedback and for raising this insightful question.

To address your question, we controlled the FPR by selecting multiple threshold values (tau) to plot the complete ROC curve. Our approach, OSLO, is capable of achieving an FPR of less than 0.1%, and in most cases, even a 0% FPR. We then identify and report the TPR corresponding to an FPR of 0.1% on the curve. This process is analogous to adjusting the loss to generate a complete ROC curve for loss-based attacks. We hope this explanation clarifies the method we employed. Please let us know if you have any further questions.
Thank the authors for the clarification. I do see the distinction between [1, 2] and the novelty of the paper now. I really appreciate it. Therefore, I increase my score accordingly.

Meanwhile, I have one question: how do you control the FPR accurately? I see you can control the threshold $\tau$ to change FPR, but how do you get the exact value, such as FPR = 0.1%?