approfondimento - Computer Security and Privacy - # Probabilistic Trigger Set-Based Watermarking of Neural Networks

Probabilistic Approach for Robust Watermarking of Neural Networks

Q: How can the proposed approach be extended to provide stronger integrity guarantees, ensuring that independent (not stolen) models are not falsely detected as stolen?

To enhance the integrity guarantees of the proposed watermarking approach, it is essential to refine the verification procedure to distinguish between stolen models and independent models effectively. One potential extension involves implementing a dual verification mechanism that not only checks for agreement among the proxy models but also incorporates a rejection criterion for models that do not belong to the parametric set of proxy models ( B_{\delta, \tau}(f) ). This can be achieved by defining a complementary set ( \overline{B_{\delta, \tau}(f)} ) that includes models with significantly different parameters or architectures. The verification process can be modified to require that, in addition to the agreement among the proxy models, the predicted class label from the source model must differ from the predictions of models in ( \overline{B_{\delta, \tau}(f)} ). This dual-check mechanism would reduce the likelihood of falsely identifying independent models as stolen, as it ensures that only models closely resembling the source model are flagged. Moreover, incorporating a statistical analysis of the prediction distributions from both the proxy and independent models can provide additional insights into their similarities. By employing techniques such as hypothesis testing or confidence intervals, the method can quantify the likelihood that a model is indeed a stolen version rather than an independent one, thus bolstering the integrity guarantees of the watermarking approach.

Q: What are the theoretical limits of the transferability of the trigger set to the stolen models, and how can these limits be characterized?

The theoretical limits of the transferability of the trigger set to stolen models can be characterized by examining the underlying properties of the model architectures, the nature of the training data, and the specific stealing attack employed. Transferability is fundamentally influenced by the degree of similarity between the source model and the surrogate models, which can be quantified using metrics such as the ( L_2 )-norm of the weight differences between the models. One way to formalize these limits is through the concept of a common decision boundary. If the surrogate model's decision boundary is significantly different from that of the source model, the likelihood of successful transferability of the trigger set diminishes. This can be mathematically expressed by defining a threshold for the weight differences ( \delta ) and performance discrepancies ( \tau ) that delineate the boundaries of the parametric set ( B_{\delta, \tau}(f) ). Additionally, the transferability can be influenced by the complexity of the input space and the distribution of the training data. For instance, if the trigger set is constructed from samples that lie near the decision boundary of the source model, the transferability to a surrogate model that has been fine-tuned or altered through knowledge distillation may be compromised. Thus, the theoretical limits can be characterized by establishing conditions under which the trigger set remains effective, such as ensuring that the samples are sufficiently distant from the decision boundary of both the source and surrogate models.

Q: How can the proposed approach be adapted to handle more complex model stealing attacks, such as those involving adversarial examples or model fine-tuning?

To adapt the proposed watermarking approach for resilience against more complex model stealing attacks, such as those involving adversarial examples or model fine-tuning, several strategies can be employed. Firstly, the trigger set generation process can be enhanced by incorporating adversarial training techniques. By generating trigger samples that are not only convex combinations of benign data points but also adversarially perturbed versions of these points, the watermarking method can ensure that the trigger set remains effective even when the surrogate model is subjected to adversarial attacks. This can be achieved by utilizing adversarial training algorithms, such as Projected Gradient Descent (PGD), to create robust trigger samples that are less likely to be misclassified by both the source and surrogate models. Secondly, the verification process can be modified to account for model fine-tuning. This can involve dynamically adjusting the parameters ( \delta ) and ( \tau ) based on the observed performance of the surrogate models during the fine-tuning process. By continuously monitoring the accuracy of the surrogate models on the trigger set, the approach can adaptively refine the criteria for verifying ownership, ensuring that even fine-tuned models that may have diverged from the original architecture can still be accurately assessed. Lastly, incorporating ensemble methods into the verification process can enhance robustness against various stealing strategies. By utilizing multiple proxy models with diverse architectures or training regimes, the method can create a more comprehensive assessment of the trigger set's transferability. This ensemble approach can help mitigate the risks posed by sophisticated stealing attacks, as it leverages the collective knowledge of multiple models to validate the ownership of the original model more effectively.

Concetti Chiave

A novel probabilistic approach for enhancing the robustness of trigger set-based watermarking techniques against model stealing attacks.

Sintesi

The paper introduces a novel probabilistic approach for enhancing the robustness of trigger set-based watermarking techniques against model stealing attacks. The key idea is to compute a parametric set of proxy models that mimic the set of stolen models, and then verify the transferability of the trigger set to these proxy models. This ensures that the trigger set is transferable to the stolen models with high probability, even if the stolen model does not belong to the set of proxy models.

The authors first describe the process of computing the trigger set candidates as convex combinations of pairs of points from the hold-out dataset. Then, they introduce the parametric set of proxy models and the procedure of verifying the transferability of the trigger set to these proxy models. The authors provide probabilistic guarantees on the transferability of the trigger set from the source model to the stolen models.

The experimental results show that the proposed approach outperforms current state-of-the-art watermarking techniques in terms of the accuracy of the source model, the accuracy of the surrogate models on the trigger set, and the robustness to various model stealing attacks, including soft-label, hard-label, and regularization-based attacks.

The authors also discuss the integrity of the method, demonstrating that it can distinguish between stolen models and independent (not stolen) models. They provide experiments on the integrity of the method, showing that the least similar independent models are the ones trained on different datasets, regardless of architecture.

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Statistiche

The l2-norm of the difference between the parameters of the source model and the surrogate models is reported in Table 1. This shows that the surrogate models do not belong to the proxy set used in the proposed approach.

Citazioni

"The key idea of our method is to compute the trigger set, which is transferable between the source model and the set of proxy models with a high probability."
"We analyze the probability that a given trigger set is transferable to the set of proxy models that mimic the stolen models."
"We experimentally show that, even if the stolen model does not belong to the set of proxy models, the trigger set is still transferable to the stolen model."

Approfondimenti chiave tratti da

Probabilistically Robust Watermarking of Neural Networks

by Mikhail Paut... alle arxiv.org 09-19-2024

https://arxiv.org/pdf/2401.08261.pdf

Probabilistically Robust Watermarking of Neural Networks

Domande più approfondite

How can the proposed approach be extended to provide stronger integrity guarantees, ensuring that independent (not stolen) models are not falsely detected as stolen?

To enhance the integrity guarantees of the proposed watermarking approach, it is essential to refine the verification procedure to distinguish between stolen models and independent models effectively. One potential extension involves implementing a dual verification mechanism that not only checks for agreement among the proxy models but also incorporates a rejection criterion for models that do not belong to the parametric set of proxy models ( B_{\delta, \tau}(f) ).
This can be achieved by defining a complementary set ( \overline{B_{\delta, \tau}(f)} ) that includes models with significantly different parameters or architectures. The verification process can be modified to require that, in addition to the agreement among the proxy models, the predicted class label from the source model must differ from the predictions of models in ( \overline{B_{\delta, \tau}(f)} ). This dual-check mechanism would reduce the likelihood of falsely identifying independent models as stolen, as it ensures that only models closely resembling the source model are flagged.
Moreover, incorporating a statistical analysis of the prediction distributions from both the proxy and independent models can provide additional insights into their similarities. By employing techniques such as hypothesis testing or confidence intervals, the method can quantify the likelihood that a model is indeed a stolen version rather than an independent one, thus bolstering the integrity guarantees of the watermarking approach.

What are the theoretical limits of the transferability of the trigger set to the stolen models, and how can these limits be characterized?

The theoretical limits of the transferability of the trigger set to stolen models can be characterized by examining the underlying properties of the model architectures, the nature of the training data, and the specific stealing attack employed. Transferability is fundamentally influenced by the degree of similarity between the source model and the surrogate models, which can be quantified using metrics such as the ( L_2 )-norm of the weight differences between the models.
One way to formalize these limits is through the concept of a common decision boundary. If the surrogate model's decision boundary is significantly different from that of the source model, the likelihood of successful transferability of the trigger set diminishes. This can be mathematically expressed by defining a threshold for the weight differences ( \delta ) and performance discrepancies ( \tau ) that delineate the boundaries of the parametric set ( B_{\delta, \tau}(f) ).
Additionally, the transferability can be influenced by the complexity of the input space and the distribution of the training data. For instance, if the trigger set is constructed from samples that lie near the decision boundary of the source model, the transferability to a surrogate model that has been fine-tuned or altered through knowledge distillation may be compromised. Thus, the theoretical limits can be characterized by establishing conditions under which the trigger set remains effective, such as ensuring that the samples are sufficiently distant from the decision boundary of both the source and surrogate models.

How can the proposed approach be adapted to handle more complex model stealing attacks, such as those involving adversarial examples or model fine-tuning?

To adapt the proposed watermarking approach for resilience against more complex model stealing attacks, such as those involving adversarial examples or model fine-tuning, several strategies can be employed.
Firstly, the trigger set generation process can be enhanced by incorporating adversarial training techniques. By generating trigger samples that are not only convex combinations of benign data points but also adversarially perturbed versions of these points, the watermarking method can ensure that the trigger set remains effective even when the surrogate model is subjected to adversarial attacks. This can be achieved by utilizing adversarial training algorithms, such as Projected Gradient Descent (PGD), to create robust trigger samples that are less likely to be misclassified by both the source and surrogate models.
Secondly, the verification process can be modified to account for model fine-tuning. This can involve dynamically adjusting the parameters ( \delta ) and ( \tau ) based on the observed performance of the surrogate models during the fine-tuning process. By continuously monitoring the accuracy of the surrogate models on the trigger set, the approach can adaptively refine the criteria for verifying ownership, ensuring that even fine-tuned models that may have diverged from the original architecture can still be accurately assessed.
Lastly, incorporating ensemble methods into the verification process can enhance robustness against various stealing strategies. By utilizing multiple proxy models with diverse architectures or training regimes, the method can create a more comprehensive assessment of the trigger set's transferability. This ensemble approach can help mitigate the risks posed by sophisticated stealing attacks, as it leverages the collective knowledge of multiple models to validate the ownership of the original model more effectively.