Verifiably Robust Conformal Prediction
Summary
Paper digest
What problem does the paper attempt to solve? Is this a new problem?
The paper aims to address the challenge of maintaining valid prediction sets in the presence of adversarial perturbations during inference . This problem is tackled by introducing the Verifiably Robust Conformal Prediction (VRCP) framework, which leverages conformal prediction and neural network verification to ensure prediction sets maintain coverage under adversarial attacks . The paper introduces two variants of VRCP: VRCP–C, which applies verification at calibration time, and VRCP–I, which applies verification at inference time . This problem of maintaining valid prediction sets under adversarial perturbations is a novel one, and the paper's approach represents a new contribution to the field .
What scientific hypothesis does this paper seek to validate?
This paper aims to validate the scientific hypothesis that by leveraging neural network verification algorithms, it is possible to construct prediction sets that are robust against adversarial perturbations at inference time, ensuring statistically valid prediction sets despite the presence of adversarial attacks . The proposed framework, Verifiably Robust Conformal Prediction (VRCP), combines neural network verification methods with conformal prediction to create prediction sets that are guaranteed to include the true output with a specified probability, even in the presence of adversarial perturbations . The paper introduces two variants of VRCP, namely VRCP via Robust Inference (VRCP-I) and VRCP via Robust Calibration (VRCP-C), which enable the construction of adversarially robust prediction sets by leveraging neural network verification techniques .
What new ideas, methods, or models does the paper propose? What are the characteristics and advantages compared to previous methods?
The paper "Verifiably Robust Conformal Prediction" introduces the Verifiably Robust Conformal Prediction (VRCP) framework, which combines conformal prediction (CP) and neural network (NN) verification to create prediction sets that maintain coverage under adversarial perturbations . This framework offers two variants: VRCP–C, which applies verification at calibration time, and VRCP–I, which applies verification at inference time . VRCP is the first to extend adversarially robust conformal prediction to regression tasks and goes beyond ℓ2-norm bounded guarantees .
One key aspect of the VRCP framework is the utilization of NN verification algorithms to compute upper and lower output bounds of the underlying predictor, enabling the construction of provably robust and efficient prediction sets . By leveraging these bounds to inflate CP regions, VRCP ensures robustness against adversarial perturbations, making it a pioneering approach in combining NN verification and CP for constructing adversarially robust prediction sets .
The paper also addresses the limitations of existing methods, such as randomised smoothing, by providing theoretical guarantees and empirical evidence of the effectiveness of VRCP in uncertainty quantification of machine learning models under attack . VRCP achieves valid marginal coverage in the presence of ℓ1, ℓ2, and ℓ∞-norm bounded adversarial attacks, surpassing previous methods in accuracy and robustness . Additionally, VRCP introduces innovative techniques like robustly calibrated training (RCT) and post-training transformation (PTT) to enhance the efficiency of the framework . The Verifiably Robust Conformal Prediction (VRCP) framework introduces several key characteristics and advantages compared to previous methods:
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Adversarial Robustness: VRCP is the first framework to extend adversarially robust conformal prediction to regression tasks and surpasses existing methods by going beyond ℓ2-norm bounded guarantees . It supports perturbations bounded by arbitrary norms, including ℓ1, ℓ2, and ℓ∞, making it more versatile and robust against adversarial attacks .
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Incorporation of Neural Network Verification: VRCP leverages neural network (NN) verification algorithms to compute upper and lower output bounds of the underlying predictor, enabling the construction of provably robust and efficient prediction sets . By combining NN verification with conformal prediction, VRCP ensures coverage guarantees under adversarial perturbations, setting it apart from prior methods .
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Efficiency and Accuracy: VRCP offers more efficient and informative prediction regions compared to state-of-the-art methods, as demonstrated through empirical validation on image classification tasks like CIFAR10, CIFAR100, and TinyImageNet . It achieves above nominal coverage and produces smaller average set sizes with minor sample dependence, ensuring a more conservative marginal coverage than existing methods .
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Theoretical Guarantees: VRCP provides statistically valid prediction sets despite adversarial perturbations at inference time, ensuring that the prediction sets cover the true test output with a user-specified probability . It overcomes the limitations of prior methods, such as randomised smoothing, by offering theoretical guarantees and empirical evidence of its effectiveness in uncertainty quantification of machine learning models under attack .
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Novel Variants: VRCP introduces two versions, VRCP–C and VRCP–I, which apply verification at calibration and inference time, respectively . These variants enhance the adaptability and applicability of the framework in different scenarios, providing flexibility in ensuring robustness and accuracy in prediction sets .
In summary, VRCP stands out for its adversarial robustness, incorporation of NN verification, efficiency, accuracy, theoretical guarantees, and the introduction of novel variants, making it a pioneering framework in the field of uncertainty quantification and adversarially robust prediction sets .
Do any related researches exist? Who are the noteworthy researchers on this topic in this field?What is the key to the solution mentioned in the paper?
Several related research works exist in the field of verifiably robust conformal prediction. Noteworthy researchers in this field include:
- J. C. Duchi, P. L. Bartlett, and M. J. Wainwright
- H. Salman, J. Li, I. Razenshteyn, P. Zhang, H. Zhang, S. Bubeck, and G. Yang
- G. Yan, Y. Romano, and T.-W. Weng
- S. Ghosh, Y. Shi, T. Belkhouja, Y. Yan, J. Doppa, and B. Jones
- J. Lei, J. Robins, and L. Wasserman
- Y. Romano, E. Patterson, and E. Candes
- K. Xu, Z. Shi, H. Zhang, Y. Wang, K.-W. Chang, M. Huang, B. Kailkhura, X. Lin, and C.-J. Hsieh
- A. Gendler, T.-W. Weng, L. Daniel, and Y. Romano
The key to the solution mentioned in the paper is the introduction of VRCP (Verifiably Robust Conformal Prediction), a new framework that leverages recent neural network verification methods to recover coverage guarantees under adversarial attacks. VRCP is the first method to support perturbations bounded by arbitrary norms including ℓ1, ℓ2, and ℓ∞, as well as regression tasks. By combining neural network verification algorithms and conformal prediction, VRCP constructs adversarially robust prediction sets that provide statistically valid prediction sets despite the presence of adversarial perturbations at inference time .
How were the experiments in the paper designed?
The experiments in the paper were designed by selecting 5,000 random initial world configurations and simulating 25 Monte-Carlo trajectories of length k = 5 for each configuration. The data was partitioned into training, calibration, and test sets with specific sizes: |Dtrain| = 1,000, |Dcal| = 2,000, and |Dtest| = 2,000 . The bounds for the experiments were computed using the CROWN method with ℓ∞-bounded perturbations, and adversarially perturbed test points were generated using the Fast Gradient Sign Method . The experiments evaluated the performance of the Verifiably Robust Conformal Prediction (VRCP) framework on small to medium-sized neural networks, considering the scalability of VRCP based on the underlying neural network verifier .
What is the dataset used for quantitative evaluation? Is the code open source?
The dataset used for quantitative evaluation in the study on Verifiably Robust Conformal Prediction is comprised of image classification tasks such as CIFAR10, CIFAR100, and TinyImageNet, as well as regression tasks for deep reinforcement learning environments . The code for the Verifiably Robust Conformal Prediction framework is not explicitly mentioned to be open source in the provided context. However, the study introduces a new framework called VRCP (Verifiably Robust Conformal Prediction) that leverages neural network verification methods for recovering coverage guarantees under adversarial attacks, supporting perturbations bounded by arbitrary norms including ℓ1, ℓ2, and ℓ∞, as well as regression tasks .
Do the experiments and results in the paper provide good support for the scientific hypotheses that need to be verified? Please analyze.
The experiments and results presented in the paper provide strong support for the scientific hypotheses that need to be verified. The paper introduces the VRCP (Verifiably Robust Conformal Prediction) framework, which leverages neural network verification methods to ensure coverage guarantees under adversarial attacks, including perturbations bounded by various norms and regression tasks . The VRCP method is the first to support such perturbations and tasks, demonstrating its novelty and advancement in the field .
The experiments conducted in the paper evaluate and compare the VRCP approach on image classification tasks like CIFAR10, CIFAR100, and TinyImageNet, as well as regression tasks for deep reinforcement learning environments. The results consistently show that VRCP achieves above nominal coverage and provides more efficient and informative prediction regions compared to the State of the Art (SotA) methods . This indicates that the VRCP framework successfully addresses the challenges posed by adversarial attacks and improves the reliability of prediction sets under such conditions .
Furthermore, the paper includes detailed analysis of the experimental setup, model details, hyperparameters, verification methods used, and attack algorithms employed, providing a comprehensive overview of the methodology followed in the experiments . By using verification algorithms to compute upper and lower output bounds of the neural network, the VRCP framework ensures the construction of provably robust and efficient prediction sets, enhancing the credibility and reliability of the results .
Overall, the experiments and results presented in the paper offer substantial evidence to support the scientific hypotheses put forth by demonstrating the effectiveness and robustness of the VRCP framework in providing adversarially robust prediction sets across various tasks and perturbation scenarios . The thorough evaluation and comparison with existing methods highlight the significance and reliability of the proposed approach in addressing the challenges posed by adversarial attacks in machine learning models .
What are the contributions of this paper?
The paper makes significant contributions in the field of conformal prediction by introducing a framework called Verifiably Robust Conformal Prediction (VRCP). This framework provides statistically valid prediction sets even in the presence of adversarial perturbations during inference. VRCP leverages neural network verification algorithms to compute upper and lower output bounds, inflating the prediction regions to ensure provably robust and efficient prediction sets . Additionally, VRCP extends adversarially robust conformal prediction to regression tasks and goes beyond ℓ2-norm bounded guarantees, addressing limitations of prior methods restricted to classification tasks with overly conservative guarantees . The paper introduces two versions of VRCP that apply verification at calibration and inference time, respectively, and empirically validates the theoretical guarantees, demonstrating improved prediction set efficiency compared to previous work .
What work can be continued in depth?
Further research in the field of verifiably robust conformal prediction can be extended in several directions based on the existing work:
- Exploration of Different Neural Network Verification Methods: The current research mentions various approaches for verifying the robustness of neural networks against adversarial attacks, including complete and incomplete algorithms. Future work could focus on comparing and developing new verification methods to enhance the robustness of neural networks .
- Enhancing Adversarially Robust Conformal Prediction: Researchers can delve deeper into improving the efficiency and effectiveness of adversarially robust conformal prediction methods. This could involve refining existing techniques, exploring new algorithms, and extending the application of robust prediction sets to different types of tasks beyond classification .
- Empirical Validation and Benchmarking: Future studies could conduct more extensive empirical validations to assess the performance and scalability of verifiably robust conformal prediction methods across various datasets and model architectures. Benchmarking against existing approaches can provide insights into the strengths and limitations of different techniques .
- Incorporating Different Norms for Adversarial Attacks: The current research focuses on ℓp-bounded adversarial perturbations. Further investigations could explore the impact of different norms (e.g., ℓ∞) on the robustness of prediction sets and develop methods that can handle a wider range of adversarial attacks .
- Extension to Regression Tasks: While the existing work introduces adversarially robust conformal prediction to regression tasks, there is room for expanding this application to more regression scenarios and exploring the implications of verifiably robust prediction sets in regression analysis .