Integrating uncertainty quantification into randomized smoothing based robustness guarantees (2410.20432v1)

Abstract: Deep neural networks have proven to be extremely powerful, however, they are also vulnerable to adversarial attacks which can cause hazardous incorrect predictions in safety-critical applications. Certified robustness via randomized smoothing gives a probabilistic guarantee that the smoothed classifier's predictions will not change within an $\ell_2$-ball around a given input. On the other hand (uncertainty) score-based rejection is a technique often applied in practice to defend models against adversarial attacks. In this work, we fuse these two approaches by integrating a classifier that abstains from predicting when uncertainty is high into the certified robustness framework. This allows us to derive two novel robustness guarantees for uncertainty aware classifiers, namely (i) the radius of an $\ell_2$-ball around the input in which the same label is predicted and uncertainty remains low and (ii) the $\ell_2$-radius of a ball in which the predictions will either not change or be uncertain. While the former provides robustness guarantees with respect to attacks aiming at increased uncertainty, the latter informs about the amount of input perturbation necessary to lead the uncertainty aware model into a wrong prediction. Notably, this is on CIFAR10 up to 20.93% larger than for models not allowing for uncertainty based rejection. We demonstrate, that the novel framework allows for a systematic robustness evaluation of different network architectures and uncertainty measures and to identify desired properties of uncertainty quantification techniques. Moreover, we show that leveraging uncertainty in a smoothed classifier helps out-of-distribution detection.

• The paper introduces a novel integration of uncertainty quantification with randomized smoothing to enhance certified robustness and enable abstention in uncertain scenarios.
• It demonstrates empirical improvements, achieving up to a 20.93% increase in robustness radii on benchmarks like CIFAR10.
• The approach also improves out-of-distribution detection by ensuring classifiers only make confident predictions in low-uncertainty regions.

Integrating Uncertainty Quantification into Randomized Smoothing Based Robustness Guarantees

The integration of uncertainty quantification with randomized smoothing (RS) for robustness guarantees in classifiers presents a nuanced and forward-thinking exploration of adversarial defenses. This work presents a merging of uncertainty-based rejection capabilities with the RS framework to yield superior certified robustness. The authors propose two novel guarantees that enhance the foundational robustness through randomized smoothing: ensuring consistent and confident predictions, and establishing a robustness radius that prevents erroneous confident predictions.

The paper draws attention to the significant limitations in purely empirical robustness estimation methods. While these methods provide insights, their reliability against evolving adversarial attacks remains unproven. This gap leads to an exploration of certified robustness, which offers mathematical guarantees of prediction invariability within specific perturbation bounds. The innovation here lies in the fusion of RS — a conservative probabilistic framework — with a more granulated uncertainty assessment approach, thus refining the RS robustness metrics.

Traditionally, RS provided a robustness guarantee by transforming deterministic classifiers into randomized versions that offer probabilistic assurances against input perturbations. The robustness of a model, expressed within an $\ell_2$ perturbation radius, is determined through the addition of Gaussian noise to inputs and is evaluated for consistent prediction outcomes. The authors harness these probabilistic assurances, alongside uncertainty quantification, to optimize model predictions by enabling abstention in high-uncertainty scenarios.

The introduction of uncertainty-equipped classifiers, which strategically loop in concepts of uncertainty quantification, exemplifies a methodological sophistication aimed at bolstering model reliability. Here, they modify the mechanism for calculating certified robustness radii by incorporating an uncertainty threshold into the evaluation models. This threshold, when properly calibrated, delineates regions where a smoothed classifier can confidently refrain from making uncertain predictions, thus thwarting certain adversarial strategies.

Crucially, the paper demonstrates practical numerical evaluations that exhibit the tangible improvements this framework brings to deep neural networks (DNNs) across different architectures. Notably, in CIFAR10, the novel guarantee provides enhancement margins up to 20.93% in robustness radii compared to non-augmented models. This significant metric underlines the potential leap in defense mechanisms through their methodology. The thoroughness of empirical investigation is commendable, presenting insights across numerous network architectures and examining the implications of different uncertainty metrics.

The approach not only offers advanced static robustness guarantees but also facilitates out-of-distribution (OOD) detection. This affirms the extended utility in real-world settings, suggesting that uncertainty mechanisms inherently bolster a classifier’s resilience by recognizing and responding to OOD data that traditional models may misclassify with high confidence.

In the speculative discourse on the trajectory of these methodological integrals, the paper suggests that future deep learning models will increasingly leverage uncertainty characteristics not only as auxiliary safety measures but as core components of the learning and prediction process. This paradigm could feasibly extend to training phases, embedding these insights into model architecture designs from inception.

The research presented serves to seamlessly combine notions of pioneering certified robustness with contemporary uncertainty quantification, typifying a progressive stride in adversarial defense literature. The enhancements in robustness radii and increased confidence levels provide a robust foundation for more resilient, reliable, and straightforward defenses against adversarial threats. Future explorations are likely to build upon this work, seeking integrative solutions that further harness the synergistic potential of uncertainty within machine learning’s defensive arsenals.