Efficient Certification of Spatial Robustness (2009.09318v2)

Abstract: Recent work has exposed the vulnerability of computer vision models to vector field attacks. Due to the widespread usage of such models in safety-critical applications, it is crucial to quantify their robustness against such spatial transformations. However, existing work only provides empirical robustness quantification against vector field deformations via adversarial attacks, which lack provable guarantees. In this work, we propose novel convex relaxations, enabling us, for the first time, to provide a certificate of robustness against vector field transformations. Our relaxations are model-agnostic and can be leveraged by a wide range of neural network verifiers. Experiments on various network architectures and different datasets demonstrate the effectiveness and scalability of our method.

• The paper introduces novel convex relaxations to certify neural networks against a wide range of spatial transformations.
• It integrates vector field smoothness constraints with existing techniques like DeepPoly and MILP to tighten robustness bounds.
• Empirical evaluations on MNIST, CIFAR-10, and various architectures demonstrate significant improvements in certifiable robustness.

An Evaluation of Efficient Certification of Spatial Robustness in Neural Networks

The paper "Efficient Certification of Spatial Robustness" by Anian Ruoss et al. addresses a key vulnerability in neural networks used in computer vision: susceptibility to adversarial examples created through spatial transformations, specifically vector field attacks. The authors propose novel methodologies for certifying the robustness of neural networks against these transformations.

Key Issues

The primary challenge in certifying spatial robustness lies in neural networks' vulnerability to spatial attacks modeled by smooth vector fields, which can be visually indistinguishable from original images. While adversarial attacks provide empirical insights, they fall short of offering provable robustness guarantees. Previous works have focused on noise-based perturbations or specific geometric transformations. However, these approaches do not extend to the broader class of spatial transformations described by vector fields.

Methodological Innovation

The paper introduces novel convex relaxations, which, for the first time, enable robustness certification against a wide range of spatial transformations, beyond conventional noise-based perturbations. The method creates interval bounds on spatially transformed image vectors to allow robustness certification. This approach is distinguished by its model-agnostic nature, allowing for integration with various neural network verifiers.

The proposed convex relaxations integrate effectively with existing certification techniques like DeepPoly and MILP, tightening the over-approximation used in standard interval propagations. By incorporating vector field smoothness constraints, the authors enhance the precision of the certification process, enabling more robust and verifiable neural network models.

Empirical Results

Empirical evaluations highlight the effectiveness of the proposed certification relaxations across several datasets including MNIST and CIFAR-10, and different neural architectures (e.g., ConvSmall, ConvMed, ConvBig, and ResNet). The results show substantial increases in certifiable robustness when using the authors' methodologies, demonstrating that the relaxations efficiently enhance certification metrics. Importantly, the method scales well to larger architectures, such as ResNet on CIFAR-10, maintaining effectiveness without prohibitive computational requirements.

Theoretical and Practical Implications

Theoretically, this work advances the understanding of spatial perturbations in neural networks, framing these deformations within a certifiable bound through the use of novel smoothness constraints. Practically, the paper bridges a significant gap in the deployment of neural networks in safety-critical and adversarial environments, where robustness against a diverse range of adversarial inputs is crucial.

Future Directions

Future research could expand this method to even more complex spatial transformations and explore its application in real-world scenarios where robustness certification is required, such as autonomous vehicle navigation systems or security applications in computer vision systems. An interesting direction could be the combination of this robustness certification with other forms of neural network defenses to form a comprehensive defensive framework against adversarial attacks.

In conclusion, the paper by Ruoss et al. makes significant strides toward ensuring the spatial robustness of neural networks, by developing a certification method that is both scalable and widely applicable across different architectures. The introduction of these novel convex relaxations opens new avenues for advancing the security and reliability of AI systems against spatial adversarial attacks.