Efficient Formal Safety Analysis of Neural Networks (1809.08098v3)

Abstract: Neural networks are increasingly deployed in real-world safety-critical domains such as autonomous driving, aircraft collision avoidance, and malware detection. However, these networks have been shown to often mispredict on inputs with minor adversarial or even accidental perturbations. Consequences of such errors can be disastrous and even potentially fatal as shown by the recent Tesla autopilot crash. Thus, there is an urgent need for formal analysis systems that can rigorously check neural networks for violations of different safety properties such as robustness against adversarial perturbations within a certain $L$-norm of a given image. An effective safety analysis system for a neural network must be able to either ensure that a safety property is satisfied by the network or find a counterexample, i.e., an input for which the network will violate the property. Unfortunately, most existing techniques for performing such analysis struggle to scale beyond very small networks and the ones that can scale to larger networks suffer from high false positives and cannot produce concrete counterexamples in case of a property violation. In this paper, we present a new efficient approach for rigorously checking different safety properties of neural networks that significantly outperforms existing approaches by multiple orders of magnitude. Our approach can check different safety properties and find concrete counterexamples for networks that are 10$\times$ larger than the ones supported by existing analysis techniques. We believe that our approach to estimating tight output bounds of a network for a given input range can also help improve the explainability of neural networks and guide the training process of more robust neural networks.

• The paper introduces symbolic linear relaxation to reduce overestimation errors, enabling scalable verification of neural network safety properties.
• The paper presents directed constraint refinement that efficiently targets critical nodes, enhancing the precision of safety property identification.
• The paper details the Neurify implementation, achieving up to 5,000x speed improvements and verifying networks with over 10,000 ReLU nodes.

Overview of Efficient Formal Safety Analysis of Neural Networks

The paper entitled "Efficient Formal Safety Analysis of Neural Networks" addresses a pressing issue in the deployment of neural networks in safety-critical domains such as autonomous driving and aircraft collision avoidance systems. These systems require neural networks to maintain high accuracy under varied and often unpredictable conditions. However, the inherent susceptibility of neural networks to adversarial and incidental perturbations necessitates rigorous formal analysis to ensure the networks can maintain their accuracy under these perturbations. The authors propose a novel approach to efficiently check multiple safety properties of neural networks, vastly improving upon existing techniques in terms of scalability and speed.

Key Contributions

1. Symbolic Linear Relaxation: The authors introduce a method they call symbolic linear relaxation, which combines symbolic interval analysis with linear relaxation techniques. This approach offers a more accurate bounding of network outputs by effectively maintaining dependencies across inputs during the propagation process. The pivotal advantage here is the reduction in overestimation errors, which allows for the verification of safety properties across much larger networks than previously feasible.
2. Directed Constraint Refinement: This novel technique iteratively refines the possible overestimation during the analysis process. By focusing computational resources on potentially problematic nodes, the approach minimizes unnecessary calculations, thereby increasing efficiency significantly. The precision of this refinement process ensures that the identification of safety violations is robust and reliable, allowing practitioners to identify genuine counterexamples that violate safety properties.
3. Implementation in Neurify: These techniques have been implemented in a system named Neurify, which claims to outperform previous state-of-the-art systems by multiple orders of magnitude. Neurify has been tested on various networks, including those with complex architectures and large input spaces, such as convolutional neural networks suited for image processing tasks.

Numerical Results and Verification

The empirical results presented are impressive, showing that Neurify can speed up the verification of safety properties by up to 5,000 times compared to Reluplex, and by a factor of 20 regarding ReluVal on certain safety properties. Additionally, Neurify's capacity to scale enables it to verify properties in networks with upwards of 10,000 ReLU nodes, a context in which prior approaches typically fail or require excessive computational resources.

Practical and Theoretical Implications

The implications of this research are extensive. Practically, the system provides a tool that enhances the safety verification process for deploying neural networks in safety-critical applications, potentially preventing catastrophic failures. Theoretically, it advances the understanding of network robustness and opens avenues for future research into even more precise bounding methods or novel refinement techniques that could further push the boundaries of scalability.

The paper also hints at potential benefits for neural network training processes, suggesting that the methods could offer insights that lead to more robust model architectures inherently, thus providing both verification and design insights.

Future Directions

The method introduced has established a foundation that future work could build upon. The incorporation of other activation functions beyond ReLU, exploration into hybrid methods that combine different forms of constraint programming, and the application of these formal analysis techniques to networks trained with unconventional data types or under different architectural paradigms are promising areas for further exploration.

In summary, this paper provides substantial improvements in the formal verification of neural networks' safety properties, presenting techniques that are both efficient and capable of handling considerably larger neural networks. As artificial intelligence continues to integrate into critical systems, ensuring these systems' safety through rigorous formal methods becomes ever more important, positioning this research as a significant contribution to the field.