PRIMA: General and Precise Neural Network Certification via Scalable Convex Hull Approximations
This addresses the problem of safe adoption of neural networks in real-world applications like autonomous driving by providing a more general and precise verification method, representing a significant advance rather than an incremental improvement.
The paper tackles the challenge of designing a precise and scalable neural network verifier by introducing PRIMA, a framework that handles any non-linear activation function and computes precise convex abstractions, resulting in verifying robustness for up to 20%, 30%, and 34% more images on ReLU-, Sigmoid-, and Tanh-based networks than prior work.
Formal verification of neural networks is critical for their safe adoption in real-world applications. However, designing a precise and scalable verifier which can handle different activation functions, realistic network architectures and relevant specifications remains an open and difficult challenge. In this paper, we take a major step forward in addressing this challenge and present a new verification framework, called PRIMA. PRIMA is both (i) general: it handles any non-linear activation function, and (ii) precise: it computes precise convex abstractions involving multiple neurons via novel convex hull approximation algorithms that leverage concepts from computational geometry. The algorithms have polynomial complexity, yield fewer constraints, and minimize precision loss. We evaluate the effectiveness of PRIMA on a variety of challenging tasks from prior work. Our results show that PRIMA is significantly more precise than the state-of-the-art, verifying robustness to input perturbations for up to 20%, 30%, and 34% more images than existing work on ReLU-, Sigmoid-, and Tanh-based networks, respectively. Further, PRIMA enables, for the first time, the precise verification of a realistic neural network for autonomous driving within a few minutes.