3 research outputs found
Precise Multi-Neuron Abstractions for Neural Network Certification
Formal verification of neural networks is critical for their safe adoption in
real-world applications. However, designing a verifier which can handle
realistic networks in a precise manner remains an open and difficult challenge.
In this paper, we take a major step in addressing this challenge and present a
new framework, called PRIMA, that computes precise convex approximations of
arbitrary non-linear activations. PRIMA is based on novel approximation
algorithms that compute the convex hull of polytopes, leveraging concepts from
computational geometry. The algorithms have polynomial complexity, yield fewer
constraints, and minimize precision loss. We evaluate the effectiveness of
PRIMA on challenging neural networks with ReLU, Sigmoid, and Tanh activations.
Our results show that PRIMA is significantly more precise than the
state-of-the-art, verifying robustness for up to 16%, 30%, and 34% more images
than prior work on ReLU-, Sigmoid-, and Tanh-based networks, respectively