Part I - Introduction

an short introduction to neural network verification.

Updates 2025

For latest educational materials regarding neural network verification, you are suggested to take a look at the new course developed by Prof. Huan Zhang at UIUC. Checkout the slides at ECE598HZ: Advanced Topics in Machine Learning and Formal Methods. In particular, the following lectures will be helpful for understanding neural network verification problem settings and the representative linear bound propagation framework (CROWN) in the α,β-CROWN verifier.

• Lecture 5: Basic formulation
• Lecture 6: Integer programming and linear programming formulations
• Lecture 7: CROWN bound propagation algorithm, illustrated with examples
• Lecture 8: Branch and bound algorithms (beta-CROWN)
• Lecture 9: Bound propagation on general computational graphs
• Lecture 10: Certified training and other misc topics

Revisiting the SAT/SMT formulation in Lecture 3 - 4 may also be helpful for readers.

For a simple reference implementation of CROWN, please check out the Homework for ECE598HZ. Problem 3 comes with a complete and clean implementation of CROWN in its simplest form.

The content below is from the original AAAI 2022 tutorial, which may still be helpful but not updated anymore.

Click here: Slides for Part I - Introduction (PDF)

tl;dr: In this part, we start with several concrete examples to demonstrate the importance of neural network verification. Then we present the formulations and fundamental mathematical problems solved by neural network verifiers. We also briefly introduce the detailed formulation of neural network verification, where existing verifiers can be divided into two categories: complete and incomplete verifiers. An overview of the evolving history of the neural network verifiers, along with significant performance improvements, will be presented, encouraging more efforts in this field.