In plain words: Formal verification proves mathematically that a neural network will behave safely for every input in a range, instead of just checking a sample of test cases. This book introduces the core ideas behind such proofs and shows how to adapt them to deep learning.
Abstract · Introduction to Neural Network Verification
Deep learning has transformed the way we think of software and what it can do. But deep neural networks are fragile and their behaviors are often surprising. In many settings, we need to provide formal guarantees on the safety, security, correctness, or robustness of neural networks. This book covers foundational ideas from formal verification and their adaptation to reasoning about neural networks and deep learning.
Aws Albarghouthi
arXiv:2109.10317 · cs.LG, cs.AI, cs.PL · submitted Sep 21, 2021 · updated Oct 4, 2021
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A recent work not mentioned in the last chapter "Adversarial Training with Abstraction" is [1], which kind of explains this issue using the notions of continuity and sensitivity of the abstractions.
[1]: https://arxiv.org/abs/2102.06700