# Verified Deep Learning

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

**in-progress book** covers foundational ideas from

**formal verification** and their application to reasoning about

**deep learning**.

The book is comprised of 3 parts. A full PDF is coming soon.

## Part I Neural networks and correctness

We define neural networks as data-flow graphs, the formulation we will use for the rest of the book, and define correctness properties formally.

## Part II Constraint-based verification

We discuss constraint-based (complete) techniques for verification, where we reduce the verification problem to a form of constraint-solving.

## Part III Abstraction-based verification

We discuss abstraction-based (approximate) techniques for verification, where we evaluate a neural network on an infinite set of inputs efficiently!

Parts 2 and 3 are disjoint; the reader may go directly from Part 1 to Part 3 without losing context.

For comments, contact the

author.

Please use the following to cite this book.

```
@book{albarghouthi-book,
title = {Verified Deep Learning},
author = {Aws Albarghouthi},
publisher = {verifieddeeplearning.com},
note = {\url{http://verifieddeeplearning.com}},
year = {2021}
}
```

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