Solving Probabilistic Verification Problems of Neural Networks using Branch and Bound

David Boetius, Stefan Leue, Tobias Sutter

TL;DR: A sound and complete branch and bound algorithm for solving probabilistic verification problems of neural networks significantly outpacing existing algorithms.

Abstract: Probabilistic verification problems of neural networks are concerned with formally analysing the output distribution of a neural network under a probability distribution of the inputs. Examples of probabilistic verification problems include verifying the demographic parity fairness notion or quantifying the safety of a neural network. We present a new algorithm for solving probabilistic verification problems of neural networks based on an algorithm for computing and iteratively refining lower and upper bounds on probabilities over the outputs of a neural network. By applying state-of-the-art bound propagation and branch and bound techniques from non-probabilistic neural network verification, our algorithm significantly outpaces existing probabilistic verification algorithms, reducing solving times for various benchmarks from the literature from tens of minutes to tens of seconds. Furthermore, our algorithm compares favourably even to dedicated algorithms for restricted probabilistic verification problems. We complement our empirical evaluation with a theoretical analysis, proving that our algorithm is sound and, under mildly restrictive conditions, also complete when using a suitable set of heuristics.

Lay Summary:

An artificial neural network that suggests hiring someone for a job should be impartial to gender.
This could mean that applicants of all genders have an equal chance of being hired.
Artificial neural networks are also used in autonomous cars.
In this use case, the network should not brake sharply too often.
Questions like these are difficult to answer because artificial neural networks are very complex internally.

We created a computer program to answer such questions.
What makes our program special is that it always gives the correct answer.
However, our program may take some time to come up with an answer.
Still, it is much faster than similar programs.

Link To Code: https://github.com/sen-uni-kn/probspecs

Primary Area: Deep Learning->Everything Else

Keywords: neural network verification, probabilistic verification, fairness, safety, branch and bound

Submission Number: 1788