# Formal Verification of Piece-Wise Linear Feed-Forward Neural Networks

## TL;DR

This paper introduces a novel verification method for piece-wise linear neural networks using a global linear approximation and specialized search algorithms, improving the verification process for safety-critical applications.

## Contribution

It proposes a new verification approach combining linear approximation with a search algorithm that infers node phases and conflict clauses, enhancing verification efficiency.

## Key findings

- Effective on collision avoidance case studies
- Improves verification over existing SMT and ILP methods
- Applicable to handwritten digit recognition networks

## Abstract

We present an approach for the verification of feed-forward neural networks in which all nodes have a piece-wise linear activation function. Such networks are often used in deep learning and have been shown to be hard to verify for modern satisfiability modulo theory (SMT) and integer linear programming (ILP) solvers. The starting point of our approach is the addition of a global linear approximation of the overall network behavior to the verification problem that helps with SMT-like reasoning over the network behavior. We present a specialized verification algorithm that employs this approximation in a search process in which it infers additional node phases for the non-linear nodes in the network from partial node phase assignments, similar to unit propagation in classical SAT solving. We also show how to infer additional conflict clauses and safe node fixtures from the results of the analysis steps performed during the search. The resulting approach is evaluated on collision avoidance and handwritten digit recognition case studies.