# Optimization and Abstraction: A Synergistic Approach for Analyzing Neural Network Robustness

## TL;DR

This paper introduces Charon, a new verification tool that combines optimization and abstraction techniques to efficiently verify neural network robustness, outperforming existing methods on numerous benchmarks.

## Contribution

The paper presents a novel synergistic algorithm that integrates gradient-based optimization with abstraction-based proof search for neural network robustness verification.

## Key findings

- Charon significantly outperforms state-of-the-art tools
- The approach is sound and δ-complete
- Experimental results on hundreds of benchmarks

## Abstract

In recent years, the notion of local robustness (or robustness for short) has emerged as a desirable property of deep neural networks. Intuitively, robustness means that small perturbations to an input do not cause the network to perform misclassifications. In this paper, we present a novel algorithm for verifying robustness properties of neural networks. Our method synergistically combines gradient-based optimization methods for counterexample search with abstraction-based proof search to obtain a sound and ({\delta}-)complete decision procedure. Our method also employs a data-driven approach to learn a verification policy that guides abstract interpretation during proof search. We have implemented the proposed approach in a tool called Charon and experimentally evaluated it on hundreds of benchmarks. Our experiments show that the proposed approach significantly outperforms three state-of-the-art tools, namely AI^2 , Reluplex, and Reluval.