Verifying Low-dimensional Input Neural Networks via Input Quantization

TL;DR

This paper introduces an input quantization layer for low-dimensional neural networks, enabling efficient and exact verification of safety properties, especially for systems like ACAS Xu, by simplifying the analysis process.

Contribution

It proposes a novel input quantization method that bounds verification complexity and ensures accuracy, improving safety verification of neural controllers with low-dimensional inputs.

Findings

Quantization enables efficient input state enumeration for verification.

The method provides exact verification results immune to floating-point errors.

Applicable to neural networks with low-dimensional sensory inputs, like ACAS Xu.

Abstract

Deep neural networks are an attractive tool for compressing the control policy lookup tables in systems such as the Airborne Collision Avoidance System (ACAS). It is vital to ensure the safety of such neural controllers via verification techniques. The problem of analyzing ACAS Xu networks has motivated many successful neural network verifiers. These verifiers typically analyze the internal computation of neural networks to decide whether a property regarding the input/output holds. The intrinsic complexity of neural network computation renders such verifiers slow to run and vulnerable to floating-point error. This paper revisits the original problem of verifying ACAS Xu networks. The networks take low-dimensional sensory inputs with training data provided by a precomputed lookup table. We propose to prepend an input quantization layer to the network. Quantization allows efficient verification via input state enumeration, whose complexity is bounded by the size of the quantization space. Quantization is equivalent to nearest-neighbor interpolation at run time, which has been shown to provide acceptable accuracy for ACAS in simulation. Moreover, our technique can deliver exact verification results immune to floating-point error if we directly enumerate the network outputs on the target inference implementation or on an accurate simulation of the target implementation.