QVIP: An ILP-based Formal Verification Approach for Quantized Neural Networks

TL;DR

This paper introduces QVIP, a novel ILP-based formal verification method for quantized neural networks, enabling efficient and complete verification by reducing the problem to integer linear constraints, outperforming existing methods.

Contribution

The paper presents the first encoding that reduces QNN verification to ILP solving, providing a sound, complete, and more efficient approach than prior techniques.

Findings

QVIP is two orders of magnitude faster than state-of-the-art methods.

The approach successfully verifies local robustness and computes robustness radius.

Experimental results confirm the effectiveness and efficiency of QVIP.

Abstract

Deep learning has become a promising programming paradigm in software development, owing to its surprising performance in solving many challenging tasks. Deep neural networks (DNNs) are increasingly being deployed in practice, but are limited on resource-constrained devices owing to their demand for computational power. Quantization has emerged as a promising technique to reduce the size of DNNs with comparable accuracy as their floating-point numbered counterparts. The resulting quantized neural networks (QNNs) can be implemented energy-efficiently. Similar to their floating-point numbered counterparts, quality assurance techniques for QNNs, such as testing and formal verification, are essential but are currently less explored. In this work, we propose a novel and efficient formal verification approach for QNNs. In particular, we are the first to propose an encoding that reduces the verification problem of QNNs into the solving of integer linear constraints, which can be solved using off-the-shelf solvers. Our encoding is both sound and complete. We demonstrate the application of our approach on local robustness verification and maximum robustness radius computation. We implement our approach in a prototype tool QVIP and conduct a thorough evaluation. Experimental results on QNNs with different quantization bits confirm the effectiveness and efficiency of our approach, e.g., two orders of magnitude faster and able to solve more verification tasks in the same time limit than the state-of-the-art methods.