QEBVerif: Quantization Error Bound Verification of Neural Networks

TL;DR

QEBVerif is a verification method that rigorously bounds quantization errors in neural networks, ensuring their properties remain valid after quantization, which is crucial for deploying DNNs on edge devices.

Contribution

It introduces a combined differential reachability analysis and MILP-based approach for verifying quantization error bounds in fully quantized neural networks.

Findings

QEBVerif provides tight error bounds efficiently.

The method is sound and complete.

Experimental results demonstrate its effectiveness.

Abstract

To alleviate the practical constraints for deploying deep neural networks (DNNs) on edge devices, quantization is widely regarded as one promising technique. It reduces the resource requirements for computational power and storage space by quantizing the weights and/or activation tensors of a DNN into lower bit-width fixed-point numbers, resulting in quantized neural networks (QNNs). While it has been empirically shown to introduce minor accuracy loss, critical verified properties of a DNN might become invalid once quantized. Existing verification methods focus on either individual neural networks (DNNs or QNNs) or quantization error bound for partial quantization. In this work, we propose a quantization error bound verification method, named QEBVerif, where both weights and activation tensors are quantized. QEBVerif consists of two parts, i.e., a differential reachability analysis (DRA) and a mixed-integer linear programming (MILP) based verification method. DRA performs difference analysis between the DNN and its quantized counterpart layer-by-layer to compute a tight quantization error interval efficiently. If DRA fails to prove the error bound, then we encode the verification problem into an equivalent MILP problem which can be solved by off-the-shelf solvers. Thus, QEBVerif is sound, complete, and reasonably efficient. We implement QEBVerif and conduct extensive experiments, showing its effectiveness and efficiency.