Quantized Convolutional Neural Networks Robustness under Perturbation

Contemporary machine learning models are increasingly becoming restricted by size and subsequent operations per forward pass, demanding increasing compute requirements. Quantization has emerged as a convenient approach to addressing this, in which weights and activations are mapped from their conventionally used floating-point 32-bit numeric representations to lower precision integers. This process introduces significant reductions in inference time and simplifies the hardware requirements. It is a well-studied result that the performance of such reduced precision models is congruent with their floating-point counterparts. However, there is a lack of literature that addresses the performance of quantized models in a perturbed input space, as is common when stress testing regular full-precision models, particularly for real-world deployments. We focus on addressing this gap in the context of 8-bit quantized convolutional neural networks (CNNs). We study three state-of-the-art CNNs: ResNet-18, VGG-16, and SqueezeNet1_1, and subject their floating point and fixed point forms to various noise regimes with varying intensities. We characterize performance in terms of traditional metrics, including top-1 and top-5 accuracy, as well as the F1 score. We also introduce a new metric, the Kullback-Liebler divergence of the two output distributions for a given floating-point/fixed-point model pair, as a means to examine how the model's output distribution has changed as a result of quantization, which, we contend, can be interpreted as a proxy for model similarity in decision making. We find that across all three models and under each perturbation scheme, the relative error between the quantized and full-precision model was consistently low. We also find that Kullback-Liebler divergence was on the same order of magnitude as the unperturbed tests across all perturbation regimes except Brownian noise, where significant divergences were observed for VGG-16 and SqueezeNet1_1.