Vulnerability Under Adversarial Machine Learning: Bias or Variance?
This work addresses the vulnerability of deep neural networks to adversarial attacks, providing theoretical insights into bias-variance relationships and proposing a more efficient adversarial algorithm, though it is incremental in building on existing adversarial machine learning research.
The study investigates how adversarial perturbations affect the bias and variance of deep neural networks, deriving bias-variance trade-offs for classification and regression, and introduces a new adversarial algorithm with lower computational complexity than methods like PGD while achieving high success rates in fooling networks with lower perturbation magnitudes.
Prior studies have unveiled the vulnerability of the deep neural networks in the context of adversarial machine learning, leading to great recent attention into this area. One interesting question that has yet to be fully explored is the bias-variance relationship of adversarial machine learning, which can potentially provide deeper insights into this behaviour. The notion of bias and variance is one of the main approaches to analyze and evaluate the generalization and reliability of a machine learning model. Although it has been extensively used in other machine learning models, it is not well explored in the field of deep learning and it is even less explored in the area of adversarial machine learning. In this study, we investigate the effect of adversarial machine learning on the bias and variance of a trained deep neural network and analyze how adversarial perturbations can affect the generalization of a network. We derive the bias-variance trade-off for both classification and regression applications based on two main loss functions: (i) mean squared error (MSE), and (ii) cross-entropy. Furthermore, we perform quantitative analysis with both simulated and real data to empirically evaluate consistency with the derived bias-variance tradeoffs. Our analysis sheds light on why the deep neural networks have poor performance under adversarial perturbation from a bias-variance point of view and how this type of perturbation would change the performance of a network. Moreover, given these new theoretical findings, we introduce a new adversarial machine learning algorithm with lower computational complexity than well-known adversarial machine learning strategies (e.g., PGD) while providing a high success rate in fooling deep neural networks in lower perturbation magnitudes.