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Prior studies have unveiled the vulnerability of the deep neural networks inthe context of adversarial machine learning, leading to great recent attentioninto this area. One interesting question that has yet to be fully explored isthe bias-variance relationship of adversarial machine learning, which canpotentially provide deeper insights into this behaviour. The notion of bias andvariance is one of the main approaches to analyze and evaluate thegeneralization and reliability of a machine learning model. Although it hasbeen extensively used in other machine learning models, it is not well exploredin the field of deep learning and it is even less explored in the area ofadversarial machine learning.  In this study, we investigate the effect of adversarial machine learning onthe bias and variance of a trained deep neural network and analyze howadversarial perturbations can affect the generalization of a network. We derivethe bias-variance trade-off for both classification and regression applicationsbased on two main loss functions: (i) mean squared error (MSE), and (ii)cross-entropy. Furthermore, we perform quantitative analysis with bothsimulated and real data to empirically evaluate consistency with the derivedbias-variance tradeoffs. Our analysis sheds light on why the deep neuralnetworks have poor performance under adversarial perturbation from abias-variance point of view and how this type of perturbation would change theperformance of a network. Moreover, given these new theoretical findings, weintroduce a new adversarial machine learning algorithm with lower computationalcomplexity than well-known adversarial machine learning strategies (e.g., PGD)while providing a high success rate in fooling deep neural networks in lowerperturbation magnitudes.

Vulnerability Under Adversarial Machine Learning: Bias or Variance?