Probing Innocuous Overfitting within Robust Linear Analytical Classifications

Zhenghan Chen, Mengzhu Wang, Nan Yin, Ye Wang, Junyang Chen

Keywords: Overfitting, Classifications, Robust

Abstract: The phenomena of "Overfitting," where algorithms train on noise-laden data yet uphold superior generalization capabilities, has sparked considerable discourse within the field of machine learning. Numerous studies have sought to rationalize this seemingly paradoxical occurrence, delving into over-parameterized linear regression, classification, and assorted kernel methodologies. Nonetheless, the probable manifestation of benign overfitting amidst adversarial instances—specifically, those involving minimal, deliberate alterations designed to deceive algorithms—remains ambiguous. This study elucidates the incidence of benign overfitting within the realm of adversarial instruction, a structured strategy contrived to counter adversarial instances, particularly in the context of subGaussian mixture data. We meticulously substantiate the risk confines of adversarially instructed linear classifiers processing mixtures of sub-Gaussian data amidst adversarial distortions. Our insights infer that, under subtle distortions, adversarially trained linear classifiers are capable of attaining proximate optimal standard and adversarial risks, notwithstanding the overfitting of noise-infused training datasets. The empirical analyses performed corroborate our theoretical assertions.

Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning

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Submission Number: 8132