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Robustly Learning a Single Neuron via Sharpness

Puqian Wang · Nikos Zarifis · Ilias Diakonikolas · Jelena Diakonikolas

Ballroom A

Abstract: We study the problem of learning a single neuron with respect to the $L_2^2$-loss in the presence of adversarial label noise. We give an efficient algorithm that, for a broad family of activations including ReLUs, approximates the optimal $L_2^2$-error within a constant factor. Notably, our algorithm succeeds under much milder distributional assumptions compared to prior work. The key ingredient enabling our results is a novel connection to local error bounds from optimization theory.

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