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Defense Against Adversarial Attacks via Controlling Gradient Leaking on Embedded Manifolds

Deep neural networks are vulnerable to adversarial attacks. Though various attempts have been made, it is still largely open to fully understand the existence of adversarial samples and thereby develop effective defense strategies. In this paper, we present a new perspective, namely gradient leaking hypothesis, to understand the existence of adversarial examples and to further motivate effective defense strategies. Specifically, we consider the low dimensional manifold structure of natural images, and empirically verify that the leakage of the gradient (w.r.t input) along the (approximately) perpendicular direction to the tangent space of data manifold is a reason for the vulnerability over adversarial attacks. Based on our investigation, we further present a new robust learning algorithm which encourages a larger gradient component in the tangent space of data manifold, suppressing the gradient leaking phenomenon consequently. Experiments on various tasks demonstrate the effectiveness of our algorithm despite its simplicity.

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