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Recent works show that adversarial examples exist for random neural networks [Daniely and Shacham, 2020] and that these examples can be found using a single step of gradient ascent [Bubeck et al., 2021]. In this work, we extend this line of work to the “lazy training” of neural networks – a dominant model in deep learning theory in which neural networks are provably efficiently learnable. We show that over-parametrized neural networks that are guaranteed to generalize well and enjoy strong computational guarantees remain vulnerable to attacks generated using a single step of gradient ascent.
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null (Ed.)We investigate the capacity control provided by dropout in various machine learning problems. First, we study dropout for matrix completion, where it induces a distribution-dependent regularizer that equals the weighted trace-norm of the product of the factors. In deep learning, we show that the distribution-dependent regularizer due to dropout directly controls the Rademacher complexity of the underlying class of deep neural networks. These developments enable us to give concrete generalization error bounds for the dropout algorithm in both matrix completion as well as training deep neural networks.more » « less
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We investigate the robustness of stochastic approximation approaches against data poisoning attacks. We focus on two-layer neural networks with ReLU activation and show that under a specific notion of separability in the RKHS induced by the infinite-width network, training (finite-width) networks with stochastic gradient descent is robust against data poisoning attacks. Interestingly, we find that in addition to a lower bound on the width of the network, which is standard in the literature, we also require a distribution-dependent upper bound on the width for robust generalization. We provide extensive empirical evaluations that support and validate our theoretical results.more » « less
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null (Ed.)We study dropout in two-layer neural networks with rectified linear unit (ReLU) activations. Under mild overparametrization and assuming that the limiting kernel can separate the data distribution with a positive margin, we show that dropout training with logistic loss achieves $$\epsilon$$-suboptimality in test error in $$O(1/\epsilon)$$ iterations.more » « less
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We investigate the capacity control provided by dropout in various machine learning problems. First, we study dropout for matrix completion, where it induces a distribution-dependent regularizer that equals the weighted trace-norm of the product of the factors. In deep learning, we show that the distribution-dependent regularizer due to dropout directly controls the Rademacher complexity of the underlying class of deep neural networks. These developments enable us to give concrete generalization error bounds for the dropout algorithm in both matrix completion as well as training deep neural networks.more » « less
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