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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.
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Adversarial training is an approach for increasing models resilience against adversarial perturbations. Such approaches have been demonstrated to result in models with feature representations that generalize better. However, limited works have been done on adversarial training of models on graph data. In this paper, we raise such a question { does adversarial training improve the generalization of graph representations. We formulate L2 and
While adversarial training can improve robust accuracy (against an adversary), it sometimes hurts standard accuracy (when there is no adversary). Previous work has studied this tradeoff between standard and robust accuracy, but only in the setting where no predictor performs well on both objectives in the infinite data limit. In this paper, we show that even when the optimal predictor with infinite data performs well on both objectives, a tradeoff can still manifest itself with finite data. Furthermore, since our construction is based on a convex learning problem, we rule out optimization concerns, thus laying bare a fundamental tension between robustness and generalization. Finally, we show that robust self-training mostly eliminates this tradeoff by leveraging unlabeled data.
In this work, we propose a novel technique to boost training efficiency of a neural network. Our work is based on an excellent idea that whitening the inputs of neural networks can achieve a fast convergence speed. Given the well-known fact that independent components must be whitened, we introduce a novel Independent-Component (IC) layer before each weight layer, whose inputs would be made more independent. However, determining independent components is a computationally intensive task. To overcome this challenge, we propose to implement an IC layer by combining two popular techniques, Batch Normalization and Dropout, in a new manner that we can rigorously prove that Dropout can quadratically reduce the mutual information and linearly reduce the correlation between any pair of neurons with respect to the dropout layer parameter $p$. As demonstrated experimentally, the IC layer consistently outperforms the baseline approaches with more stable training process, faster convergence speed and better convergence limit on CIFAR10/100 and ILSVRC2012 datasets. The implementation of our IC layer makes us rethink the common practices in the design of neural networks. For example, we should not place Batch Normalization before ReLU since the non-negative responses of ReLU will make the weight layer updated in a suboptimal way, and we can achieve better performance by combining Batch Normalization and Dropout together as an IC layer.
Dropout and its extensions (eg. DropBlock and DropConnect) are popular heuristics for training neural networks, which have been shown to improve generalization performance in practice. However, a theoretical understanding of their optimization and regularization properties remains elusive. Recent work shows that in the case of single hidden-layer linear networks, Dropout is a stochastic gradient descent method for minimizing a regularized loss, and that the regularizer induces solutions that are low-rank and balanced. In this work we show that for single hidden-layer linear networks, DropBlock induces spectral k-support norm regularization, and promotes solutions that are low-rank and have factors with equal norm. We also show that the global minimizer for DropBlock can be computed in closed form, and that DropConnect is equivalent to Dropout. We then show that some of these results can be extended to a general class of Dropout-strategies, and, with some assumptions, to deep non-linear networks when Dropout is applied to the last layer. We verify our theoretical claims and assumptions experimentally with commonly used network architectures.
We analyze the convergence rate of gradient flows on objective functions induced by Dropout and Dropconnect, when applying them to shallow linear Neural Networks (NNs) - which can also be viewed as doing matrix factorization using a particular regularizer. Dropout algorithms such as these are thus regularization techniques that use 0,1-valued random variables to filter weights during training in order to avoid coadaptation of features. By leveraging a recent result on nonconvex optimization and conducting a careful analysis of the set of minimizers as well as the Hessian of the loss function, we are able to obtain (i) a local convergence proof of the gradient flow and (ii) a bound on the convergence rate that depends on the data, the dropout probability, and the width of the NN. Finally, we compare this theoretical bound to numerical simulations, which are in qualitative agreement with the convergence bound and match it when starting sufficiently close to a minimizer.
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