相关论文: On Convergence and Generalization of Dropout Train…

Recurrent neural networks (RNNs) are important class of architectures among neural networks useful for language modeling and sequential prediction. However, optimizing RNNs is known to be harder compared to feed-forward neural networks. A…

Existing Natural Language Understanding (NLU) models have been shown to incorporate dataset biases leading to strong performance on in-distribution (ID) test sets but poor performance on out-of-distribution (OOD) ones. We introduce a simple…

This paper studies the approximation capacity of ReLU neural networks with norm constraint on the weights. We prove upper and lower bounds on the approximation error of these networks for smooth function classes. The lower bound is derived…

This paper introduces the first globally optimal algorithm for the empirical risk minimization problem of two-layer maxout and ReLU networks, i.e., minimizing the number of misclassifications. The algorithm has a worst-case time complexity…

When optimizing over-parameterized models, such as deep neural networks, a large set of parameters can achieve zero training error. In such cases, the choice of the optimization algorithm and its respective hyper-parameters introduces…

While metric and similarity learning has been extensively studied from several theoretical perspectives, a rigorous understanding of its generalization performance is still lacking. In this paper, we investigate the generalization behavior…

Amongst others, the adoption of Rectified Linear Units (ReLUs) is regarded as one of the ingredients of the success of deep learning. ReLU activation has been shown to mitigate the vanishing gradient issue, to encourage sparsity in the…

Classifiers used in the wild, in particular for safety-critical systems, should not only have good generalization properties but also should know when they don't know, in particular make low confidence predictions far away from the training…

Most of convolutional neural networks share the same characteristic: each convolutional layer is followed by a nonlinear activation layer where Rectified Linear Unit (ReLU) is the most widely used. In this paper, we argue that the designed…

Neural networks are regularly employed in adaptive control of nonlinear systems and related methods of reinforcement learning. A common architecture uses a neural network with a single hidden layer (i.e. a shallow network), in which the…

It is well-known that modern neural networks are vulnerable to adversarial examples. To mitigate this problem, a series of robust learning algorithms have been proposed. However, although the robust training error can be near zero via some…

Deep neural networks have been successful in many predictive modeling tasks, such as image and language recognition, where large neural networks are often used to obtain good accuracy. Consequently, it is challenging to deploy these…

This paper shows that dropout training in Generalized Linear Models is the minimax solution of a two-player, zero-sum game where an adversarial nature corrupts a statistician's covariates using a multiplicative nonparametric…

In this paper, we explore theoretical properties of training a two-layered ReLU network $g(\mathbf{x}; \mathbf{w}) = \sum_{j=1}^K \sigma(\mathbf{w}_j^T\mathbf{x})$ with centered $d$-dimensional spherical Gaussian input $\mathbf{x}$…

Dropout has been witnessed with great success in training deep neural networks by independently zeroing out the outputs of neurons at random. It has also received a surge of interest for shallow learning, e.g., logistic regression. However,…

Dropout is a simple but effective technique for learning in neural networks and other settings. A sound theoretical understanding of dropout is needed to determine when dropout should be applied and how to use it most effectively. In this…

For most state-of-the-art architectures, Rectified Linear Unit (ReLU) becomes a standard component accompanied with each layer. Although ReLU can ease the network training to an extent, the character of blocking negative values may suppress…

We present a theoretical study of the robustness of parameterized networks to random input perturbations. Specifically, we analyze local robustness at a given network input by quantifying the probability that a small additive random…

In this paper, we study the implicit regularization of the gradient descent algorithm in homogeneous neural networks, including fully-connected and convolutional neural networks with ReLU or LeakyReLU activations. In particular, we study…

Dropout and other feature noising schemes control overfitting by artificially corrupting the training data. For generalized linear models, dropout performs a form of adaptive regularization. Using this viewpoint, we show that the dropout…