Dropout is commonly used to help reduce overfitting in deep neural networks. Sparsity is a potentially important property of neural networks, but is not explicitly controlled by Dropout-based regularization. In this work, we propose Sparseout a simple and efficient variant of Dropout that can be used to control the sparsity of the activations in a neural network. We theoretically prove that Sparseout is equivalent to an (L_q ) penalty on the features of a generalized linear model and that Dropout is a special case of Sparseout for neural networks. We empirically demonstrate that Sparseout is computationally inexpensive and is able to control the desired level of sparsity in the activations. We evaluated Sparseout on image classification and language modelling tasks to see the effect of sparsity on these tasks. We found that sparsity of the activations is favorable for language modelling performance while image classification benefits from denser activations. Sparseout provides a way to investigate sparsity in state-of-the-art deep learning models. Source code for Sparseout could be found at https: github.com najeebkhan sparseout.
Due to the over-parameterization of deep neural networks, they suffer from large generalization error, specifically, when the dataset size is relatively small. This phenomenon is known as over-fitting. Generalization error is upper bounded by the model complexity @cite_32 thus overfitting could be reduced by controlling the complexity of the model.
@cite_32
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Neural networks exhibit good generalization behavior in the over-parameterized regime, where the number of network parameters exceeds the number of observations. Nonetheless, current generalization bounds for neural networks fail to explain this phenomenon. In an attempt to bridge this gap, we study the problem of learning a two-layer over-parameterized neural network, when the data is generated by a linearly separable function. In the case where the network has Leaky ReLU activations, we provide both optimization and generalization guarantees for over-parameterized networks. Specifically, we prove convergence rates of SGD to a global minimum and provide generalization guarantees for this global minimum that are independent of the network size. Therefore, our result clearly shows that the use of SGD for optimization both finds a global minimum, and avoids overfitting despite the high capacity of the model. This is the first theoretical demonstration that SGD can avoid overfitting, when learning over-specified neural network classifiers. Abstract: One major challenge in training Deep Neural Networks is preventing overfitting. Many techniques such as data augmentation and novel regularizers such as Dropout have been proposed to prevent overfitting without requiring a massive amount of training data. In this work, we propose a new regularizer called DeCov which leads to significantly reduced overfitting (as indicated by the difference between train and val performance), and better generalization. Our regularizer encourages diverse or non-redundant representations in Deep Neural Networks by minimizing the cross-covariance of hidden activations. This simple intuition has been explored in a number of past works but surprisingly has never been applied as a regularizer in supervised learning. Experiments across a range of datasets and network architectures show that this loss always reduces overfitting while almost always maintaining or increasing generalization performance and often improving performance over Dropout. One major challenge in training Deep Neural Networks is preventing overfitting. Many techniques such as data augmentation and novel regularizers such as Dropout have been proposed to prevent overfitting without requiring a massive amount of training data. In this work, we propose a new regularizer called DeCov which leads to significantly reduced overfitting (as indicated by the difference between train and val performance), and better generalization. Our regularizer encourages diverse or non-redundant representations in Deep Neural Networks by minimizing the cross-covariance of hidden activations. This simple intuition has been explored in a number of past works but surprisingly has never been applied as a regularizer in supervised learning. Experiments across a range of datasets and network architectures show that this loss always reduces overfitting while almost always maintaining or increasing generalization performance and often improving performance over Dropout. We perform an average case analysis of the generalization dynamics of large neural networks trained using gradient descent. We study the practically-relevant "high-dimensional" regime where the number of free parameters in the network is on the order of or even larger than the number of examples in the dataset. Using random matrix theory and exact solutions in linear models, we derive the generalization error and training error dynamics of learning and analyze how they depend on the dimensionality of data and signal to noise ratio of the learning problem. We find that the dynamics of gradient descent learning naturally protect against overtraining and overfitting in large networks. Overtraining is worst at intermediate network sizes, when the effective number of free parameters equals the number of samples, and thus can be reduced by making a network smaller or larger. Additionally, in the high-dimensional regime, low generalization error requires starting with small initial weights. We then turn to non-linear neural networks, and show that making networks very large does not harm their generalization performance. On the contrary, it can in fact reduce overtraining, even without early stopping or regularization of any sort. We identify two novel phenomena underlying this behavior in overcomplete models: first, there is a frozen subspace of the weights in which no learning occurs under gradient descent; and second, the statistical properties of the high-dimensional regime yield better-conditioned input correlations which protect against overtraining. We demonstrate that naive application of worst-case theories such as Rademacher complexity are inaccurate in predicting the generalization performance of deep neural networks, and derive an alternative bound which incorporates the frozen subspace and conditioning effects and qualitatively matches the behavior observed in simulation.