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.
Stochastic methods randomly perturb the weights so as to achieve minimal co-dependency between neurons @cite_34 @cite_14 @cite_29 as well as regularizing the model at the same time. Stochastic regularization has become the standard practice in training deep learning models and have outperformed deterministic regularization methods on many tasks. Stochastic regularization techniques have a Bayesian model averaging interpretation as well as they posses an equivalence to weight penalties for linear models. In terms of Bayesian estimation, weight penalties are equivalent to imposing a prior distribution on the model weights.
@cite_14 @cite_29 @cite_34
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A major challenge in training deep neural networks is overfitting, i.e. inferior performance on unseen test examples compared to performance on training examples. To reduce overfitting, stochastic regularization methods have shown superior performance compared to deterministic weight penalties on a number of image recognition tasks. Stochastic methods such as Dropout and Shakeout, in expectation, are equivalent to imposing a ridge and elastic-net penalty on the model parameters, respectively. However, the choice of the norm of weight penalty is problem dependent and is not restricted to @math . Therefore, in this paper we propose the Bridgeout stochastic regularization technique and prove that it is equivalent to an @math penalty on the weights, where the norm @math can be learned as a hyperparameter from data. Experimental results show that Bridgeout results in sparse model weights, improved gradients and superior classification performance compared to Dropout and Shakeout on synthetic and real datasets. We propose a practical method for @math norm regularization for neural networks: pruning the network during training by encouraging weights to become exactly zero. Such regularization is interesting since (1) it can greatly speed up training and inference, and (2) it can improve generalization. AIC and BIC, well-known model selection criteria, are special cases of @math regularization. However, since the @math norm of weights is non-differentiable, we cannot incorporate it directly as a regularization term in the objective function. We propose a solution through the inclusion of a collection of non-negative stochastic gates, which collectively determine which weights to set to zero. We show that, somewhat surprisingly, for certain distributions over the gates, the expected @math regularized objective is differentiable with respect to the distribution parameters. We further propose the distribution for the gates, which is obtained by stretching'' a binary concrete distribution and then transforming its samples with a hard-sigmoid. The parameters of the distribution over the gates can then be jointly optimized with the original network parameters. As a result our method allows for straightforward and efficient learning of model structures with stochastic gradient descent and allows for conditional computation in a principled way. We perform various experiments to demonstrate the effectiveness of the resulting approach and regularizer. We propose a practical method for @math norm regularization for neural networks: pruning the network during training by encouraging weights to become exactly zero. Such regularization is interesting since (1) it can greatly speed up training and inference, and (2) it can improve generalization. AIC and BIC, well-known model selection criteria, are special cases of @math regularization. However, since the @math norm of weights is non-differentiable, we cannot incorporate it directly as a regularization term in the objective function. We propose a solution through the inclusion of a collection of non-negative stochastic gates, which collectively determine which weights to set to zero. We show that, somewhat surprisingly, for certain distributions over the gates, the expected @math norm of the resulting gated weights is differentiable with respect to the distribution parameters. We further propose the distribution for the gates, which is obtained by "stretching" a binary concrete distribution and then transforming its samples with a hard-sigmoid. The parameters of the distribution over the gates can then be jointly optimized with the original network parameters. As a result our method allows for straightforward and efficient learning of model structures with stochastic gradient descent and allows for conditional computation in a principled way. We perform various experiments to demonstrate the effectiveness of the resulting approach and regularizer. We investigate the generalizability of deep learning based on the sensitivity to input perturbation. We hypothesize that the high sensitivity to the perturbation of data degrades the performance on it. To reduce the sensitivity to perturbation, we propose a simple and effective regularization method, referred to as spectral norm regularization, which penalizes the high spectral norm of weight matrices in neural networks. We provide supportive evidence for the abovementioned hypothesis by experimentally confirming that the models trained using spectral norm regularization exhibit better generalizability than other baseline methods.