We introduce the concept of dynamically growing a neural network during training. In particular, an untrainable deep network starts as a trainable shallow network and newly added layers are slowly, organically added during training, thereby increasing the network's depth. This is accomplished by a new layer, which we call DropIn. The DropIn layer starts by passing the output from a previous layer (effectively skipping over the newly added layers), then increasingly including units from the new layers for both feedforward and backpropagation. We show that deep networks, which are untrainable with conventional methods, will converge with DropIn layers interspersed in the architecture. In addition, we demonstrate that DropIn provides regularization during training in an analogous way as dropout. Experiments are described with the MNIST dataset and various expanded LeNet architectures, CIFAR-10 dataset with its architecture expanded from 3 to 11 layers, and on the ImageNet dataset with the AlexNet architecture expanded to 13 layers and the VGG 16-layer architecture.
The well-known dropout @cite_6 @cite_29 method is an effective means to improve the training of deep neural networks. During training dropout randomly zeros a neuron's output activation with a probability @math , called the , so that the network cannot rely on a particular configuration. This reduces overfitting to the training data and the resulting network is more robust and better generalizes to unseen data. While dropout samples from an exponential number of different thinned' networks'' @cite_34 , samples from an exponential number of different thinner and shallower sub-networks. Like dropout, randomly changes the configuration so that the network cannot rely on a particular configuration.
@cite_29 @cite_34 @cite_6
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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, the independent sampling for dropout could be suboptimal for the sake of convergence. In this paper, we propose to use multinomial sampling for dropout, i.e., sampling features or neurons according to a multinomial distribution with different probabilities for different features neurons. To exhibit the optimal dropout probabilities, we analyze the shallow learning with multinomial dropout and establish the risk bound for stochastic optimization. By minimizing a sampling dependent factor in the risk bound, we obtain a distribution-dependent dropout with sampling probabilities dependent on the second order statistics of the data distribution. To tackle the issue of evolving distribution of neurons in deep learning, we propose an efficient adaptive dropout (named ) that computes the sampling probabilities on-the-fly from a mini-batch of examples. Empirical studies on several benchmark datasets demonstrate that the proposed dropouts achieve not only much faster convergence and but also a smaller testing error than the standard dropout. For example, on the CIFAR-100 data, the evolutional dropout achieves relative improvements over 10 on the prediction performance and over 50 on the convergence speed compared to the standard dropout. The dropout technique is a data-driven regularization method for neural networks. It consists in randomly setting some activations from a given hidden layer to zero during training. Repeating the procedure for each training example, it is equivalent to sample a network from an exponential number of architectures that share weights. The goal of dropout is to prevent feature detectors to rely on each other. Dropout has successfully been applied to Deep MLPs and to convolutional neural networks, for various tasks of Speech Recognition and Computer Vision. We recently proposed a way to use dropout in MDLSTM-RNNs for handwritten word and line recognition. In this paper, we show that further improvement can be achieved by implementing dropout differently, more specifically by applying it at better positions relative to the LSTM units. Deep neural nets with a large number of parameters are very powerful machine learning systems. However, overfitting is a serious problem in such networks. Large networks are also slow to use, making it difficult to deal with overfitting by combining the predictions of many different large neural nets at test time. Dropout is a technique for addressing this problem. The key idea is to randomly drop units (along with their connections) from the neural network during training. This prevents units from co-adapting too much. During training, dropout samples from an exponential number of different "thinned" networks. At test time, it is easy to approximate the effect of averaging the predictions of all these thinned networks by simply using a single unthinned network that has smaller weights. This significantly reduces overfitting and gives major improvements over other regularization methods. We show that dropout improves the performance of neural networks on supervised learning tasks in vision, speech recognition, document classification and computational biology, obtaining state-of-the-art results on many benchmark data sets. Recent years have witnessed the success of deep neural networks in dealing with a plenty of practical problems. The invention of effective training techniques largely contributes to this success. The so-called "Dropout" training scheme is one of the most powerful tool to reduce over-fitting. From the statistic point of view, Dropout works by implicitly imposing an L2 regularizer on the weights. In this paper, we present a new training scheme: Shakeout. Instead of randomly discarding units as Dropout does at the training stage, our method randomly chooses to enhance or inverse the contributions of each unit to the next layer. We show that our scheme leads to a combination of L1 regularization and L2 regularization imposed on the weights, which has been proved effective by the Elastic Net models in practice. We have empirically evaluated the Shakeout scheme and demonstrated that sparse network weights are obtained via Shakeout training. Our classification experiments on real-life image datasets MNIST and CIFAR-10 show that Shakeout deals with over-fitting effectively.