We present novel techniques to accelerate the convergence of Deep Learning algorithms by conducting low overhead removal of redundant neurons -- apoptosis of neurons -- which do not contribute to model learning, during the training phase itself. We provide in-depth theoretical underpinnings of our heuristics (bounding accuracy loss and handling apoptosis of several neuron types), and present the methods to conduct adaptive neuron apoptosis. Specifically, we are able to improve the training time for several datasets by 2-3x, while reducing the number of parameters by up to 30x (4-5x on average) on datasets such as ImageNet classification. For the Higgs Boson dataset, our implementation improves the accuracy (measured by Area Under Curve (AUC)) for classification from 0.88 1 to 0.94 1, while reducing the number of parameters by 3x in comparison to existing literature. The proposed methods achieve a 2.44x speedup in comparison to the default (no apoptosis) algorithm.
Several researchers have conducted offline neuron apoptosis -- after the completion of the training phase. This is in sharp contrast to our proposed approach, in which apoptosis is conducted during the training phase itself, which reduces the overall training time, while reducing the space requirements. For offline apoptosis, researchers have conducted neuron apoptosis due to a lack of computational resources @cite_25 , regularization to prevent overfitting @cite_30 , which provides algorithms for removing synapses and possibly neurons. Kamruzzman have demonstrated similar results @cite_22 , where the fundamental objective is to remove redundant weights, and possibly neurons. The pruning has been also applied for generating human-usable rules for classification @cite_34 . Other researchers have considered temporary neuron pruning -- typically referred as Dropout , proposed by Hinton @cite_5 . A selective Dropout is proposed by other authors @cite_1 . However, since the Dropout is temporary, they do not affect the final topology of the neural network -- although they help with regularization.
@cite_30 @cite_22 @cite_1 @cite_5 @cite_34 @cite_25
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To reduce the significant redundancy in deep Convolutional Neural Networks (CNNs), most existing methods prune neurons by only considering statistics of an individual layer or two consecutive layers (e.g., prune one layer to minimize the reconstruction error of the next layer), ignoring the effect of error propagation in deep networks. In contrast, we argue that it is essential to prune neurons in the entire neuron network jointly based on a unified goal: minimizing the reconstruction error of important responses in the "final response layer" (FRL), which is the second-to-last layer before classification, for a pruned network to retrain its predictive power. Specifically, we apply feature ranking techniques to measure the importance of each neuron in the FRL, and formulate network pruning as a binary integer optimization problem and derive a closed-form solution to it for pruning neurons in earlier layers. Based on our theoretical analysis, we propose the Neuron Importance Score Propagation (NISP) algorithm to propagate the importance scores of final responses to every neuron in the network. The CNN is pruned by removing neurons with least importance, and then fine-tuned to retain its predictive power. NISP is evaluated on several datasets with multiple CNN models and demonstrated to achieve significant acceleration and compression with negligible accuracy loss. To reduce the significant redundancy in deep Convolutional Neural Networks (CNNs), most existing methods prune neurons by only considering the statistics of an individual layer or two consecutive layers (e.g., prune one layer to minimize the reconstruction error of the next layer), ignoring the effect of error propagation in deep networks. In contrast, we argue that for a pruned network to retain its predictive power, it is essential to prune neurons in the entire neuron network jointly based on a unified goal: minimizing the reconstruction error of important responses in the "final response layer" (FRL), which is the second-to-last layer before classification. Specifically, we apply feature ranking techniques to measure the importance of each neuron in the FRL, formulate network pruning as a binary integer optimization problem, and derive a closed-form solution to it for pruning neurons in earlier layers. Based on our theoretical analysis, we propose the Neuron Importance Score Propagation (NISP) algorithm to propagate the importance scores of final responses to every neuron in the network. The CNN is pruned by removing neurons with least importance, and it is then fine-tuned to recover its predictive power. NISP is evaluated on several datasets with multiple CNN models and demonstrated to achieve significant acceleration and compression with negligible accuracy loss. 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. Recently, neuron activations extracted from a pre-trained convolutional neural network (CNN) show promising performance in various visual tasks. However, due to the domain and task bias, using the features generated from the model pre-trained for image classification as image representations for instance retrieval is problematic. In this paper, we propose quartet-net learning to improve the discriminative power of CNN features for instance retrieval. The general idea is to map the features into a space where the image similarity can be better evaluated. Our network differs from the traditional Siamese-net in two ways. First, we adopt a double-margin contrastive loss with a dynamic margin tuning strategy to train the network which leads to more robust performance. Second, we introduce in the mimic learning regularization to improve the generalization ability of the network by preventing it from overfitting to the training data. Catering for the network learning, we collect a large-scale dataset, namely GeoPair, which consists of 68k matching image pairs and 63k non-matching pairs. Experiments on several standard instance retrieval datasets demonstrate the effectiveness of our method.