Survey of Dropout Methods for Deep Neural Networks
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paper_title: Improving neural networks by preventing co-adaptation of feature detectors

paper_content:

When a large feedforward neural network is trained on a small training set, it typically performs poorly on held-out test data. This "overfitting" is greatly reduced by randomly omitting half of the feature detectors on each training case. This prevents complex co-adaptations in which a feature detector is only helpful in the context of several other specific feature detectors. Instead, each neuron learns to detect a feature that is generally helpful for producing the correct answer given the combinatorially large variety of internal contexts in which it must operate. Random "dropout" gives big improvements on many benchmark tasks and sets new records for speech and object recognition.
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paper_title: ImageNet classification with deep convolutional neural networks

paper_content:

We trained a large, deep convolutional neural network to classify the 1.2 million high-resolution images in the ImageNet LSVRC-2010 contest into the 1000 different classes. On the test data, we achieved top-1 and top-5 error rates of 37.5% and 17.0%, respectively, which is considerably better than the previous state-of-the-art. The neural network, which has 60 million parameters and 650,000 neurons, consists of five convolutional layers, some of which are followed by max-pooling layers, and three fully connected layers with a final 1000-way softmax. To make training faster, we used non-saturating neurons and a very efficient GPU implementation of the convolution operation. To reduce overfitting in the fully connected layers we employed a recently developed regularization method called "dropout" that proved to be very effective. We also entered a variant of this model in the ILSVRC-2012 competition and achieved a winning top-5 test error rate of 15.3%, compared to 26.2% achieved by the second-best entry.
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paper_title: Adaptive dropout for training deep neural networks

paper_content:

Recently, it was shown that deep neural networks can perform very well if the activities of hidden units are regularized during learning, e.g, by randomly dropping out 50% of their activities. We describe a method called 'standout' in which a binary belief network is overlaid on a neural network and is used to regularize of its hidden units by selectively setting activities to zero. This 'adaptive dropout network' can be trained jointly with the neural network by approximately computing local expectations of binary dropout variables, computing derivatives using back-propagation, and using stochastic gradient descent. Interestingly, experiments show that the learnt dropout network parameters recapitulate the neural network parameters, suggesting that a good dropout network regularizes activities according to magnitude. When evaluated on the MNIST and NORB datasets, we found that our method achieves lower classification error rates than other feature learning methods, including standard dropout, denoising auto-encoders, and restricted Boltzmann machines. For example, our method achieves 0.80% and 5.8% errors on the MNIST and NORB test sets, which is better than state-of-the-art results obtained using feature learning methods, including those that use convolutional architectures.
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paper_title: Variational Dropout and the Local Reparameterization Trick

paper_content:

We explore an as yet unexploited opportunity for drastically improving the efficiency of stochastic gradient variational Bayes (SGVB) with global model parameters. Regular SGVB estimators rely on sampling of parameters once per minibatch of data, and have variance that is constant w.r.t. the minibatch size. The efficiency of such estimators can be drastically improved upon by translating uncertainty about global parameters into local noise that is independent across datapoints in the minibatch. Such reparameterizations with local noise can be trivially parallelized and have variance that is inversely proportional to the minibatch size, generally leading to much faster convergence.We find an important connection with regularization by dropout: the original Gaussian dropout objective corresponds to SGVB with local noise, a scale-invariant prior and proportionally fixed posterior variance. Our method allows inference of more flexibly parameterized posteriors; specifically, we propose \emph{variational dropout}, a generalization of Gaussian dropout, but with a more flexibly parameterized posterior, often leading to better generalization. The method is demonstrated through several experiments.
---
paper_title: Fast dropout training

paper_content:

Preventing feature co-adaptation by encouraging independent contributions from different features often improves classification and regression performance. Dropout training (Hinton et al., 2012) does this by randomly dropping out (zeroing) hidden units and input features during training of neural networks. However, repeatedly sampling a random subset of input features makes training much slower. Based on an examination of the implied objective function of dropout training, we show how to do fast dropout training by sampling from or integrating a Gaussian approximation, instead of doing Monte Carlo optimization of this objective. This approximation, justified by the central limit theorem and empirical evidence, gives an order of magnitude speedup and more stability. We show how to do fast dropout training for classification, regression, and multilayer neural networks. Beyond dropout, our technique is extended to integrate out other types of noise and small image transformations.
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paper_title: Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning

paper_content:

Deep learning tools have gained tremendous attention in applied machine learning. However such tools for regression and classification do not capture model uncertainty. In comparison, Bayesian models offer a mathematically grounded framework to reason about model uncertainty, but usually come with a prohibitive computational cost. In this paper we develop a new theoretical framework casting dropout training in deep neural networks (NNs) as approximate Bayesian inference in deep Gaussian processes. A direct result of this theory gives us tools to model uncertainty with dropout NNs -- extracting information from existing models that has been thrown away so far. This mitigates the problem of representing uncertainty in deep learning without sacrificing either computational complexity or test accuracy. We perform an extensive study of the properties of dropout's uncertainty. Various network architectures and non-linearities are assessed on tasks of regression and classification, using MNIST as an example. We show a considerable improvement in predictive log-likelihood and RMSE compared to existing state-of-the-art methods, and finish by using dropout's uncertainty in deep reinforcement learning.
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paper_title: On the State of the Art of Evaluation in Neural Language Models

paper_content:

Ongoing innovations in recurrent neural network architectures have provided a steady influx of apparently state-of-the-art results on language modelling benchmarks. However, these have been evaluated using differing code bases and limited computational resources, which represent uncontrolled sources of experimental variation. We reevaluate several popular architectures and regularisation methods with large-scale automatic black-box hyperparameter tuning and arrive at the somewhat surprising conclusion that standard LSTM architectures, when properly regularised, outperform more recent models. We establish a new state of the art on the Penn Treebank and Wikitext-2 corpora, as well as strong baselines on the Hutter Prize dataset.
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paper_title: Regularizing and Optimizing LSTM Language Models

paper_content:

Recurrent neural networks (RNNs), such as long short-term memory networks (LSTMs), serve as a fundamental building block for many sequence learning tasks, including machine translation, language modeling, and question answering. In this paper, we consider the specific problem of word-level language modeling and investigate strategies for regularizing and optimizing LSTM-based models. We propose the weight-dropped LSTM which uses DropConnect on hidden-to-hidden weights as a form of recurrent regularization. Further, we introduce NT-ASGD, a variant of the averaged stochastic gradient method, wherein the averaging trigger is determined using a non-monotonic condition as opposed to being tuned by the user. Using these and other regularization strategies, we achieve state-of-the-art word level perplexities on two data sets: 57.3 on Penn Treebank and 65.8 on WikiText-2. In exploring the effectiveness of a neural cache in conjunction with our proposed model, we achieve an even lower state-of-the-art perplexity of 52.8 on Penn Treebank and 52.0 on WikiText-2.
---
paper_title: Improving neural networks by preventing co-adaptation of feature detectors

paper_content:

When a large feedforward neural network is trained on a small training set, it typically performs poorly on held-out test data. This "overfitting" is greatly reduced by randomly omitting half of the feature detectors on each training case. This prevents complex co-adaptations in which a feature detector is only helpful in the context of several other specific feature detectors. Instead, each neuron learns to detect a feature that is generally helpful for producing the correct answer given the combinatorially large variety of internal contexts in which it must operate. Random "dropout" gives big improvements on many benchmark tasks and sets new records for speech and object recognition.
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paper_title: An empirical analysis of dropout in piecewise linear networks

paper_content:

Abstract: The recently introduced dropout training criterion for neural networks has been the subject of much attention due to its simplicity and remarkable effectiveness as a regularizer, as well as its interpretation as a training procedure for an exponentially large ensemble of networks that share parameters. In this work we empirically investigate several questions related to the efficacy of dropout, specifically as it concerns networks employing the popular rectified linear activation function. We investigate the quality of the test time weight-scaling inference procedure by evaluating the geometric average exactly in small models, as well as compare the performance of the geometric mean to the arithmetic mean more commonly employed by ensemble techniques. We explore the effect of tied weights on the ensemble interpretation by training ensembles of masked networks without tied weights. Finally, we investigate an alternative criterion based on a biased estimator of the maximum likelihood ensemble gradient.
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paper_title: Dropout: a simple way to prevent neural networks from overfitting

paper_content:

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.
---
paper_title: Improving neural networks by preventing co-adaptation of feature detectors

paper_content:

When a large feedforward neural network is trained on a small training set, it typically performs poorly on held-out test data. This "overfitting" is greatly reduced by randomly omitting half of the feature detectors on each training case. This prevents complex co-adaptations in which a feature detector is only helpful in the context of several other specific feature detectors. Instead, each neuron learns to detect a feature that is generally helpful for producing the correct answer given the combinatorially large variety of internal contexts in which it must operate. Random "dropout" gives big improvements on many benchmark tasks and sets new records for speech and object recognition.
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paper_title: Understanding Dropout

paper_content:

Dropout is a relatively new algorithm for training neural networks which relies on stochastically "dropping out" neurons during training in order to avoid the co-adaptation of feature detectors. We introduce a general formalism for studying dropout on either units or connections, with arbitrary probability values, and use it to analyze the averaging and regularizing properties of dropout in both linear and non-linear networks. For deep neural networks, the averaging properties of dropout are characterized by three recursive equations, including the approximation of expectations by normalized weighted geometric means. We provide estimates and bounds for these approximations and corroborate the results with simulations. Among other results, we also show how dropout performs stochastic gradient descent on a regularized error function.
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paper_title: Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning

paper_content:

Deep learning tools have gained tremendous attention in applied machine learning. However such tools for regression and classification do not capture model uncertainty. In comparison, Bayesian models offer a mathematically grounded framework to reason about model uncertainty, but usually come with a prohibitive computational cost. In this paper we develop a new theoretical framework casting dropout training in deep neural networks (NNs) as approximate Bayesian inference in deep Gaussian processes. A direct result of this theory gives us tools to model uncertainty with dropout NNs -- extracting information from existing models that has been thrown away so far. This mitigates the problem of representing uncertainty in deep learning without sacrificing either computational complexity or test accuracy. We perform an extensive study of the properties of dropout's uncertainty. Various network architectures and non-linearities are assessed on tasks of regression and classification, using MNIST as an example. We show a considerable improvement in predictive log-likelihood and RMSE compared to existing state-of-the-art methods, and finish by using dropout's uncertainty in deep reinforcement learning.
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paper_title: Concrete Dropout

paper_content:

Dropout is used as a practical tool to obtain uncertainty estimates in large vision models and reinforcement learning (RL) tasks. But to obtain well-calibrated uncertainty estimates, a grid-search over the dropout probabilities is necessary—a prohibitive operation with large models, and an impossible one with RL. We propose a new dropout variant which gives improved performance and better calibrated uncertainties. Relying on recent developments in Bayesian deep learning, we use a continuous relaxation of dropout’s discrete masks. Together with a principled optimisation objective, this allows for automatic tuning of the dropout probability in large models, and as a result faster experimentation cycles. In RL this allows the agent to adapt its uncertainty dynamically as more data is observed. We analyse the proposed variant extensively on a range of tasks, and give insights into common practice in the field where larger dropout probabilities are often used in deeper model layers.
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paper_title: Dropout: a simple way to prevent neural networks from overfitting

paper_content:

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.
---
paper_title: Adaptive dropout for training deep neural networks

paper_content:

Recently, it was shown that deep neural networks can perform very well if the activities of hidden units are regularized during learning, e.g, by randomly dropping out 50% of their activities. We describe a method called 'standout' in which a binary belief network is overlaid on a neural network and is used to regularize of its hidden units by selectively setting activities to zero. This 'adaptive dropout network' can be trained jointly with the neural network by approximately computing local expectations of binary dropout variables, computing derivatives using back-propagation, and using stochastic gradient descent. Interestingly, experiments show that the learnt dropout network parameters recapitulate the neural network parameters, suggesting that a good dropout network regularizes activities according to magnitude. When evaluated on the MNIST and NORB datasets, we found that our method achieves lower classification error rates than other feature learning methods, including standard dropout, denoising auto-encoders, and restricted Boltzmann machines. For example, our method achieves 0.80% and 5.8% errors on the MNIST and NORB test sets, which is better than state-of-the-art results obtained using feature learning methods, including those that use convolutional architectures.
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paper_title: A Theoretically Grounded Application of Dropout in Recurrent Neural Networks

paper_content:

Recurrent neural networks (RNNs) stand at the forefront of many recent developments in deep learning. Yet a major difficulty with these models is their tendency to overfit, with dropout shown to fail when applied to recurrent layers. Recent results at the intersection of Bayesian modelling and deep learning offer a Bayesian interpretation of common deep learning techniques such as dropout. This grounding of dropout in approximate Bayesian inference suggests an extension of the theoretical results, offering insights into the use of dropout with RNN models. We apply this new variational inference based dropout technique in LSTM and GRU models, assessing it on language modelling and sentiment analysis tasks. The new approach outperforms existing techniques, and to the best of our knowledge improves on the single model state-of-the-art in language modelling with the Penn Treebank (73.4 test perplexity). This extends our arsenal of variational tools in deep learning.
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paper_title: Variational Dropout and the Local Reparameterization Trick

paper_content:

We explore an as yet unexploited opportunity for drastically improving the efficiency of stochastic gradient variational Bayes (SGVB) with global model parameters. Regular SGVB estimators rely on sampling of parameters once per minibatch of data, and have variance that is constant w.r.t. the minibatch size. The efficiency of such estimators can be drastically improved upon by translating uncertainty about global parameters into local noise that is independent across datapoints in the minibatch. Such reparameterizations with local noise can be trivially parallelized and have variance that is inversely proportional to the minibatch size, generally leading to much faster convergence.We find an important connection with regularization by dropout: the original Gaussian dropout objective corresponds to SGVB with local noise, a scale-invariant prior and proportionally fixed posterior variance. Our method allows inference of more flexibly parameterized posteriors; specifically, we propose \emph{variational dropout}, a generalization of Gaussian dropout, but with a more flexibly parameterized posterior, often leading to better generalization. The method is demonstrated through several experiments.
---
paper_title: Fast dropout training

paper_content:

Preventing feature co-adaptation by encouraging independent contributions from different features often improves classification and regression performance. Dropout training (Hinton et al., 2012) does this by randomly dropping out (zeroing) hidden units and input features during training of neural networks. However, repeatedly sampling a random subset of input features makes training much slower. Based on an examination of the implied objective function of dropout training, we show how to do fast dropout training by sampling from or integrating a Gaussian approximation, instead of doing Monte Carlo optimization of this objective. This approximation, justified by the central limit theorem and empirical evidence, gives an order of magnitude speedup and more stability. We show how to do fast dropout training for classification, regression, and multilayer neural networks. Beyond dropout, our technique is extended to integrate out other types of noise and small image transformations.
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paper_title: Maxout Networks

paper_content:

We consider the problem of designing models to leverage a recently introduced approximate model averaging technique called dropout. We define a simple new model called maxout (so named because its output is the max of a set of inputs, and because it is a natural companion to dropout) designed to both facilitate optimization by dropout and improve the accuracy of dropout's fast approximate model averaging technique. We empirically verify that the model successfully accomplishes both of these tasks. We use maxout and dropout to demonstrate state of the art classification performance on four benchmark datasets: MNIST, CIFAR-10, CIFAR-100, and SVHN.
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paper_title: Towards Dropout Training for Convolutional Neural Networks

paper_content:

Recently, dropout has seen increasing use in deep learning. For deep convolutional neural networks, dropout is known to work well in fully-connected layers. However, its effect in convolutional and pooling layers is still not clear. This paper demonstrates that max-pooling dropout is equivalent to randomly picking activation based on a multinomial distribution at training time. In light of this insight, we advocate employing our proposed probabilistic weighted pooling, instead of commonly used max-pooling, to act as model averaging at test time. Empirical evidence validates the superiority of probabilistic weighted pooling. We also empirically show that the effect of convolutional dropout is not trivial, despite the dramatically reduced possibility of over-fitting due to the convolutional architecture. Elaborately designing dropout training simultaneously in max-pooling and fully-connected layers, we achieve state-of-the-art performance on MNIST, and very competitive results on CIFAR-10 and CIFAR-100, relative to other approaches without data augmentation. Finally, we compare max-pooling dropout and stochastic pooling, both of which introduce stochasticity based on multinomial distributions at pooling stage.
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paper_title: Analysis on the Dropout Effect in Convolutional Neural Networks

paper_content:

Regularizing neural networks is an important task to reduce overfitting. Dropout [1] has been a widely-used regularization trick for neural networks. In convolutional neural networks (CNNs), dropout is usually applied to the fully connected layers. Meanwhile, the regularization effect of dropout in the convolutional layers has not been thoroughly analyzed in the literature. In this paper, we analyze the effect of dropout in the convolutional layers, which is indeed proved as a powerful generalization method. We observed that dropout in CNNs regularizes the networks by adding noise to the output feature maps of each layer, yielding robustness to variations of images. Based on this observation, we propose a stochastic dropout whose drop ratio varies for each iteration. Furthermore, we propose a new regularization method which is inspired by behaviors of image filters. Rather than randomly drop the activation, we selectively drop the activations which have high values across the feature map or across the channels. Experimental results validate the regularization performance of selective max-drop and stochastic dropout is competitive to the dropout or spatial dropout [2].
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paper_title: Efficient object localization using Convolutional Networks

paper_content:

Recent state-of-the-art performance on human-body pose estimation has been achieved with Deep Convolutional Networks (ConvNets). Traditional ConvNet architectures include pooling and sub-sampling layers which reduce computational requirements, introduce invariance and prevent over-training. These benefits of pooling come at the cost of reduced localization accuracy. We introduce a novel architecture which includes an efficient ‘position refinement’ model that is trained to estimate the joint offset location within a small region of the image. This refinement model is jointly trained in cascade with a state-of-the-art ConvNet model [21] to achieve improved accuracy in human joint location estimation. We show that the variance of our detector approaches the variance of human annotations on the FLIC [20] dataset and outperforms all existing approaches on the MPII-human-pose dataset [1].
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paper_title: Improved Regularization of Convolutional Neural Networks with Cutout

paper_content:

Convolutional neural networks are capable of learning powerful representational spaces, which are necessary for tackling complex learning tasks. However, due to the model capacity required to capture such representations, they are often susceptible to overfitting and therefore require proper regularization in order to generalize well. In this paper, we show that the simple regularization technique of randomly masking out square regions of input during training, which we call cutout, can be used to improve the robustness and overall performance of convolutional neural networks. Not only is this method extremely easy to implement, but we also demonstrate that it can be used in conjunction with existing forms of data augmentation and other regularizers to further improve model performance. We evaluate this method by applying it to current state-of-the-art architectures on the CIFAR-10, CIFAR-100, and SVHN datasets, yielding new state-of-the-art results of 2.56%, 15.20%, and 1.30% test error respectively. Code is available at this https URL
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paper_title: Effective and Efficient Dropout for Deep Convolutional Neural Networks

paper_content:

Machine-learning-based data-driven applications have become ubiquitous, e.g., health-care analysis and database system optimization. Big training data and large (deep) models are crucial for good performance. Dropout has been widely used as an efficient regularization technique to prevent large models from overfitting. However, many recent works show that dropout does not bring much performance improvement for deep convolutional neural networks (CNNs), a popular deep learning model for data-driven applications. In this paper, we revisit the problem and investigate its failure. We attribute the failure to the conflict between the conventional dropout and the batch normalization operation after it. We propose to adjust the order of the dropout operations to address the conflict; and further, other structurally more suited dropout variants are also examined and introduced for more efficient and effective regularization for CNNs. These dropout variants can be easily integrated into the building blocks of CNNs implemented by existing deep learning libraries, e.g., Apache Singa, to provide effective regularization for CNNs. Extensive experiments on benchmark datasets CIFAR, SVHN and ImageNet are conducted to compare the existing building blocks and the proposed building blocks with the proposed customizable dropout methods. The results confirm the superiority of our building blocks due to the regularization and implicit model ensemble effect of dropout. In particular, we improve over state-of-the-art CNNs with significantly better performance of 3.17%, 16.15%, 1.44%, 21.68% error rate on CIFAR-10, CIFAR-100, SVHN and ImageNet respectively.
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paper_title: Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift

paper_content:

Training Deep Neural Networks is complicated by the fact that the distribution of each layer's inputs changes during training, as the parameters of the previous layers change. This slows down the training by requiring lower learning rates and careful parameter initialization, and makes it notoriously hard to train models with saturating nonlinearities. We refer to this phenomenon as internal covariate shift, and address the problem by normalizing layer inputs. Our method draws its strength from making normalization a part of the model architecture and performing the normalization for each training mini-batch. Batch Normalization allows us to use much higher learning rates and be less careful about initialization, and in some cases eliminates the need for Dropout. Applied to a state-of-the-art image classification model, Batch Normalization achieves the same accuracy with 14 times fewer training steps, and beats the original model by a significant margin. Using an ensemble of batch-normalized networks, we improve upon the best published result on ImageNet classification: reaching 4.82% top-5 test error, exceeding the accuracy of human raters.
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paper_title: Deep Residual Learning for Image Recognition

paper_content:

Deeper neural networks are more difficult to train. We present a residual learning framework to ease the training of networks that are substantially deeper than those used previously. We explicitly reformulate the layers as learning residual functions with reference to the layer inputs, instead of learning unreferenced functions. We provide comprehensive empirical evidence showing that these residual networks are easier to optimize, and can gain accuracy from considerably increased depth. On the ImageNet dataset we evaluate residual nets with a depth of up to 152 layers—8× deeper than VGG nets [40] but still having lower complexity. An ensemble of these residual nets achieves 3.57% error on the ImageNet test set. This result won the 1st place on the ILSVRC 2015 classification task. We also present analysis on CIFAR-10 with 100 and 1000 layers. The depth of representations is of central importance for many visual recognition tasks. Solely due to our extremely deep representations, we obtain a 28% relative improvement on the COCO object detection dataset. Deep residual nets are foundations of our submissions to ILSVRC & COCO 2015 competitions1, where we also won the 1st places on the tasks of ImageNet detection, ImageNet localization, COCO detection, and COCO segmentation.
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paper_title: Variational Dropout Sparsifies Deep Neural Networks

paper_content:

We explore a recently proposed Variational Dropout technique that provided an elegant Bayesian interpretation to Gaussian Dropout. We extend Variational Dropout to the case when dropout rates are unbounded, propose a way to reduce the variance of the gradient estimator and report first experimental results with individual dropout rates per weight. Interestingly, it leads to extremely sparse solutions both in fully-connected and convolutional layers. This effect is similar to automatic relevance determination effect in empirical Bayes but has a number of advantages. We reduce the number of parameters up to 280 times on LeNet architectures and up to 68 times on VGG-like networks with a negligible decrease of accuracy.
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paper_title: Ising-dropout: A Regularization Method for Training and Compression of Deep Neural Networks

paper_content:

Overfitting is a major problem in training machine learning models, specifically deep neural networks. This problem may be caused by imbalanced datasets and initialization of the model parameters, which conforms the model too closely to the training data and negatively affects the generalization performance of the model for unseen data. The original dropout is a regularization technique to drop hidden units randomly during training. In this paper, we propose an adaptive technique to wisely drop the visible and hidden units in a deep neural network using Ising energy of the network. The preliminary results show that the proposed approach can keep the classification performance competitive to the original network while eliminating optimization of unnecessary network parameters in each training cycle. The dropout state of units can also be applied to the trained (inference) model. This technique could compress the network in terms of number of parameters up to 41.18% and 55.86% for the classification task on the MNIST and Fashion-MNIST datasets, respectively.
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paper_title: Recurrent Neural Network Regularization

paper_content:

We present a simple regularization technique for Recurrent Neural Networks (RNNs) with Long Short-Term Memory (LSTM) units. Dropout, the most successful technique for regularizing neural networks, does not work well with RNNs and LSTMs. In this paper, we show how to correctly apply dropout to LSTMs, and show that it substantially reduces overfitting on a variety of tasks. These tasks include language modeling, speech recognition, image caption generation, and machine translation.
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paper_title: Recurrent Dropout without Memory Loss

paper_content:

This paper presents a novel approach to recurrent neural network (RNN) regularization. Differently from the widely adopted dropout method, which is applied to \textit{forward} connections of feed-forward architectures or RNNs, we propose to drop neurons directly in \textit{recurrent} connections in a way that does not cause loss of long-term memory. Our approach is as easy to implement and apply as the regular feed-forward dropout and we demonstrate its effectiveness for Long Short-Term Memory network, the most popular type of RNN cells. Our experiments on NLP benchmarks show consistent improvements even when combined with conventional feed-forward dropout.
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paper_title: RNNDROP: A novel dropout for RNNS in ASR

paper_content:

Recently, recurrent neural networks (RNN) have achieved the state-of-the-art performance in several applications that deal with temporal data, e.g., speech recognition, handwriting recognition and machine translation. While the ability of handling long-term dependency in data is the key for the success of RNN, combating over-fitting in training the models is a critical issue for achieving the cutting-edge performance particularly when the depth and size of the network increase. To that end, there have been some attempts to apply the dropout, a popular regularization scheme for the feed-forward neural networks, to RNNs, but they do not perform as well as other regularization scheme such as weight noise injection. In this paper, we propose rnnDrop, a novel variant of the dropout tailored for RNNs. Unlike the existing methods where dropout is applied only to the non-recurrent connections, the proposed method applies dropout to the recurrent connections as well in such a way that RNNs generalize well. Our experiments show that rnnDrop is a better regularization method than others including weight noise injection. Namely, when deep bidirectional long short-term memory (LSTM) RNNs were trained with rnnDrop as acoustic models for phoneme and speech recognition, they significantly outperformed the current state-of-the-arts; we achieved the phoneme error rate of 16.29% on the TIMIT core test set for phoneme recognition and the word error rate of 5.53% on the Wall Street Journal (WSJ) dataset, dev93, for speech recognition, which are the best reported results on both of the datasets.
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paper_title: Dropout: a simple way to prevent neural networks from overfitting

paper_content:

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.
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paper_title: Structured Bayesian Pruning via Log-Normal Multiplicative Noise

paper_content:

Dropout-based regularization methods can be regarded as injecting random noise with pre-defined magnitude to different parts of the neural network during training. It was recently shown that Bayesian dropout procedure not only improves generalization but also leads to extremely sparse neural architectures by automatically setting the individual noise magnitude per weight. However, this sparsity can hardly be used for acceleration since it is unstructured. In the paper, we propose a new Bayesian model that takes into account the computational structure of neural networks and provides structured sparsity, e.g. removes neurons and/or convolutional channels in CNNs. To do this we inject noise to the neurons outputs while keeping the weights unregularized. We establish the probabilistic model with a proper truncated log-uniform prior over the noise and truncated log-normal variational approximation that ensures that the KL-term in the evidence lower bound is computed in closed-form. The model leads to structured sparsity by removing elements with a low SNR from the computation graph and provides significant acceleration on a number of deep neural architectures. The model is easy to implement as it can be formulated as a separate dropout-like layer.
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paper_title: Recent Advances in Recurrent Neural Networks

paper_content:

Recurrent neural networks (RNNs) are capable of learning features and long term dependencies from sequential and time-series data. The RNNs have a stack of non-linear units where at least one connection between units forms a directed cycle. A well-trained RNN can model any dynamical system; however, training RNNs is mostly plagued by issues in learning long-term dependencies. In this paper, we present a survey on RNNs and several new advances for newcomers and professionals in the field. The fundamentals and recent advances are explained and the research challenges are introduced.
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paper_title: A Theoretically Grounded Application of Dropout in Recurrent Neural Networks

paper_content:

Recurrent neural networks (RNNs) stand at the forefront of many recent developments in deep learning. Yet a major difficulty with these models is their tendency to overfit, with dropout shown to fail when applied to recurrent layers. Recent results at the intersection of Bayesian modelling and deep learning offer a Bayesian interpretation of common deep learning techniques such as dropout. This grounding of dropout in approximate Bayesian inference suggests an extension of the theoretical results, offering insights into the use of dropout with RNN models. We apply this new variational inference based dropout technique in LSTM and GRU models, assessing it on language modelling and sentiment analysis tasks. The new approach outperforms existing techniques, and to the best of our knowledge improves on the single model state-of-the-art in language modelling with the Penn Treebank (73.4 test perplexity). This extends our arsenal of variational tools in deep learning.
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paper_title: Variational Dropout and the Local Reparameterization Trick

paper_content:

We explore an as yet unexploited opportunity for drastically improving the efficiency of stochastic gradient variational Bayes (SGVB) with global model parameters. Regular SGVB estimators rely on sampling of parameters once per minibatch of data, and have variance that is constant w.r.t. the minibatch size. The efficiency of such estimators can be drastically improved upon by translating uncertainty about global parameters into local noise that is independent across datapoints in the minibatch. Such reparameterizations with local noise can be trivially parallelized and have variance that is inversely proportional to the minibatch size, generally leading to much faster convergence.We find an important connection with regularization by dropout: the original Gaussian dropout objective corresponds to SGVB with local noise, a scale-invariant prior and proportionally fixed posterior variance. Our method allows inference of more flexibly parameterized posteriors; specifically, we propose \emph{variational dropout}, a generalization of Gaussian dropout, but with a more flexibly parameterized posterior, often leading to better generalization. The method is demonstrated through several experiments.
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paper_title: Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding

paper_content:

Neural networks are both computationally intensive and memory intensive, making them difficult to deploy on embedded systems with limited hardware resources. To address this limitation, we introduce "deep compression", a three stage pipeline: pruning, trained quantization and Huffman coding, that work together to reduce the storage requirement of neural networks by 35x to 49x without affecting their accuracy. Our method first prunes the network by learning only the important connections. Next, we quantize the weights to enforce weight sharing, finally, we apply Huffman coding. After the first two steps we retrain the network to fine tune the remaining connections and the quantized centroids. Pruning, reduces the number of connections by 9x to 13x; Quantization then reduces the number of bits that represent each connection from 32 to 5. On the ImageNet dataset, our method reduced the storage required by AlexNet by 35x, from 240MB to 6.9MB, without loss of accuracy. Our method reduced the size of VGG-16 by 49x from 552MB to 11.3MB, again with no loss of accuracy. This allows fitting the model into on-chip SRAM cache rather than off-chip DRAM memory. Our compression method also facilitates the use of complex neural networks in mobile applications where application size and download bandwidth are constrained. Benchmarked on CPU, GPU and mobile GPU, compressed network has 3x to 4x layerwise speedup and 3x to 7x better energy efficiency.
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paper_title: Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning

paper_content:

Deep learning tools have gained tremendous attention in applied machine learning. However such tools for regression and classification do not capture model uncertainty. In comparison, Bayesian models offer a mathematically grounded framework to reason about model uncertainty, but usually come with a prohibitive computational cost. In this paper we develop a new theoretical framework casting dropout training in deep neural networks (NNs) as approximate Bayesian inference in deep Gaussian processes. A direct result of this theory gives us tools to model uncertainty with dropout NNs -- extracting information from existing models that has been thrown away so far. This mitigates the problem of representing uncertainty in deep learning without sacrificing either computational complexity or test accuracy. We perform an extensive study of the properties of dropout's uncertainty. Various network architectures and non-linearities are assessed on tasks of regression and classification, using MNIST as an example. We show a considerable improvement in predictive log-likelihood and RMSE compared to existing state-of-the-art methods, and finish by using dropout's uncertainty in deep reinforcement learning.
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paper_title: Adversarial Dropout for Supervised and Semi-supervised Learning

paper_content:

Recently, the training with adversarial examples, which are generated by adding a small but worst-case perturbation on input examples, has been proved to improve generalization performance of neural networks. In contrast to the individually biased inputs to enhance the generality, this paper introduces adversarial dropout, which is a minimal set of dropouts that maximize the divergence between the outputs from the network with the dropouts and the training supervisions. The identified adversarial dropout are used to reconfigure the neural network to train, and we demonstrated that training on the reconfigured sub-network improves the generalization performance of supervised and semi-supervised learning tasks on MNIST and CIFAR-10. We analyzed the trained model to reason the performance improvement, and we found that adversarial dropout increases the sparsity of neural networks more than the standard dropout does.
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paper_title: Adversarial Dropout Regularization

paper_content:

We present a method for transferring neural representations from label-rich source domains to unlabeled target domains. Recent adversarial methods proposed for this task learn to align features across domains by fooling a special domain critic network. However, a drawback of this approach is that the critic simply labels the generated features as in-domain or not, without considering the boundaries between classes. This can lead to ambiguous features being generated near class boundaries, reducing target classification accuracy. We propose a novel approach, Adversarial Dropout Regularization (ADR), to encourage the generator to output more discriminative features for the target domain. Our key idea is to replace the critic with one that detects non-discriminative features, using dropout on the classifier network. The generator then learns to avoid these areas of the feature space and thus creates better features. We apply our ADR approach to the problem of unsupervised domain adaptation for image classification and semantic segmentation tasks, and demonstrate significant improvement over the state of the art. We also show that our approach can be used to train Generative Adversarial Networks for semi-supervised learning.
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paper_title: Adversarial Dropout for Recurrent Neural Networks

paper_content:

Successful application processing sequential data, such as text and speech, requires an improved generalization performance of recurrent neural networks (RNNs). Dropout techniques for RNNs were introduced to respond to these demands, but we conjecture that the dropout on RNNs could have been improved by adopting the adversarial concept. This paper investigates ways to improve the dropout for RNNs by utilizing intentionally generated dropout masks. Specifically, the guided dropout used in this research is called as adversarial dropout, which adversarially disconnects neurons that are dominantly used to predict correct targets over time. Our analysis showed that our regularizer, which consists of a gap between the original and the reconfigured RNNs, was the upper bound of the gap between the training and the inference phases of the random dropout. We demonstrated that minimizing our regularizer improved the effectiveness of the dropout for RNNs on sequential MNIST tasks, semi-supervised text classification tasks, and language modeling tasks.
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paper_title: Fast dropout training

paper_content:

Preventing feature co-adaptation by encouraging independent contributions from different features often improves classification and regression performance. Dropout training (Hinton et al., 2012) does this by randomly dropping out (zeroing) hidden units and input features during training of neural networks. However, repeatedly sampling a random subset of input features makes training much slower. Based on an examination of the implied objective function of dropout training, we show how to do fast dropout training by sampling from or integrating a Gaussian approximation, instead of doing Monte Carlo optimization of this objective. This approximation, justified by the central limit theorem and empirical evidence, gives an order of magnitude speedup and more stability. We show how to do fast dropout training for classification, regression, and multilayer neural networks. Beyond dropout, our technique is extended to integrate out other types of noise and small image transformations.
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Title: Survey of Dropout Methods for Deep Neural Networks

Section 1: Introduction
Description 1: Introduce the topic of deep neural networks and the importance of dropout methods, along with a brief history and overview of various dropout techniques.

Section 2: Notation
Description 2: Describe the common notation conventions used in the paper.

Section 3: Standard Dropout
Description 3: Explain the original dropout method introduced in 2012, including its implementation and efficacy in preventing overfitting.

Section 4: Dropout Methods for Training
Description 4: Discuss various dropout methods used for regularizing dense feedforward neural network layers during training, including dropconnect, standout, fast dropout, variational dropout, and concrete dropout.

Section 5: Convolutional Layers
Description 5: Outline dropout methods catered to convolutional neural networks (CNNs), such as naive dropout, spatial dropout, max-pooling dropout, and cutout.

Section 6: Dropout and Batch Normalization
Description 6: Examine the interaction between dropout methods and batch normalization in CNN training and recent research on using both together effectively.

Section 7: Recurrent Layers
Description 7: Describe dropout methods specialized for recurrent neural networks (RNNs), including techniques for LSTM networks like RNNdrop, Bayesian RNN dropout, and recurrent dropout.

Section 8: Dropout Methods for Model Compression
Description 8: Detail the use of dropout methods to promote sparsity and compress neural network models, including recent advancements and techniques like variational dropout for sparsification.

Section 9: Monte Carlo Dropout
Description 9: Explain Monte Carlo dropout, its Bayesian interpretation, and its application in measuring model uncertainty.

Section 10: Discussion
Description 10: Summarize the ongoing research trends, potential future advancements, and broader applications of dropout methods within deep learning.