Dropout is a crucial regularization technique for the Recurrent Neural Network (RNN) models of Natural Language Inference (NLI). However, dropout has not been evaluated for the effectiveness at different layers and dropout rates in NLI models. In this paper, we propose a novel RNN model for NLI and empirically evaluate the effect of applying dropout at different layers in the model. We also investigate the impact of varying dropout rates at these layers. Our empirical evaluation on a large (Stanford Natural Language Inference (SNLI)) and a small (SciTail) dataset suggest that dropout at each feed-forward connection severely affects the model accuracy at increasing dropout rates. We also show that regularizing the embedding layer is efficient for SNLI whereas regularizing the recurrent layer improves the accuracy for SciTail. Our model achieved an accuracy (86.14 ) on the SNLI dataset and (77.05 ) on SciTail.
Evaluations in previous research were conducted on datasets with fewer samples. We evaluate the RNN model on a large, SNLI dataset (570,000 data sample) as well as on a smaller SciTail dataset (27,000 data samples). Furthermore, previous studies concentrate only on the location of dropout in the network with fixed dropout rate.We further investigate the effect of varying dropout rates. We focus on the application of widely used conventional dropout @cite_18 to non-recurrent connection in RNNs.
@cite_18
2095705004
Recurrent neural networks (RNNs) with Long Short-Term memory cells currently hold the best known results in unconstrained handwriting recognition. We show that their performance can be greatly improved using dropout - a recently proposed regularization method for deep architectures. While previous works showed that dropout gave superior performance in the context of convolutional networks, it had never been applied to RNNs. In our approach, dropout is carefully used in the network so that it does not affect the recurrent connections, hence the power of RNNs in modeling sequence is preserved. Extensive experiments on a broad range of handwritten databases confirm the effectiveness of dropout on deep architectures even when the network mainly consists of recurrent and shared connections. Recurrent neural networks (RNNs) with Long Short-Term memory cells currently hold the best known results in unconstrained handwriting recognition. We show that their performance can be greatly improved using dropout - a recently proposed regularization method for deep architectures. While previous works showed that dropout gave superior performance in the context of convolutional networks, it had never been applied to RNNs. In our approach, dropout is carefully used in the network so that it does not affect the recurrent connections, hence the power of RNNs in modeling sequences is preserved. Extensive experiments on a broad range of handwritten databases confirm the effectiveness of dropout on deep architectures even when the network mainly consists of recurrent and shared connections. 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. Unlike machines, humans learn through rapid, Abstract model-building. The role of a teacher is not simply to hammer home right or wrong answers, but rather to provide intuitive comments, comparisons, and explanations to a pupil. This is what the Learning Under Privileged Information (LUPI) paradigm endeavors to model by utilizing extra knowledge only available during training. We propose a new LUPI algorithm specifically designed for Convolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs). We propose to use a heteroscedastic dropout (i.e. dropout with a varying variance) and make the variance of the dropout a function of privileged information. Intuitively, this corresponds to using the privileged information to control the uncertainty of the model output. We perform experiments using CNNs and RNNs for the tasks of image classification and machine translation. Our method significantly increases the sample efficiency during learning, resulting in higher accuracy with a large margin when the number of training examples is limited. We also theoretically justify the gains in sample efficiency by providing a generalization error bound decreasing with O(1 n), where n is the number of training examples, in an oracle case. Neural language models (LMs) based on recurrent neural networks (RNN) are some of the most successful word and character-level LMs. Why do they work so well, in particular better than linear neural LMs? Possible explanations are that RNNs have an implicitly better regularization or that RNNs have a higher capacity for storing patterns due to their nonlinearities or both. Here we argue for the first explanation in the limit of little training data and the second explanation for large amounts of text data. We show state-of-the-art performance on the popular and small Penn dataset when RNN LMs are regularized with random dropout. Nonetheless, we show even better performance from a simplified, much less expressive linear RNN model without off-diagonal entries in the recurrent matrix. We call this model an impulse-response LM (IRLM). Using random dropout, column normalization and annealed learning rates, IRLMs develop neurons that keep a memory of up to 50 words in the past and achieve a perplexity of 102.5 on the Penn dataset. On two large datasets however, the same regularization methods are unsuccessful for both models and the RNN's expressivity allows it to overtake the IRLM by 10 and 20 percent perplexity, respectively. Despite the perplexity gap, IRLMs still outperform RNNs on the Microsoft Research Sentence Completion (MRSC) task. We develop a slightly modified IRLM that separates long-context units (LCUs) from short-context units and show that the LCUs alone achieve a state-of-the-art performance on the MRSC task of 60.8 . Our analysis indicates that a fruitful direction of research for neural LMs lies in developing more accessible internal representations, and suggests an optimization regime of very high momentum terms for effectively training such models. 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. We introduce DropConnect, a generalization of Dropout (, 2012), for regularizing large fully-connected layers within neural networks. When training with Dropout, a randomly selected subset of activations are set to zero within each layer. DropConnect instead sets a randomly selected subset of weights within the network to zero. Each unit thus receives input from a random subset of units in the previous layer. We derive a bound on the generalization performance of both Dropout and DropConnect. We then evaluate DropConnect on a range of datasets, comparing to Dropout, and show state-of-the-art results on several image recognition benchmarks by aggregating multiple DropConnect-trained models. We investigate the use of Deep Neural Networks for the classification of image datasets where texture features are important for generating class-conditional discriminative representations. To this end, we first derive the size of the feature space for some standard textural features extracted from the input dataset and then use the theory of Vapnik-Chervonenkis dimension to show that hand-crafted feature extraction creates low-dimensional representations which help in reducing the overall excess error rate. As a corollary to this analysis, we derive for the first time upper bounds on the VC dimension of Convolutional Neural Network as well as Dropout and Dropconnect networks and the relation between excess error rate of Dropout and Dropconnect networks. The concept of intrinsic dimension is used to validate the intuition that texture-based datasets are inherently higher dimensional as compared to handwritten digits or other object recognition datasets and hence more difficult to be shattered by neural networks. We then derive the mean distance from the centroid to the nearest and farthest sampling points in an n-dimensional manifold and show that the Relative Contrast of the sample data vanishes as dimensionality of the underlying vector space tends to infinity. 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. 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. As deep neural networks (DNNs) are applied to increasingly challenging problems, they will need to be able to represent their own uncertainty. Modeling uncertainty is one of the key features of Bayesian methods. Using Bernoulli dropout with sampling at prediction time has recently been proposed as an efficient and well performing variational inference method for DNNs. However, sampling from other multiplicative noise based variational distributions has not been investigated in depth. We evaluated Bayesian DNNs trained with Bernoulli or Gaussian multiplicative masking of either the units (dropout) or the weights (dropconnect). We tested the calibration of the probabilistic predictions of Bayesian convolutional neural networks (CNNs) on MNIST and CIFAR-10. Sampling at prediction time increased the calibration of the DNNs' probabalistic predictions. Sampling weights, whether Gaussian or Bernoulli, led to more robust representation of uncertainty compared to sampling of units. However, using either Gaussian or Bernoulli dropout led to increased test set classification accuracy. Based on these findings we used both Bernoulli dropout and Gaussian dropconnect concurrently, which we show approximates the use of a spike-and-slab variational distribution without increasing the number of learned parameters. We found that spike-and-slab sampling had higher test set performance than Gaussian dropconnect and more robustly represented its uncertainty compared to Bernoulli dropout. We propose zoneout, a novel method for regularizing RNNs. At each timestep, zoneout stochastically forces some hidden units to maintain their previous values. Like dropout, zoneout uses random noise to train a pseudo-ensemble, improving generalization. But by preserving instead of dropping hidden units, gradient information and state information are more readily propagated through time, as in feedforward stochastic depth networks. We perform an empirical investigation of various RNN regularizers, and find that zoneout gives significant performance improvements across tasks. We achieve competitive results with relatively simple models in character- and word-level language modelling on the Penn Treebank and Text8 datasets, and combining with recurrent batch normalization yields state-of-the-art results on permuted sequential MNIST. Distance metric learning (DML) aims to learn a distance metric better than Euclidean distance. It has been successfully applied to various tasks, e.g., classification, clustering and information retrieval. Many DML algorithms suffer from the over-fitting problem because of a large number of parameters to be determined in DML. In this paper, we exploit the dropout technique, which has been successfully applied in deep learning to alleviate the over-fitting problem, for DML. Different from the previous studies that only apply dropout to training data, we apply dropout to both the learned metrics and the training data. We illustrate that application of dropout to DML is essentially equivalent to matrix norm based regularization. Compared with the standard regularization scheme in DML, dropout is advantageous in simulating the structured regularizers which have shown consistently better performance than non structured regularizers. We verify, both empirically and theoretically, that dropout is effective in regulating the learned metric to avoid the over-fitting problem. Last, we examine the idea of wrapping the dropout technique in the state-of-art DML methods and observe that the dropout technique can significantly improve the performance of the original DML methods. Deep neural networks often work well when they are over-parameterized and trained with a massive amount of noise and regularization, such as weight decay and dropout. Although dropout is widely used as a regularization technique for fully connected layers, it is often less effective for convolutional layers. This lack of success of dropout for convolutional layers is perhaps due to the fact that neurons in a contiguous region in convolutional layers are strongly correlated so information can still flow through convolutional networks despite dropout. Thus a structured form of dropout is needed to regularize convolutional networks. In this paper, we introduce DropBlock, a form of structured dropout, where neurons in a contiguous region of a feature map are dropped together. Extensive experiments show that DropBlock works much better than dropout in regularizing convolutional networks. On ImageNet, DropBlock with ResNet-50 architecture achieves 77.65 accuracy, which is more than 1 improvement on the previous result of this architecture. We introduce DropAll, a generalization of DropOut [1] and DropConnect [2], for regularization of fully-connected layers within convolutional neural networks. Applying these methods amounts to sub-sampling a neural network by dropping units. Training with DropOut, a randomly selected subset of activations are dropped, when training with DropConnect we drop a randomly subsets of weights. With DropAll we can perform both methods. We show the validity of our proposal by improving the classification error of networks trained with DropOut and DropConnect, on a common image classification dataset. To improve the classification, we also used a new method for combining networks, which was proposed in [3]. Recurrent Neural Networks (RNNs) are rich models for the processing of sequential data. Recent work on advancing the state of the art has been focused on the optimization or modelling of RNNs, mostly motivated by adressing the problems of the vanishing and exploding gradients. The control of overfitting has seen considerably less attention. This paper contributes to that by analyzing fast dropout, a recent regularization method for generalized linear models and neural networks from a back-propagation inspired perspective. We show that fast dropout implements a quadratic form of an adaptive, per-parameter regularizer, which rewards large weights in the light of underfitting, penalizes them for overconfident predictions and vanishes at minima of an unregularized training loss. The derivatives of that regularizer are exclusively based on the training error signal. One consequence of this is the absense of a global weight attractor, which is particularly appealing for RNNs, since the dynamics are not biased towards a certain regime. We positively test the hypothesis that this improves the performance of RNNs on four musical data sets. 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. The state of Wisconsin has one of the highest four year graduation rates in the nation, but deep disparities among student subgroups remain. To address this the state has created the Wisconsin Dropout Early Warning System (DEWS), a predictive model of student dropout risk for students in grades six through nine. The Wisconsin DEWS is in use statewide and currently provides predictions on the likelihood of graduation for over 225,000 students. DEWS represents a novel statistical learning based approach to the challenge of assessing the risk of non-graduation for students and provides highly accurate predictions for students in the middle grades without expanding beyond mandated administrative data collections. Similar dropout early warning systems are in place in many jurisdictions across the country. Prior research has shown that in many cases the indicators used by such systems do a poor job of balancing the trade off between correct classification of likely dropouts and false-alarm (, 2013). Building on this work, DEWS uses the receiver-operating characteristic (ROC) metric to identify the best possible set of statistical models for making predictions about individual students. This paper describes the DEWS approach and the software behind it, which leverages the open source statistical language R (R Core Team, 2013). As a result DEWS is a flexible series of software modules that can adapt to new data, new algorithms, and new outcome variables to not only predict dropout, but also impute key predictors as well. The design and implementation of each of these modules is described in detail as well as the open-source R package, EWStools, that serves as the core of DEWS (Knowles, 2014). 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. We investigate a local reparameterizaton technique for greatly reducing the variance of stochastic gradients for variational Bayesian inference (SGVB) of a posterior over model parameters, while retaining parallelizability. This local reparameterization translates uncertainty about global parameters into local noise that is independent across datapoints in the minibatch. Such parameterizations can be trivially parallelized and have variance that is inversely proportional to the mini-batch size, generally leading to much faster convergence. Additionally, we explore a connection with dropout: Gaussian dropout objectives correspond to SGVB with local reparameterization, a scale-invariant prior and proportionally fixed posterior variance. Our method allows inference of more flexibly parameterized posteriors; specifically, we propose variational dropout, a generalization of Gaussian dropout where the dropout rates are learned, often leading to better models. The method is demonstrated through several experiments.