Dropout is an effective strategy for the regularization of deep neural networks. Applying tabu to the units that have been dropped in the recent epoch and retaining them for training ensures diversification in dropout. In this paper, we improve the Tabu Dropout mechanism for training deep neural networks in two ways. Firstly, we propose to use tabu tenure, or the number of epochs a particular unit will not be dropped. Different tabu tenures provide diversification to boost the training of deep neural networks based on the search landscape. Secondly, we propose an adaptive tabu algorithm that automatically selects the tabu tenure based on the training performances through epochs. On several standard benchmark datasets, the experimental results show that the adaptive tabu dropout and tabu tenure dropout diversify and perform significantly better compared to the standard dropout and basic tabu dropout mechanisms.
Dropout has proven to be an effective technique for regularization and preventing the co-adaptation of neurons in deep neural networks (DNN). It randomly drops units with a probability $p$ during the training stage of DNN. Dropout also provides a way of approximately combining exponentially many different neural network architectures efficiently. In this work, we add a diversification strategy into dropout, which aims at generating more different neural network architectures in a proper times of iterations. The dropped units in last forward propagation will be marked. Then the selected units f…
University of Michigan, Ann Arbor（密歇根大学安娜堡分校）；Microsoft（微软）
Sparsely activated transformers, such as Mixture of Experts (MoE), have received great interest due to their outrageous scaling capability which enables dramatical increases in model size without significant increases in computational cost. To achieve this, MoE models replace the feedforward sub-layer with Mixture-of-Experts sub-layer in transformers and use a gating network to route each token to its assigned experts. Since the common practice for efficient training of such models requires distributing experts and tokens across different machines, this routing strategy often incurs huge cross…
Fully connected deep neural networks (DNN) often include redundant weights leading to overfitting and high memory requirements. Additionally, the performance of DNN is often challenged by traditional machine learning models in tabular data classification. In this paper, we propose periodical perturbations (prune and regrow) of DNN weights, especially at the self-supervised pre-training stage of deep autoencoders. The proposed weight perturbation strategy outperforms dropout learning in four out of six tabular data sets in downstream classification tasks. The L1 or L2 regularization of weights …
Stanford University（斯坦福大学）；Microsoft Research（微软研究院）；University of Washington（华盛顿大学）
Dropout is a widely-used regularization technique, often required to obtain state-of-the-art for a number of architectures. This work demonstrates that dropout introduces two distinct but entangled regularization effects: an explicit effect (also studied in prior work) which occurs since dropout modifies the expected training objective, and, perhaps surprisingly, an additional implicit effect from the stochasticity in the dropout training update. This implicit regularization effect is analogous to the effect of stochasticity in small mini-batch stochastic gradient descent. We disentangle these…
Dropout Regularization, serving to reduce variance, is nearly ubiquitous in Deep Learning models. We explore the relationship between the dropout rate and model complexity by training 2,000 neural networks configured with random combinations of the dropout rate and the number of hidden units in each dense layer, on each of the three data sets we selected. The generated figures, with binary cross entropy loss and binary accuracy on the z-axis, question the common assumption that adding depth to a dense layer while increasing the dropout rate will certainly enhance performance. We also discover …
Among the most successful methods for sparsifying deep (neural) networks are those that adaptively mask the network weights throughout training. By examining this masking, or dropout, in the linear case, we uncover a duality between such adaptive methods and regularization through the so-called "$η$-trick" that casts both as iteratively reweighted optimizations. We show that any dropout strategy that adapts to the weights in a monotonic way corresponds to an effective subquadratic regularization penalty, and therefore leads to sparse solutions. We obtain the effective penalties for several pop…
Dropout Regularization in Extended Generalized Linear Models based on Double Exponential Families
University of Hamburg（汉堡大学）；National University of Singapore（新加坡国立大学）；Technische Universität Dortmund（多特蒙德工业大学）；Research Center Trustworthy Data Science and Security（可信数据科学与安全研究中心）
Dropout and other feature noising schemes control overfitting by artificially corrupting the training data. For generalized linear models, dropout performs a form of adaptive regularization. Using this viewpoint, we show that the dropout regularizer is first-order equivalent to an L2 regularizer applied after scaling the features by an estimate of the inverse diagonal Fisher information matrix. We also establish a connection to AdaGrad, an online learning algorithm, and find that a close relative of AdaGrad operates by repeatedly solving linear dropout-regularized problems. By casting dropout …
Mathematical Institute for Data Science, Johns Hopkins University（约翰斯·霍普金斯大学数据科学数学研究所）
Dropout and its extensions (eg. DropBlock and DropConnect) are popular heuristics for training neural networks, which have been shown to improve generalization performance in practice. However, a theoretical understanding of their optimization and regularization properties remains elusive. Recent work shows that in the case of single hidden-layer linear networks, Dropout is a stochastic gradient descent method for minimizing a regularized loss, and that the regularizer induces solutions that are low-rank and balanced. In this work we show that for single hidden-layer linear networks, DropBlock…
National University of Singapore（新加坡国立大学）；Zhejiang University（浙江大学）；Beijing Institute of Technology（北京理工大学）
Convolutional Neural networks (CNNs) based applications have become ubiquitous, where proper regularization is greatly needed. To prevent large neural network models from overfitting, dropout has been widely used as an efficient regularization technique in practice. However, many recent works show that the standard dropout is ineffective or even detrimental to the training of CNNs. In this paper, we revisit this issue and examine various dropout variants in an attempt to improve existing dropout-based regularization techniques for CNNs. We attribute the failure of standard dropout to the confl…
Dropout is a simple but effective technique for learning in neural networks and other settings. A sound theoretical understanding of dropout is needed to determine when dropout should be applied and how to use it most effectively. In this paper we continue the exploration of dropout as a regularizer pioneered by Wager, et.al. We focus on linear classification where a convex proxy to the misclassification loss (i.e. the logistic loss used in logistic regression) is minimized. We show: (a) when the dropout-regularized criterion has a unique minimizer, (b) when the dropout-regularization penalty …
Dropout is a very effective method in preventing overfitting and has become the go-to regularizer for multi-layer neural networks in recent years. Hierarchical mixture of experts is a hierarchically gated model that defines a soft decision tree where leaves correspond to experts and decision nodes correspond to gating models that softly choose between its children, and as such, the model defines a soft hierarchical partitioning of the input space. In this work, we propose a variant of dropout for hierarchical mixture of experts that is faithful to the tree hierarchy defined by the model, as op…
We give a formal and complete characterization of the explicit regularizer induced by dropout in deep linear networks with squared loss. We show that (a) the explicit regularizer is composed of an $\ell_2$-path regularizer and other terms that are also re-scaling invariant, (b) the convex envelope of the induced regularizer is the squared nuclear norm of the network map, and (c) for a sufficiently large dropout rate, we characterize the global optima of the dropout objective. We validate our theoretical findings with empirical results.
School of Electrical Engineering（工程学院）；Tel Aviv University（特拉维夫大学）
Dropout is a popular regularization technique in deep learning. Yet, the reason for its success is still not fully understood. This paper provides a new interpretation of Dropout from a frame theory perspective. By drawing a connection to recent developments in analog channel coding, we suggest that for a certain family of autoencoders with a linear encoder, optimizing the encoder with dropout regularization leads to an equiangular tight frame (ETF). Since this optimization is non-convex, we add another regularization that promotes such structures by minimizing the cross-correlation between fi…
An important problem in training deep networks with high capacity is to ensure that the trained network works well when presented with new inputs outside the training dataset. Dropout is an effective regularization technique to boost the network generalization in which a random subset of the elements of the given data and the extracted features are set to zero during the training process. In this paper, a new randomized regularization technique in which we withhold a random part of the data without necessarily turning off the neurons/data-elements is proposed. In the proposed method, of which …
This paper proposes a new regularization algorithm referred to as macro-block dropout. The overfitting issue has been a difficult problem in training large neural network models. The dropout technique has proven to be simple yet very effective for regularization by preventing complex co-adaptations during training. In our work, we define a macro-block that contains a large number of units from the input to a Recurrent Neural Network (RNN). Rather than applying dropout to each unit, we apply random dropout to each macro-block. This algorithm has the effect of applying different drop out rates f…
In order to develop complex relationships between their inputs and outputs, deep neural networks train and adjust large number of parameters. To make these networks work at high accuracy, vast amounts of data are needed. Sometimes, however, the quantity of data needed is not present or obtainable for training. Neuron-specific dropout (NSDropout) is a tool to address this problem. NSDropout looks at both the training pass, and validation pass, of a layer in a model. By comparing the average values produced by each neuron for each class in a data set, the network is able to drop targeted units. …
Dropout, a simple and effective way to train deep neural networks, has led to a number of impressive empirical successes and spawned many recent theoretical investigations. However, the gap between dropout's training and inference phases, introduced due to tractability considerations, has largely remained under-appreciated. In this work, we first formulate dropout as a tractable approximation of some latent variable model, leading to a clean view of parameter sharing and enabling further theoretical analysis. Then, we introduce (approximate) expectation-linear dropout neural networks, whose in…
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 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 weig…
Regularization is an important component of predictive model building. The hybrid bootstrap is a regularization technique that functions similarly to dropout except that features are resampled from other training points rather than replaced with zeros. We show that the hybrid bootstrap offers superior performance to dropout. We also present a sampling based technique to simplify hyperparameter choice. Next, we provide an alternative sampling technique for convolutional neural networks. Finally, we demonstrate the efficacy of the hybrid bootstrap on non-image tasks using tree-based models.
Institute of Computer Science（计算机科学研究所）；University of Hildesheim（希尔德斯海姆大学）
Diverse regularization techniques have been developed such as L2 regularization, Dropout, DisturbLabel (DL) to prevent overfitting. DL, a newcomer on the scene, regularizes the loss layer by flipping a small share of the target labels at random and training the neural network on this distorted data so as to not learn the training data. It is observed that high confidence labels during training cause the overfitting problem and DL selects disturb labels at random regardless of the confidence of labels. To solve this shortcoming of DL, we propose Directional DisturbLabel (DDL) a novel regulariza…
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 prelimi…
University of Freiburg（弗莱堡大学）；Leibniz University Hannover（莱布尼茨汉诺威大学）；Bosch Center for Artificial Intelligence（博世人工智能中心）
Tabular datasets are the last "unconquered castle" for deep learning, with traditional ML methods like Gradient-Boosted Decision Trees still performing strongly even against recent specialized neural architectures. In this paper, we hypothesize that the key to boosting the performance of neural networks lies in rethinking the joint and simultaneous application of a large set of modern regularization techniques. As a result, we propose regularizing plain Multilayer Perceptron (MLP) networks by searching for the optimal combination/cocktail of 13 regularization techniques for each dataset using …
Rudolf Peierls Centre for Theoretical Physics, University of Oxford（奥xford大学鲁道夫佩尔尔斯理论物理中心）；Graduate Center, City University of New York（纽约城市大学研究生中心）；Joseph Henry Laboratories of Physics, Princeton University（普林斯顿大学约瑟夫亨利物理实验室）
Large datasets often have unreliable labels-such as those obtained from Amazon's Mechanical Turk or social media platforms-and classifiers trained on mislabeled datasets often exhibit poor performance. We present a simple, effective technique for accounting for label noise when training deep neural networks. We augment a standard deep network with a softmax layer that models the label noise statistics. Then, we train the deep network and noise model jointly via end-to-end stochastic gradient descent on the (perhaps mislabeled) dataset. The augmented model is overdetermined, so in order to enco…
Beihang University（北京航空航天大学）；Microsoft Research Asia（微软亚洲研究院）
In this paper, we introduce DropHead, a structured dropout method specifically designed for regularizing the multi-head attention mechanism, which is a key component of transformer, a state-of-the-art model for various NLP tasks. In contrast to the conventional dropout mechanisms which randomly drop units or connections, the proposed DropHead is a structured dropout method. It drops entire attention-heads during training and It prevents the multi-head attention model from being dominated by a small portion of attention heads while also reduces the risk of overfitting the training data, thus ma…
In this paper, we propose a novel regularization method, RotationOut, for neural networks. Different from Dropout that handles each neuron/channel independently, RotationOut regards its input layer as an entire vector and introduces regularization by randomly rotating the vector. RotationOut can also be used in convolutional layers and recurrent layers with small modifications. We further use a noise analysis method to interpret the difference between RotationOut and Dropout in co-adaptation reduction. Using this method, we also show how to use RotationOut/Dropout together with Batch Normaliza…
Deep neural networks are learning models with a very high capacity and therefore prone to over-fitting. Many regularization techniques such as Dropout, DropConnect, and weight decay all attempt to solve the problem of over-fitting by reducing the capacity of their respective models (Srivastava et al., 2014), (Wan et al., 2013), (Krogh & Hertz, 1992). In this paper we introduce a new form of regularization that guides the learning problem in a way that reduces over-fitting without sacrificing the capacity of the model. The mistakes that models make in early stages of training carry information …
Relevance-driven Input Dropout: an Explanation-guided Regularization Technique
Fraunhofer Heinrich Hertz Institute, Department of Artificial Intelligence（弗劳恩霍夫海因里希·赫茨研究所人工智能部门）；Lehrstuhl für Angewandte Mathematik, University of Bayreuth（拜罗伊特大学应用数学研究所）；Technische Universität Berlin（柏林技术大学）；BIFOLD – Berlin Institute for the Foundations of Learning and Data（柏林学习与数据基础研究所）；Centre of eXplainable Artificial Intelligence, Technological University Dublin（解释性人工智能中心，都柏林技术大学）
The Graduate University for Advanced Studies (SOKENDAI)（综合研究大学院大学（SOKENDAI））；The Institute of Statistical Mathematics（统计数学研究所）
Dropout is one of the most popular regularization techniques in neural network training. Because of its power and simplicity of idea, dropout has been analyzed extensively and many variants have been proposed. In this paper, several properties of dropout are discussed in a unified manner from the viewpoint of information geometry. We showed that dropout flattens the model manifold and that their regularization performance depends on the amount of the curvature. Then, we showed that dropout essentially corresponds to a regularization that depends on the Fisher information, and support this resu…
Indian Association for the Cultivation of Science（印度科学培养协会）
Dropout is a widely used regularization trick to resolve the overfitting issue in large feedforward neural networks trained on a small dataset, which performs poorly on the held-out test subset. Although the effectiveness of this regularization trick has been extensively studied for convolutional neural networks, there is a lack of analysis of it for unsupervised models and in particular, VAE-based neural topic models. In this paper, we have analyzed the consequences of dropout in the encoder as well as in the decoder of the VAE architecture in three widely used neural topic models, namely, co…
Despite their impressive performance, Deep Neural Networks (DNNs) typically underperform Gradient Boosting Trees (GBTs) on many tabular-dataset learning tasks. We propose that applying a different regularization coefficient to each weight might boost the performance of DNNs by allowing them to make more use of the more relevant inputs. However, this will lead to an intractable number of hyperparameters. Here, we introduce Regularization Learning Networks (RLNs), which overcome this challenge by introducing an efficient hyperparameter tuning scheme which minimizes a new Counterfactual Loss. Our…
It is important to understand how the popular regularization method dropout helps the neural network training find a good generalization solution. In this work, we show that the training with dropout finds the neural network with a flatter minimum compared with standard gradient descent training. We further find that the variance of a noise induced by the dropout is larger at the sharper direction of the loss landscape and the Hessian of the loss landscape at the found minima aligns with the noise covariance matrix by experiments on various datasets, i.e., MNIST, CIFAR-10, CIFAR-100 and Multi3…
Beyond Limits Inc（Beyond Limits公司）；University of Southern California（南加州大学）
Long Short-Term Memory (LSTM) neural networks have been widely used for time series forecasting problems. However, LSTMs are prone to overfitting and performance reduction during test phases. Several different regularization techniques have been shown in literature to prevent overfitting problems in neural networks. In this paper, first, we introduce application of kernel flow methods for time series forecasting in general. Afterward, we examine the effectiveness of applying kernel flow regularization on LSTM layers to avoid overfitting problems. We describe a regularization method by applying…
Istituto Italiano di Tecnologia（意大利技术研究院）；Johns Hopkins University（约翰斯·霍普金斯大学）
Regularization for matrix factorization (MF) and approximation problems has been carried out in many different ways. Due to its popularity in deep learning, dropout has been applied also for this class of problems. Despite its solid empirical performance, the theoretical properties of dropout as a regularizer remain quite elusive for this class of problems. In this paper, we present a theoretical analysis of dropout for MF, where Bernoulli random variables are used to drop columns of the factors. We demonstrate the equivalence between dropout and a fully deterministic model for MF in which the…
Ecole Polytechnique（巴黎综合理工学院）；Université Paris Dauphine-PSL（巴黎第九大学-巴黎文理研究大学）
Deep Learning (DL) is considered the state-of-the-art in computer vision, speech recognition and natural language processing. Until recently, it was also widely accepted that DL is irrelevant for learning tasks on tabular data, especially in the small sample regime where ensemble methods are acknowledged as the gold standard. We present a new end-to-end differentiable method to train a standard FFNN. Our method, \textbf{Muddling labels for Regularization} (\texttt{MLR}), penalizes memorization through the generation of uninformative labels and the application of a differentiable close-form reg…
Deep neural networks with their large number of parameters are highly flexible learning systems. The high flexibility in such networks brings with some serious problems such as overfitting, and regularization is used to address this problem. A currently popular and effective regularization technique for controlling the overfitting is dropout. Often, large data collections required for neural networks contain sensitive information such as the medical histories of patients, and the privacy of the training data should be protected. In this paper, we modify the recently proposed variational dropou…
Variational Adaptive Noise and Dropout towards Stable Recurrent Neural Networks
National Institute of Informatics (NII)（国家信息研究所）；The Graduate University for Advanced Studies (SOKENDAI)（高级研究大学）；Department of Electronics and Electrical Engineering, Faculty of Science and Technology, Keio University（科技学部电子电气工学科，庆应大学）
VinAI Research（VinAI研究院）；University of Texas, Austin（德克萨斯大学奥斯汀分校）；Hanoi University of Science and Technology（河内科技大学）
Approximate inference in Bayesian deep networks exhibits a dilemma of how to yield high fidelity posterior approximations while maintaining computational efficiency and scalability. We tackle this challenge by introducing a novel variational structured approximation inspired by the Bayesian interpretation of Dropout regularization. Concretely, we focus on the inflexibility of the factorized structure in Dropout posterior and then propose an improved method called Variational Structured Dropout (VSD). VSD employs an orthogonal transformation to learn a structured representation on the variation…
This tutorial gives a concise overview of existing PAC-Bayesian theory focusing on three generalization bounds. The first is an Occam bound which handles rules with finite precision parameters and which states that generalization loss is near training loss when the number of bits needed to write the rule is small compared to the sample size. The second is a PAC-Bayesian bound providing a generalization guarantee for posterior distributions rather than for individual rules. The PAC-Bayesian bound naturally handles infinite precision rule parameters, $L_2$ regularization, {\em provides a bound f…
Matrix factorization (MF) and Autoencoder (AE) are among the most successful approaches of unsupervised learning. While MF based models have been extensively exploited in the graph modeling and link prediction literature, the AE family has not gained much attention. In this paper we investigate both MF and AE's application to the link prediction problem in sparse graphs. We show the connection between AE and MF from the perspective of multiview learning, and further propose MF+AE: a model training MF and AE jointly with shared parameters. We apply dropout to training both the MF and AE parts, …
Idiap Research Institute（伊迪亚普研究所）；Adobe Research（奥多比研究院）
In this paper, we explore various approaches for semi supervised learning in an end to end automatic speech recognition (ASR) framework. The first step in our approach involves training a seed model on the limited amount of labelled data. Additional unlabelled speech data is employed through a data selection mechanism to obtain the best hypothesized output, further used to retrain the seed model. However, uncertainties of the model may not be well captured with a single hypothesis. As opposed to this technique, we apply a dropout mechanism to capture the uncertainty by obtaining multiple hypot…
São Paulo State University（圣保罗州立大学）；ARMTEC Tecnologia em Robótica（ARMTEC机器人技术公司）
Deep learning architectures have been widely fostered throughout the last years, being used in a wide range of applications, such as object recognition, image reconstruction, and signal processing. Nevertheless, such models suffer from a common problem known as overfitting, which limits the network from predicting unseen data effectively. Regularization approaches arise in an attempt to address such a shortcoming. Among them, one can refer to the well-known Dropout, which tackles the problem by randomly shutting down a set of neurons and their connections according to a certain probability. Th…
Soochow University（苏州大学）；Microsoft Research Asia（微软亚洲研究院）
Dropout is a powerful and widely used technique to regularize the training of deep neural networks. In this paper, we introduce a simple regularization strategy upon dropout in model training, namely R-Drop, which forces the output distributions of different sub models generated by dropout to be consistent with each other. Specifically, for each training sample, R-Drop minimizes the bidirectional KL-divergence between the output distributions of two sub models sampled by dropout. Theoretical analysis reveals that R-Drop reduces the freedom of the model parameters and complements dropout. Exper…
