While many real-world data streams imply that they change frequently in a nonstationary way, most of deep learning methods optimize neural networks on training data, and this leads to severe performance degradation when dataset shift happens. However, it is less possible to annotate or inspect newly streamed data by humans, and thus it is desired to measure model drift at inference time in an unsupervised manner. In this paper, we propose a novel method of model drift estimation by exploiting statistics of batch normalization layer on unlabeled test data. To remedy possible sampling error of streamed input data, we adopt low-rank approximation to each representational layer. We show the effectiveness of our method not only on dataset shift detection but also on model selection when there are multiple candidate models among model zoo or training trajectories in an unsupervised way. We further demonstrate the consistency of our method by comparing model drift scores between different network architectures.
Imperial College London（帝国理工学院）；Shanghai Jiao Tong University（上海交通大学）；Queen Mary University of London（伦敦玛丽女王大学）；Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））
Deep Convolutional Neural Networks (DCNNs) are hard and time-consuming to train. Normalization is one of the effective solutions. Among previous normalization methods, Batch Normalization (BN) performs well at medium and large batch sizes and is with good generalizability to multiple vision tasks, while its performance degrades significantly at small batch sizes. In this paper, we find that BN saturates at extreme large batch sizes, i.e., 128 images per worker, i.e., GPU, as well and propose that the degradation/saturation of BN at small/extreme large batch sizes is caused by noisy/confused st…
University of Michigan（密歇根大学）；Stanford University（斯坦福大学）；NTT Research, Inc.（NTT研究院）
Inspired by BatchNorm, there has been an explosion of normalization layers in deep learning. Recent works have identified a multitude of beneficial properties in BatchNorm to explain its success. However, given the pursuit of alternative normalization layers, these properties need to be generalized so that any given layer's success/failure can be accurately predicted. In this work, we take a first step towards this goal by extending known properties of BatchNorm in randomly initialized deep neural networks (DNNs) to several recently proposed normalization layers. Our primary findings follow: (…
A key component of most neural network architectures is the use of normalization layers, such as Batch Normalization. Despite its common use and large utility in optimizing deep architectures, it has been challenging both to generically improve upon Batch Normalization and to understand the circumstances that lend themselves to other enhancements. In this paper, we identify four improvements to the generic form of Batch Normalization and the circumstances under which they work, yielding performance gains across all batch sizes while requiring no additional computation during training. These co…
Blue Well 8, LLC（Blue Well 8有限责任公司）；Pioneer Square Labs（先锋广场实验室）
Adapting a model to perform well on unforeseen data outside its training set is a common problem that continues to motivate new approaches. We demonstrate that application of batch normalization in the output layer, prior to softmax activation, results in improved generalization across visual data domains in a refined ResNet model. The approach adds negligible computational complexity yet outperforms many domain adaptation methods that explicitly learn to align data domains. We benchmark this technique on the Office-Home dataset and show that batch normalization is competitive with other leadi…
Batch Normalization (BN) uses mini-batch statistics to normalize the activations during training, introducing dependence between mini-batch elements. This dependency can hurt the performance if the mini-batch size is too small, or if the elements are correlated. Several alternatives, such as Batch Renormalization and Group Normalization (GN), have been proposed to address this issue. However, they either do not match the performance of BN for large batches, or still exhibit degradation in performance for smaller batches, or introduce artificial constraints on the model architecture. In this pa…
Pohang University of Science and Technology（浦项科技大学）
For the stable optimization of deep neural networks, regularization methods such as dropout and batch normalization have been used in various tasks. Nevertheless, the correct position to apply dropout has rarely been discussed, and different positions have been employed depending on the practitioners. In this study, we investigate the correct position to apply dropout. We demonstrate that for a residual network with batch normalization, applying dropout at certain positions increases the performance, whereas applying dropout at other positions decreases the performance. Based on theoretical an…
Batch-Normalization (BN) layers have become fundamental components in the evermore complex deep neural network architectures. Such models require acceleration processes for deployment on edge devices. However, BN layers add computation bottlenecks due to the sequential operation processing: thus, a key, yet often overlooked component of the acceleration process is BN layers folding. In this paper, we demonstrate that the current BN folding approaches are suboptimal in terms of how many layers can be removed. We therefore provide a necessary and sufficient condition for BN folding and a corresp…
Batch Normalization (BN) is one of the most widely used techniques in Deep Learning field. But its performance can awfully degrade with insufficient batch size. This weakness limits the usage of BN on many computer vision tasks like detection or segmentation, where batch size is usually small due to the constraint of memory consumption. Therefore many modified normalization techniques have been proposed, which either fail to restore the performance of BN completely, or have to introduce additional nonlinear operations in inference procedure and increase huge consumption. In this paper, we reve…
In this paper, we propose a novel domain adaptation method for the source-free setting. In this setting, we cannot access source data during adaptation, while unlabeled target data and a model pretrained with source data are given. Due to lack of source data, we cannot directly match the data distributions between domains unlike typical domain adaptation algorithms. To cope with this problem, we propose utilizing batch normalization statistics stored in the pretrained model to approximate the distribution of unobserved source data. Specifically, we fix the classifier part of the model during a…
Deep neural networks (DNN) have shown unprecedented success in various computer vision applications such as image classification and object detection. However, it is still a common annoyance during the training phase, that one has to prepare at least thousands of labeled images to fine-tune a network to a specific domain. Recent study (Tommasi et al. 2015) shows that a DNN has strong dependency towards the training dataset, and the learned features cannot be easily transferred to a different but relevant task without fine-tuning. In this paper, we propose a simple yet powerful remedy, called A…
National University of Singapore（新加坡国立大学）；Northwestern University（西北大学）；Purdue University（普渡大学）；New Oriental AI Research Academy（新东方人工智能研究院）
Batch Normalization (BN)(Ioffe and Szegedy 2015) normalizes the features of an input image via statistics of a batch of images and hence BN will bring the noise to the gradient of the training loss. Previous works indicate that the noise is important for the optimization and generalization of deep neural networks, but too much noise will harm the performance of networks. In our paper, we offer a new point of view that self-attention mechanism can help to regulate the noise by enhancing instance-specific information to obtain a better regularization effect. Therefore, we propose an attention-ba…
University of Michigan（密歇根大学）；Beihang University（北京航空航天大学）
Batch Normalization (BN) is capable of accelerating the training of deep models by centering and scaling activations within mini-batches. In this work, we propose Decorrelated Batch Normalization (DBN), which not just centers and scales activations but whitens them. We explore multiple whitening techniques, and find that PCA whitening causes a problem we call stochastic axis swapping, which is detrimental to learning. We show that ZCA whitening does not suffer from this problem, permitting successful learning. DBN retains the desirable qualities of BN and further improves BN's optimization eff…
Histopathology Image Normalization via Latent Manifold Compaction
Knight Cancer Institute, Oregon Health and Science University（骑士癌症研究所，俄勒冈健康与科学大学）；Brenden-Colson Center for Pancreatic Care, Oregon Health and Science University（布雷登-科尔森胰腺护理中心，俄勒冈健康与科学大学）
Sun Yat-sen University（中山大学）；The Chinese University of Hong Kong（香港中文大学）；SenseTime Group Ltd.（商汤集团有限公司）
As an indispensable component, Batch Normalization (BN) has successfully improved the training of deep neural networks (DNNs) with mini-batches, by normalizing the distribution of the internal representation for each hidden layer. However, the effectiveness of BN would diminish with scenario of micro-batch (e.g., less than 10 samples in a mini-batch), since the estimated statistics in a mini-batch are not reliable with insufficient samples. In this paper, we present a novel normalization method, called Batch Kalman Normalization (BKN), for improving and accelerating the training of DNNs, parti…
This study introduces a new normalization layer termed Batch Layer Normalization (BLN) to reduce the problem of internal covariate shift in deep neural network layers. As a combined version of batch and layer normalization, BLN adaptively puts appropriate weight on mini-batch and feature normalization based on the inverse size of mini-batches to normalize the input to a layer during the learning process. It also performs the exact computation with a minor change at inference times, using either mini-batch statistics or population statistics. The decision process to either use statistics of min…
College of Biomedical Engineering & Instrument Science（生物医学工程与仪器科学学院）；Zhejiang University（浙江大学）
Data-free quantization is a task that compresses the neural network to low bit-width without access to original training data. Most existing data-free quantization methods cause severe performance degradation due to inaccurate activation clipping range and quantization error, especially for low bit-width. In this paper, we present a simple yet effective data-free quantization method with accurate activation clipping and adaptive batch normalization. Accurate activation clipping (AAC) improves the model accuracy by exploiting accurate activation information from the full-precision model. Adapti…
We present Sandwich Batch Normalization (SaBN), a frustratingly easy improvement of Batch Normalization (BN) with only a few lines of code changes. SaBN is motivated by addressing the inherent feature distribution heterogeneity that one can be identified in many tasks, which can arise from data heterogeneity (multiple input domains) or model heterogeneity (dynamic architectures, model conditioning, etc.). Our SaBN factorizes the BN affine layer into one shared sandwich affine layer, cascaded by several parallel independent affine layers. Concrete analysis reveals that, during optimization, SaB…
The training dynamics of two-layer neural networks with batch normalization (BN) is studied. It is written as the training dynamics of a neural network without BN on a Riemannian manifold. Therefore, we identify BN's effect of changing the metric in the parameter space. Later, the infinite-width limit of the two-layer neural networks with BN is considered, and a mean-field formulation is derived for the training dynamics. The training dynamics of the mean-field formulation is shown to be the Wasserstein gradient flow on the manifold. Theoretical analysis are provided on the well-posedness and …
Training state-of-the-art, deep neural networks is computationally expensive. One way to reduce the training time is to normalize the activities of the neurons. A recently introduced technique called batch normalization uses the distribution of the summed input to a neuron over a mini-batch of training cases to compute a mean and variance which are then used to normalize the summed input to that neuron on each training case. This significantly reduces the training time in feed-forward neural networks. However, the effect of batch normalization is dependent on the mini-batch size and it is not …
University of Kentucky（肯塔基大学）；Ohio Wesleyan University（俄亥俄卫斯理大学）
Batch normalization (BN) is a popular and ubiquitous method in deep learning that has been shown to decrease training time and improve generalization performance of neural networks. Despite its success, BN is not theoretically well understood. It is not suitable for use with very small mini-batch sizes or online learning. In this paper, we propose a new method called Batch Normalization Preconditioning (BNP). Instead of applying normalization explicitly through a batch normalization layer as is done in BN, BNP applies normalization by conditioning the parameter gradients directly during traini…
When training early-stage deep neural networks (DNNs), generating intermediate features via convolution or linear layers occupied most of the execution time. Accordingly, extensive research has been done to reduce the computational burden of the convolution or linear layers. In recent mobile-friendly DNNs, however, the relative number of operations involved in processing these layers has significantly reduced. As a result, the proportion of the execution time of other layers, such as batch normalization layers, has increased. Thus, in this work, we conduct a detailed analysis of the batch norm…
Prairie View A&M University（普雷里维尤农工大学）；Texas A&M University System（德克萨斯农工大学系统）
The fast execution speed and energy efficiency of analog hardware has made them a strong contender for deployment of deep learning model at the edge. However, there are concerns about the presence of analog noise which causes changes to the weight of the models, leading to performance degradation of deep learning model, despite their inherent noise resistant characteristics. The effect of the popular batch normalization layer on the noise resistant ability of deep learning model is investigated in this work. This systematic study has been carried out by first training different models with and…
Northwestern University（西北大学）；Department of Industrial Engineering（工业工程系）；Department of Industrial Engineering & Management Science（工业工程与管理科学系）；Evanston, IL 60208, USA（美国伊利诺伊州埃文斯顿市60208）
In this paper, we propose a generalization of the Batch Normalization (BN) algorithm, diminishing batch normalization (DBN), where we update the BN parameters in a diminishing moving average way. BN is very effective in accelerating the convergence of a neural network training phase that it has become a common practice. Our proposed DBN algorithm remains the overall structure of the original BN algorithm while introduces a weighted averaging update to some trainable parameters. We provide an analysis of the convergence of the DBN algorithm that converges to a stationary point with respect to t…
Batch normalization is a key component of most image classification models, but it has many undesirable properties stemming from its dependence on the batch size and interactions between examples. Although recent work has succeeded in training deep ResNets without normalization layers, these models do not match the test accuracies of the best batch-normalized networks, and are often unstable for large learning rates or strong data augmentations. In this work, we develop an adaptive gradient clipping technique which overcomes these instabilities, and design a significantly improved class of Nor…
The University of Sydney（悉尼大学）；BAIDU USA LLC（百度美国有限责任公司）；University of Oxford（牛津大学）；SenseTime Group Limited（商汤科技集团）
We present BN-NAS, neural architecture search with Batch Normalization (BN-NAS), to accelerate neural architecture search (NAS). BN-NAS can significantly reduce the time required by model training and evaluation in NAS. Specifically, for fast evaluation, we propose a BN-based indicator for predicting subnet performance at a very early training stage. The BN-based indicator further facilitates us to improve the training efficiency by only training the BN parameters during the supernet training. This is based on our observation that training the whole supernet is not necessary while training onl…
ETH Zurich（苏黎世联邦理工学院）；INRIA Paris（法国国家信息与自动化研究所巴黎分部）
Randomly initialized neural networks are known to become harder to train with increasing depth, unless architectural enhancements like residual connections and batch normalization are used. We here investigate this phenomenon by revisiting the connection between random initialization in deep networks and spectral instabilities in products of random matrices. Given the rich literature on random matrices, it is not surprising to find that the rank of the intermediate representations in unnormalized networks collapses quickly with depth. In this work we highlight the fact that batch normalization…
The standard normalization method for neural network (NN) models used in Natural Language Processing (NLP) is layer normalization (LN). This is different than batch normalization (BN), which is widely-adopted in Computer Vision. The preferred use of LN in NLP is principally due to the empirical observation that a (naive/vanilla) use of BN leads to significant performance degradation for NLP tasks; however, a thorough understanding of the underlying reasons for this is not always evident. In this paper, we perform a systematic study of NLP transformer models to understand why BN has a poor perf…
A multilayer perceptron (MLP) is typically made of multiple fully connected layers with nonlinear activation functions. There have been several approaches to make them better (e.g. faster convergence, better convergence limit, etc.). But the researches lack structured ways to test them. We test different MLP architectures by carrying out the experiments on the age and gender datasets. We empirically show that by whitening inputs before every linear layer and adding skip connections, our proposed MLP architecture can result in better performance. Since the whitening process includes dropouts, i…
Microsoft Research AI（微软研究院人工智能）；Google Brain（谷歌大脑）
We develop a mean field theory for batch normalization in fully-connected feedforward neural networks. In so doing, we provide a precise characterization of signal propagation and gradient backpropagation in wide batch-normalized networks at initialization. Our theory shows that gradient signals grow exponentially in depth and that these exploding gradients cannot be eliminated by tuning the initial weight variances or by adjusting the nonlinear activation function. Indeed, batch normalization itself is the cause of gradient explosion. As a result, vanilla batch-normalized networks without ski…
University of California, Berkeley（加州大学伯克利分校）；Google AI（谷歌人工智能）
A significant advance in accelerating neural network training has been the development of normalization methods, permitting the training of deep models both faster and with better accuracy. These advances come with practical challenges: for instance, batch normalization ties the prediction of individual examples with other examples within a batch, resulting in a network that is heavily dependent on batch size. Layer normalization and group normalization are data-dependent and thus must be continually used, even at test-time. To address the issues that arise from using explicit normalization te…
University of Southern California（南加州大学）；Facebook AI
We present a simple and effective way to estimate the batch-norm statistics during test time, to fast adapt a source model to target test samples. Known as Test-Time Adaptation, most prior works studying this task follow two assumptions in their evaluation where (1) test samples come together as a large batch, and (2) all from a single test distribution. However, in practice, these two assumptions may not stand, the reasons for which we propose two new evaluation settings where batch sizes are arbitrary and multiple distributions are considered. Unlike the previous methods that require a large…
LIRIS - UMR 5205 CNRS（法国国家科学研究中心LIRIS联合研究单位5205）；Ecole Centrale de Lyon（里昂中央理工学院）；LVMH Recherche - Parfums et cosmetiques（路威酩轩香水化妆品研究中心）
The lack of transparency of neural networks stays a major break for their use. The Layerwise Relevance Propagation technique builds heat-maps representing the relevance of each input in the model s decision. The relevance spreads backward from the last to the first layer of the Deep Neural Network. Layer-wise Relevance Propagation does not manage normalization layers, in this work we suggest a method to include normalization layers. Specifically, we build an equivalent network fusing normalization layers and convolutional or fully connected layers. Heatmaps obtained with our method on MNIST an…
ETH Zürich（苏黎世联邦理工学院）；MIT（麻省理工学院）；INRIA-ENS-PSL Paris（巴黎法国国家信息与自动化研究所-巴黎高等师范学院-巴黎文理研究大学）
Mean field theory is widely used in the theoretical studies of neural networks. In this paper, we analyze the role of depth in the concentration of mean-field predictions, specifically for deep multilayer perceptron (MLP) with batch normalization (BN) at initialization. By scaling the network width to infinity, it is postulated that the mean-field predictions suffer from layer-wise errors that amplify with depth. We demonstrate that BN stabilizes the distribution of representations that avoids the error propagation of mean-field predictions. This stabilization, which is characterized by a geom…
In this work we investigate the reasons why Batch Normalization (BN) improves the generalization performance of deep networks. We argue that one major reason, distinguishing it from data-independent normalization methods, is randomness of batch statistics. This randomness appears in the parameters rather than in activations and admits an interpretation as a practical Bayesian learning. We apply this idea to other (deterministic) normalization techniques that are oblivious to the batch size. We show that their generalization performance can be improved significantly by Bayesian learning of the …
Department of Information Engineering and Computer Science, University of Trento（信息工程与计算机科学系，特伦托大学）；Computing and Mathematical Sciences, Caltech（计算与数学科学系，加州理工学院）；School of Artificial Intelligence and Computer Science, Jiangnan University（人工智能与计算机科学学院，江南大学）
Over the past few years, Batch-Normalization has been commonly used in deep networks, allowing faster training and high performance for a wide variety of applications. However, the reasons behind its merits remained unanswered, with several shortcomings that hindered its use for certain tasks. In this work, we present a novel view on the purpose and function of normalization methods and weight-decay, as tools to decouple weights' norm from the underlying optimized objective. This property highlights the connection between practices such as normalization, weight decay and learning-rate adjustme…
Normalization methods play an important role in enhancing the performance of deep learning while their theoretical understandings have been limited. To theoretically elucidate the effectiveness of normalization, we quantify the geometry of the parameter space determined by the Fisher information matrix (FIM), which also corresponds to the local shape of the loss landscape under certain conditions. We analyze deep neural networks with random initialization, which is known to suffer from a pathologically sharp shape of the landscape when the network becomes sufficiently wide. We reveal that batc…
Batch normalization has been widely used to improve optimization in deep neural networks. While the uncertainty in batch statistics can act as a regularizer, using these dataset statistics specific to the training set impairs generalization in certain tasks. Recently, alternative methods for normalizing feature activations in neural networks have been proposed. Among them, group normalization has been shown to yield similar, in some domains even superior performance to batch normalization. All these methods utilize a learned affine transformation after the normalization operation to increase r…
We investigate the reasons for the performance degradation incurred with batch-independent normalization. We find that the prototypical techniques of layer normalization and instance normalization both induce the appearance of failure modes in the neural network's pre-activations: (i) layer normalization induces a collapse towards channel-wise constant functions; (ii) instance normalization induces a lack of variability in instance statistics, symptomatic of an alteration of the expressivity. To alleviate failure mode (i) without aggravating failure mode (ii), we introduce the technique "Proxy…
Batch Normalization (BN) has become an out-of-box technique to improve deep network training. However, its effectiveness is limited for micro-batch training, i.e., each GPU typically has only 1-2 images for training, which is inevitable for many computer vision tasks, e.g., object detection and semantic segmentation, constrained by memory consumption. To address this issue, we propose Weight Standardization (WS) and Batch-Channel Normalization (BCN) to bring two success factors of BN into micro-batch training: 1) the smoothing effects on the loss landscape and 2) the ability to avoid harmful e…
ITMO University（ITMO大学）；Artificial Intelligence Research Institute（人工智能研究所）；Tubingen Universitat（图宾根大学）
It was shown that adversarial examples improve object recognition. But what about their opposite side, easy examples? Easy examples are samples that the machine learning model classifies correctly with high confidence. In our paper, we are making the first step toward exploring the potential benefits of using easy examples in the training procedure of neural networks. We propose to use an auxiliary batch normalization for easy examples for the standard and robust accuracy improvement.
Batch Normalization (BN) is a milestone technique in the development of deep learning, enabling various networks to train. However, normalizing along the batch dimension introduces problems --- BN's error increases rapidly when the batch size becomes smaller, caused by inaccurate batch statistics estimation. This limits BN's usage for training larger models and transferring features to computer vision tasks including detection, segmentation, and video, which require small batches constrained by memory consumption. In this paper, we present Group Normalization (GN) as a simple alternative to BN…
Google Research（谷歌研究院）；University of Maryland, College Park（马里兰大学帕克分校）
Batch normalization (BN) has been very effective for deep learning and is widely used. However, when training with small minibatches, models using BN exhibit a significant degradation in performance. In this paper we study this peculiar behavior of BN to gain a better understanding of the problem, and identify a cause. We propose 'EvalNorm' to address the issue by estimating corrected normalization statistics to use for BN during evaluation. EvalNorm supports online estimation of the corrected statistics while the model is being trained, and does not affect the training scheme of the model. As…
LG Electronics Canada（LG电子加拿大公司）；LG Electronics USA（LG电子美国公司）
Batch Normalization (BN) is a popular technique for training Deep Neural Networks (DNNs). BN uses scaling and shifting to normalize activations of mini-batches to accelerate convergence and improve generalization. The recently proposed Iterative Normalization (IterNorm) method improves these properties by whitening the activations iteratively using Newton's method. However, since Newton's method initializes the whitening matrix independently at each training step, no information is shared between consecutive steps. In this work, instead of exact computation of whitening matrix at each time ste…
Tsinghua University（清华大学）；Microsoft Research Asia（微软亚洲研究院）
A well-known issue of Batch Normalization is its significantly reduced effectiveness in the case of small mini-batch sizes. When a mini-batch contains few examples, the statistics upon which the normalization is defined cannot be reliably estimated from it during a training iteration. To address this problem, we present Cross-Iteration Batch Normalization (CBN), in which examples from multiple recent iterations are jointly utilized to enhance estimation quality. A challenge of computing statistics over multiple iterations is that the network activations from different iterations are not compar…
Batch Normalization (BN) has been a standard component in designing deep neural networks (DNNs). Although the standard BN can significantly accelerate the training of DNNs and improve the generalization performance, it has several underlying limitations which may hamper the performance in both training and inference. In the training stage, BN relies on estimating the mean and variance of data using a single minibatch. Consequently, BN can be unstable when the batch size is very small or the data is poorly sampled. In the inference stage, BN often uses the so called moving mean and moving varia…
Xi’an Jiaotong University（西安交通大学）；University of Science and Technology of China（中国科学技术大学）；Microsoft Research Asia（微软亚洲研究院）
Deep neural networks often suffer the data distribution shift between training and testing, and the batch statistics are observed to reflect the shift. In this paper, targeting of alleviating distribution shift in test time, we revisit the batch normalization (BN) in the training process and reveals two key insights benefiting test-time optimization: $(i)$ preserving the same gradient backpropagation form as training, and $(ii)$ using dataset-level statistics for robust optimization and inference. Based on the two insights, we propose a novel test-time BN layer design, GpreBN, which is optimiz…
Inception Institute of Artificial Intelligence (IIAI)（人工智能起源研究所）
Batch Normalization (BN) is ubiquitously employed for accelerating neural network training and improving the generalization capability by performing standardization within mini-batches. Decorrelated Batch Normalization (DBN) further boosts the above effectiveness by whitening. However, DBN relies heavily on either a large batch size, or eigen-decomposition that suffers from poor efficiency on GPUs. We propose Iterative Normalization (IterNorm), which employs Newton's iterations for much more efficient whitening, while simultaneously avoiding the eigen-decomposition. Furthermore, we develop a c…
Ulm University（乌尔姆大学）；University College London（伦敦大学学院）
Appropriate weight initialization has been of key importance to successfully train neural networks. Recently, batch normalization has diminished the role of weight initialization by simply normalizing each layer based on batch statistics. Unfortunately, batch normalization has several drawbacks when applied to small batch sizes, as they are required to cope with memory limitations when learning on point clouds. While well-founded weight initialization strategies can render batch normalization unnecessary and thus avoid these drawbacks, no such approaches have been proposed for point convolutio…
We propose a reparameterization of LSTM that brings the benefits of batch normalization to recurrent neural networks. Whereas previous works only apply batch normalization to the input-to-hidden transformation of RNNs, we demonstrate that it is both possible and beneficial to batch-normalize the hidden-to-hidden transition, thereby reducing internal covariate shift between time steps. We evaluate our proposal on various sequential problems such as sequence classification, language modeling and question answering. Our empirical results show that our batch-normalized LSTM consistently leads to f…
Batch normalization dramatically increases the largest trainable depth of residual networks, and this benefit has been crucial to the empirical success of deep residual networks on a wide range of benchmarks. We show that this key benefit arises because, at initialization, batch normalization downscales the residual branch relative to the skip connection, by a normalizing factor on the order of the square root of the network depth. This ensures that, early in training, the function computed by normalized residual blocks in deep networks is close to the identity function (on average). We use th…
