DOCSLIB.ORG

Batch Normalization: Accelerating Deep Network Training By

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Batch Normalization: Accelerating Deep Network Training By Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift Sergey Ioffe Christian Szegedy Google Inc., [email protected] Google Inc., [email protected] Abstract Using mini-batches of examples, as opposed to one exam- ple at a time, is helpful in several ways. First, the gradient Training Deep Neural Networks is complicated by the fact of the loss over a mini-batch is an estimate of the gradient that the distribution of each layer’s inputs changes during over the training set, whose quality improves as the batch training, as the parameters of the previous layers change. size increases. Second, computation over a batch can be This slows down the training by requiring lower learning much more efficient than m computations for individual rates and careful parameter initialization, and makes it no- examples, due to the parallelism afforded by the modern toriously hard to train models with saturating nonlineari- computing platforms. ties. We refer to this phenomenon as internal covariate While stochastic gradient is simple and effective, it shift, and address the problem by normalizing layer in- requires careful tuning of the model hyper-parameters, puts. Our method draws its strength from making normal- specifically the learning rate used in optimization, as well ization a part of the model architecture and performingthe as the initial values for the model parameters. The train- normalization for each training mini-batch. Batch Nor- ing is complicated by the fact that the inputs to each layer malization allows us to use much higher learning rates and are affected by the parameters of all preceding layers – so be less careful about initialization. It also acts as a regu- that small changes to the network parameters amplify as larizer, in some cases eliminating the need for Dropout. the network becomes deeper. Applied to a state-of-the-art image classification model, The change in the distributions of layers’ inputs Batch Normalization achieves the same accuracy with 14 presents a problem because the layers need to continu- times fewer training steps, and beats the original model ously adapt to the new distribution. When the input dis- by a significant margin. Using an ensemble of batch- tribution to a learning system changes, it is said to experi- normalized networks, we improveupon the best published ence covariate shift (Shimodaira, 2000). This is typically result on ImageNet classification: reaching 4.9% top-5 handled via domain adaptation (Jiang, 2008). However, validation error (and 4.8% test error), exceeding the ac- the notion of covariate shift can be extended beyond the curacy of human raters. learning system as a whole, to apply to its parts, such as a sub-network or a layer. Consider a network computing 1 Introduction ℓ = F2(F1(u, Θ1), Θ2) Deep learning has dramatically advanced the state of the where F1 and F2 are arbitrary transformations, and the art in vision, speech, and many other areas. Stochas- parameters Θ1, Θ2 are to be learned so as to minimize arXiv:1502.03167v3 [cs.LG] 2 Mar 2015 tic gradient descent (SGD) has proved to be an effec- the loss ℓ. Learning Θ2 can be viewed as if the inputs tive way of training deep networks, and SGD variants x= F1(u, Θ1) are fed into the sub-network such as momentum (Sutskever et al., 2013) and Adagrad (Duchi et al., 2011) have been used to achieve state of the ℓ = F2(x, Θ2). art performance. SGD optimizes the parameters Θ of the network, so as to minimize the loss For example, a gradient descent step N m 1 α ∂F2(xi, Θ2) Θ = arg min ℓ(xi, Θ) Θ2 Θ2 Θ N ← − m ∂Θ2 Xi=1 Xi=1 where x1...N is the training data set. With SGD, the train- (for batch size m and learning rate α) is exactly equivalent ing proceeds in steps, and at each step we consider a mini- to that for a stand-alone network F2 with input x. There- batch x1...m of size m. The mini-batch is used to approx- fore, the input distribution properties that make training imate the gradient of the loss function with respect to the more efficient – such as having the same distribution be- parameters, by computing tween the training and test data – apply to training the sub-network as well. As such it is advantageous for the 1 ∂ℓ(xi, Θ) . distribution of x to remain fixed over time. Then, Θ does m ∂Θ 2 1 not have to readjust to compensate for the change in the 2 Towards Reducing Internal distribution of x. Covariate Shift Fixed distribution of inputs to a sub-network would We define Internal Covariate Shift as the change in the have positive consequences for the layers outside the sub- distribution of network activations due to the change in network, as well. Consider a layer with a sigmoid activa- network parameters during training. To improve the train- tion function z = g(W u + b) where u is the layer input, ing, we seek to reduce the internal covariate shift. By the weight matrix and bias vector are the layer pa- W b fixing the distribution of the layer inputs x as the training rameters to be learned, and g(x) = 1 . As x 1+exp(−x) progresses, we expect to improvethe training speed. It has ′ | | increases, g (x) tends to zero. This means that for all di- been long known (LeCun et al., 1998b; Wiesler & Ney, mensions of x= W u+b except those with small absolute 2011) that the network training converges faster if its in- values, the gradient flowing down to u will vanish and the puts are whitened – i.e., linearly transformed to have zero model will train slowly. However, since x is affected by means and unit variances, and decorrelated. As each layer W, b and the parameters of all the layers below, changes observes the inputs produced by the layers below, it would to those parameters during training will likely move many be advantageous to achieve the same whitening of the in- dimensions of x into the saturated regime of the nonlin- puts of each layer. By whitening the inputs to each layer, earity and slow down the convergence. This effect is we would take a step towards achieving the fixed distri- amplified as the network depth increases. In practice, butions of inputs that would remove the ill effects of the the saturation problem and the resulting vanishing gradi- internal covariate shift. ents are usually addressed by using Rectified Linear Units We could consider whitening activations at every train- (Nair & Hinton, 2010) ReLU(x) = max(x, 0), careful ing step or at some interval, either by modifying the initialization (Bengio & Glorot, 2010; Saxe et al., 2013), network directly or by changing the parameters of the and small learning rates. If, however, we could ensure optimization algorithm to depend on the network ac- that the distribution of nonlinearity inputs remains more tivation values (Wiesler et al., 2014; Raiko et al., 2012; stable as the network trains, then the optimizer would be Povey et al., 2014; Desjardins & Kavukcuoglu). How- less likely to get stuck in the saturated regime, and the ever, if these modifications are interspersed with the op- training would accelerate. timization steps, then the gradient descent step may at- tempt to update the parameters in a way that requires We refer to the change in the distributions of internal the normalization to be updated, which reduces the ef- nodes of a deep network, in the course of training, as In- fect of the gradient step. For example, consider a layer ternal Covariate Shift. Eliminating it offers a promise of with the input u that adds the learned bias b, and normal- faster training. We propose a new mechanism, which we izes the result by subtracting the mean of the activation call Batch Normalization, that takes a step towards re- computed over the training data: x = x E[x] where − ducing internal covariate shift, and in doing so dramati- x = u + b, = x1...N is the set of values of x over cally accelerates the training of deep neural nets. It ac- X { } 1 bN the training set, and E[x] = N i=1 xi. If a gradient complishes this via a normalization step that fixes the descent step ignores the dependenceP of E[x] on b, then it means and variances of layer inputs. Batch Normalization will update b b + ∆b, where ∆b ∂ℓ/∂x. Then also has a beneficial effect on the gradient flow through u + (b + ∆b)← E[u + (b + ∆b)] = ∝u + −b E[u + b]. the network, by reducing the dependence of gradients Thus, the combination− of the update to b and− subsequentb on the scale of the parameters or of their initial values. change in normalization led to no change in the output This allows us to use much higher learning rates with- of the layer nor, consequently, the loss. As the training out the risk of divergence. Furthermore, batch normal- continues, b will grow indefinitely while the loss remains ization regularizes the model and reduces the need for fixed. This problem can get worse if the normalization not Dropout (Srivastava et al., 2014). Finally, Batch Normal- only centers but also scales the activations. We have ob- ization makes it possible to use saturating nonlinearities served this empirically in initial experiments, where the by preventing the network from getting stuck in the satu- model blows up when the normalization parameters are rated modes. computed outside the gradient descent step. The issue with the above approach is that the gradient In Sec.
Load more

Recommended publications
  • Batch Normalization
    Deep Learning Srihari Batch Normalization Sargur N. Srihari [email protected] 1 Deep Learning Srihari Topics in Optimization for Deep Models • Importance of Optimization in machine learning • How learning differs from optimization • Challenges in neural network optimization • Basic Optimization Algorithms • Parameter initialization strategies • Algorithms with adaptive learning rates • Approximate second-order methods • Optimization strategies and meta-algorithms 2 Deep Learning Srihari Topics in Optimization Strategies and Meta-Algorithms 1. Batch Normalization 2. Coordinate Descent 3. Polyak Averaging 4. Supervised Pretraining 5. Designing Models to Aid Optimization 6. Continuation Methods and Curriculum Learning 3 Deep Learning Srihari Overview of Optimization Strategies • Many optimization techniques are general templates that can be specialized to yield algorithms • They can be incorporated into different algorithms 4 Deep Learning Srihari Topics in Batch Normalization • Batch normalization: exciting recent innovation • Motivation is difficulty of choosing learning rate ε in deep networks • Method is to replace activations with zero-mean with unit variance activations 5 Deep Learning Srihari Adding normalization between layers • Motivated by difficulty of training deep models • Method adds an additional step between layers, in which the output of the earlier layer is normalized – By standardizing the mean and standard deviation of each individual unit • It is a method of adaptive re-parameterization – It is not an optimization
    [Show full text]
  • On Self Modulation for Generative Adver- Sarial Networks
    Published as a conference paper at ICLR 2019 ON SELF MODULATION FOR GENERATIVE ADVER- SARIAL NETWORKS Ting Chen∗ Mario Lucic, Neil Houlsby, Sylvain Gelly University of California, Los Angeles Google Brain [email protected] flucic,neilhoulsby,[email protected] ABSTRACT Training Generative Adversarial Networks (GANs) is notoriously challenging. We propose and study an architectural modification, self-modulation, which im- proves GAN performance across different data sets, architectures, losses, regu- larizers, and hyperparameter settings. Intuitively, self-modulation allows the in- termediate feature maps of a generator to change as a function of the input noise vector. While reminiscent of other conditioning techniques, it requires no labeled data. In a large-scale empirical study we observe a relative decrease of 5% − 35% in FID. Furthermore, all else being equal, adding this modification to the generator leads to improved performance in 124=144 (86%) of the studied settings. Self- modulation is a simple architectural change that requires no additional parameter tuning, which suggests that it can be applied readily to any GAN.1 1 INTRODUCTION Generative Adversarial Networks (GANs) are a powerful class of generative models successfully applied to a variety of tasks such as image generation (Zhang et al., 2017; Miyato et al., 2018; Karras et al., 2017), learned compression (Tschannen et al., 2018), super-resolution (Ledig et al., 2017), inpainting (Pathak et al., 2016), and domain transfer (Isola et al., 2016; Zhu et al., 2017). Training GANs is a notoriously challenging task (Goodfellow et al., 2014; Arjovsky et al., 2017; Lucic et al., 2018) as one is searching in a high-dimensional parameter space for a Nash equilibrium of a non-convex game.
    [Show full text]
  • A Regularization Study for Policy Gradient Methods
    Submitted by Florian Henkel Submitted at Institute of Computational Perception Supervisor Univ.-Prof. Dr. Gerhard Widmer Co-Supervisor A Regularization Study Dipl.-Ing. Matthias Dorfer for Policy Gradient July 2018 Methods Master Thesis to obtain the academic degree of Diplom-Ingenieur in the Master’s Program Computer Science JOHANNES KEPLER UNIVERSITY LINZ Altenbergerstraße 69 4040 Linz, Österreich www.jku.at DVR 0093696 Abstract Regularization is an important concept in the context of supervised machine learning. Especially with neural networks it is necessary to restrict their ca- pacity and expressivity in order to avoid overfitting to given train data. While there are several well-known and widely used regularization techniques for supervised machine learning such as L2-Normalization, Dropout or Batch- Normalization, their effect in the context of reinforcement learning is not yet investigated. In this thesis we give an overview of regularization in combination with policy gradient methods, a subclass of reinforcement learning algorithms relying on neural networks. We compare different state-of-the-art algorithms together with regularization methods for supervised learning to get a better understanding on how we can improve generalization in reinforcement learn- ing. The main motivation for exploring this line of research is our current work on score following, where we try to train reinforcement learning agents to listen to and read music. These agents should learn from given musical training pieces to follow music they have never heard and seen before. Thus, the agents have to generalize which is why this scenario is a suitable test bed for investigating generalization in the context of reinforcement learning.
    [Show full text]
  • Entropy-Based Aggregate Posterior Alignment Techniques for Deterministic Autoencoders and Implications for Adversarial Examples
    Entropy-based aggregate posterior alignment techniques for deterministic autoencoders and implications for adversarial examples by Amur Ghose A thesis presented to the University of Waterloo in fulfillment of the thesis requirement for the degree of Master of Mathematics in Computer Science Waterloo, Ontario, Canada, 2020 c Amur Ghose 2020 Author's Declaration This thesis consists of material all of which I authored or co-authored: see Statement of Contributions included in the thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii Statement of Contributions Chapters 1 and 3 consist of unpublished work solely written by myself, with proof- reading and editing suggestions from my supervisor, Pascal Poupart. Chapter 2 is (with very minor changes) an UAI 2020 paper (paper link) on which I was the lead author, wrote the manuscript, formulated the core idea and ran the majority of the experiments. Some of the experiments were ran by Abdullah Rashwan, a co-author on the paper (credited in the acknowledgements of the thesis). My supervisor Pascal Poupart again proofread and edited the manuscript and made many valuable suggestions. Note that UAI 2020 proceedings are Open Access under Creative Commons, and as such, no copyright section is provided with the thesis, and as the official proceedings are as of yet unreleased a link has been provided in lieu of a citation. iii Abstract We present results obtained in the context of generative neural models | specifically autoencoders | utilizing standard results from coding theory.
    [Show full text]
  • Arxiv:1805.10694V3 [Stat.ML] 6 Oct 2018 Ing Algorithm for These Settings
    Exponential convergence rates for Batch Normalization: The power of length-direction decoupling in non-convex optimization Jonas Kohler* Hadi Daneshmand* Aurelien Lucchi Thomas Hofmann ETH Zurich ETH Zurich ETH Zurich ETH Zurich Ming Zhou Klaus Neymeyr Universit¨atRostock Universit¨atRostock Abstract (Bn) (Ioffe and Szegedy, 2015). This technique has been proven to successfully stabilize and accelerate Normalization techniques such as Batch Nor- training of deep neural networks and is thus by now malization have been applied successfully for standard in many state-of-the art architectures such training deep neural networks. Yet, despite as ResNets (He et al., 2016) and the latest Inception its apparent empirical benefits, the reasons Nets (Szegedy et al., 2017). The success of Batch Nor- behind the success of Batch Normalization malization has promoted its key idea that normalizing are mostly hypothetical. We here aim to pro- the inner layers of a neural network stabilizes train- vide a more thorough theoretical understand- ing which recently led to the development of many ing from a classical optimization perspective. such normalization methods such as (Arpit et al., 2016; Our main contribution towards this goal is Klambauer et al., 2017; Salimans and Kingma, 2016) the identification of various problem instances and (Ba et al., 2016) to name just a few. in the realm of machine learning where Batch Yet, despite the ever more important role of Batch Normalization can provably accelerate opti- Normalization for training deep neural networks, the mization. We argue that this acceleration Machine Learning community is mostly relying on em- is due to the fact that Batch Normalization pirical evidence and thus lacking a thorough theoretical splits the optimization task into optimizing understanding that can explain such success.
    [Show full text]
  • Norm Matters: Efficient and Accurate Normalization Schemes in Deep Networks
    Norm matters: efficient and accurate normalization schemes in deep networks Elad Hoffer1,∗ Ron Banner2,∗ Itay Golan1,∗ Daniel Soudry1 {elad.hoffer, itaygolan, daniel.soudry}@gmail.com {ron.banner}@intel.com (1) Technion - Israel Institute of Technology, Haifa, Israel (2) Intel - Artificial Intelligence Products Group (AIPG) Abstract 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 adjustments. We suggest several alternatives to the widely used L2 batch-norm, using normalization in L1 and L1 spaces that can substantially improve numerical stability in low-precision implementations as well as provide computational and memory benefits. We demonstrate that such methods enable the first batch-norm alternative to work for half-precision implementations. Finally, we suggest a modification to weight-normalization, which improves its performance on large-scale tasks. 2 1 Introduction Deep neural networks are known to benefit from normalization between consecutive layers. This was made noticeable with the introduction of Batch-Normalization (BN) [19], which normalizes the output of each layer to have zero mean and unit variance for each channel across the training batch. This idea was later developed to act across channels instead of the batch dimension in Layer- normalization [2] and improved in certain tasks with methods such as Batch-Renormalization [18], arXiv:1803.01814v3 [stat.ML] 7 Feb 2019 Instance-normalization [35] and Group-Normalization [40].
    [Show full text]
  • A Batch Normalized Inference Network Keeps the KL Vanishing Away
    A Batch Normalized Inference Network Keeps the KL Vanishing Away Qile Zhu1, Wei Bi2, Xiaojiang Liu2, Xiyao Ma1, Xiaolin Li3 and Dapeng Wu1 1University of Florida, 2Tencent AI Lab, 3AI Institute, Tongdun Technology valder,maxiy,dpwu @ufl.edu victoriabi,kieranliuf [email protected] f [email protected] Abstract inference, VAE first samples the latent variable from the prior distribution and then feeds it into Variational Autoencoder (VAE) is widely used the decoder to generate an instance. VAE has been as a generative model to approximate a successfully applied in many NLP tasks, including model’s posterior on latent variables by com- bining the amortized variational inference and topic modeling (Srivastava and Sutton, 2017; Miao deep neural networks. However, when paired et al., 2016; Zhu et al., 2018), language modeling with strong autoregressive decoders, VAE of- (Bowman et al., 2016), text generation (Zhao et al., ten converges to a degenerated local optimum 2017b) and text classification (Xu et al., 2017). known as “posterior collapse”. Previous ap- An autoregressive decoder (e.g., a recurrent neu- proaches consider the Kullback–Leibler diver- ral network) is a common choice to model the gence (KL) individual for each datapoint. We text data. However, when paired with strong au- propose to let the KL follow a distribution toregressive decoders such as LSTMs (Hochreiter across the whole dataset, and analyze that it is sufficient to prevent posterior collapse by keep- and Schmidhuber, 1997) and trained under conven- ing the expectation of the KL’s distribution tional training strategy, VAE suffers from a well- positive. Then we propose Batch Normalized- known problem named the posterior collapse or VAE (BN-VAE), a simple but effective ap- the KL vanishing problem.
    [Show full text]
  • Predicting Uber Demand in NYC with Wavenet
    SMART ACCESSIBILITY 2019 : The Fourth International Conference on Universal Accessibility in the Internet of Things and Smart Environments Predicting Uber Demand in NYC with Wavenet Long Chen Konstantinos Ampountolas Piyushimita (Vonu) Thakuriah Urban Big Data Center School of Engineering Rutgers University Glasgow, UK University of Glasgow, UK New Brunswick, NJ, USA Email: [email protected] Email: [email protected] Email: [email protected] Abstract—Uber demand prediction is at the core of intelligent transportation systems when developing a smart city. However, exploiting uber real time data to facilitate the demand predic- tion is a thorny problem since user demand usually unevenly distributed over time and space. We develop a Wavenet-based model to predict Uber demand on an hourly basis. In this paper, we present a multi-level Wavenet framework which is a one-dimensional convolutional neural network that includes two sub-networks which encode the source series and decode the predicting series, respectively. The two sub-networks are combined by stacking the decoder on top of the encoder, which in turn, preserves the temporal patterns of the time series. Experiments on large-scale real Uber demand dataset of NYC demonstrate that our model is highly competitive to the existing ones. Figure 1. The structure of WaveNet, where different colours in embedding Keywords–Anything; Something; Everything else. input denote 2 × k, 3 × k, and 4 × k convolutional filter respectively. I. INTRODUCTION With the proliferation of Web 2.0, ride sharing applications, such as Uber, have become a popular way to search nearby at an hourly basis, which is a WaveNet-based neural network sharing rides.
    [Show full text]
  • Large Memory Layers with Product Keys
    Large Memory Layers with Product Keys Guillaume Lample∗y, Alexandre Sablayrolles∗, Marc’Aurelio Ranzato∗, Ludovic Denoyer∗y, Herve´ Jegou´ ∗ fglample,asablayrolles,ranzato,denoyer,[email protected] Abstract This paper introduces a structured memory which can be easily integrated into a neural network. The memory is very large by design and significantly increases the capacity of the architecture, by up to a billion parameters with a negligi- ble computational overhead. Its design and access pattern is based on product keys, which enable fast and exact nearest neighbor search. The ability to increase the number of parameters while keeping the same computational budget lets the overall system strike a better trade-off between prediction accuracy and compu- tation efficiency both at training and test time. This memory layer allows us to tackle very large scale language modeling tasks. In our experiments we consider a dataset with up to 30 billion words, and we plug our memory layer in a state- of-the-art transformer-based architecture. In particular, we found that a memory augmented model with only 12 layers outperforms a baseline transformer model with 24 layers, while being twice faster at inference time. We release our code for reproducibility purposes.3 1 Introduction Neural networks are commonly employed to address many complex tasks such as machine trans- lation [43], image classification [27] or speech recognition [16]. As more and more data becomes available for training, these networks are increasingly larger [19]. For instance, recent models both in vision [29] and in natural language processing [20, 36, 28] have more than a billion parame- ters.
    [Show full text]
  • Approach Pre-Trained Deep Learning Models with Caution Pre-Trained Models Are Easy to Use, but Are You Glossing Over Details That Could Impact Your Model Performance?
    Approach pre-trained deep learning models with caution Pre-trained models are easy to use, but are you glossing over details that could impact your model performance? Cecelia Shao Follow Apr 15 · 5 min read . How many times have you run the following snippets: import torchvision.models as models inception = models.inception_v3(pretrained=True) or from keras.applications.inception_v3 import InceptionV3 base_model = InceptionV3(weights='imagenet', include_top=False) It seems like using these pre-trained models have become a new standard for industry best practices. After all, why wouldn’t you take advantage of a model that’s been trained on more data and compute than you could ever muster by yourself? See the discussion on Reddit and HackerNews Long live pre-trained models! There are several substantial benefits to leveraging pre-trained models: • super simple to incorporate • achieve solid (same or even better) model performance quickly • there’s not as much labeled data required • versatile uses cases from transfer learning, prediction, and feature extraction Advances within the NLP space have also encouraged the use of pre- trained language models like GPT and GPT-2, AllenNLP’s ELMo, Google’s BERT, and Sebastian Ruder and Jeremy Howard’s ULMFiT (for an excellent over of these models, see this TOPBOTs post). One common technique for leveraging pretrained models is feature extraction, where you’re retrieving intermediate representations produced by the pretrained model and using those representations as inputs for a new model. These final fully-connected layers are generally assumed to capture information that is relevant for solving a new task. Everyone’s in on the game Every major framework like Tensorflow, Keras, PyTorch, MXNet, etc… offers pre-trained models like Inception V3, ResNet, AlexNet with weights: • Keras Applications • PyTorch torchvision.models • Tensorflow Official Models (and now TensorFlow Hubs) • MXNet Model Zoo • Fast.ai Applications Easy, right? .
    [Show full text]
  • Outline for Today's Presentation
    Outline for today’s presentation • We will see how RNNs and CNNs compare on variety of tasks • Then, we will go through a new approach for Sequence Modelling that has become state of the art • Finally, we will look at a few augmented RNN models RNNs vs CNNs Empirical Evaluation of Generic Networks for Sequence Modelling Let’s say you are given a sequence modelling task of text classification / music note prediction, and you are asked to develop a simple model. What would your baseline model be based on- RNNs or CNNs? Recent Trend in Sequence Modelling • Widely considered as RNNs “home turf” • Recent research has shown otherwise – • Speech Synthesis – WaveNet uses Dilated Convolutions for Synthesis • Char-to-Char Machine Translation – ByteNet uses Encoder-Decoder architecture and Dilated Convolutions. Tested on English-German dataset • Word-to-Word Machine Translation – Hybrid CNN-LSTM on English-Romanian and English-French datasets • Character-level Language Modelling – ByteNet on WikiText dataset • Word-level Language Modelling – Gated CNNs on WikiText dataset Temporal Convolutional Network (TCN) • Model that uses best practices in Convolutional network design • The properties of TCN - • Causal – there is no information leakage from future to past • Memory – It can look very far into the past for prediction/synthesis • Input - It can take any arbitrary length sequence with proper tuning to the particular task. • Simple – It uses no gating mechanism, no complex stacking mechanism and each layer output has the same length as the input •
    [Show full text]
  • Rethinking the Usage of Batch Normalization and Dropout in the Training of Deep Neural Networks
    Rethinking the Usage of Batch Normalization and Dropout in the Training of Deep Neural Networks Guangyong Chen * 1 Pengfei Chen * 2 1 Yujun Shi 3 Chang-Yu Hsieh 1 Benben Liao 1 Shengyu Zhang 2 1 Abstract sive performance. The state-of-the-art neural networks are In this work, we propose a novel technique to often complex structures comprising hundreds of layers of boost training efficiency of a neural network. Our neurons and millions of parameters. Efficient training of a work is based on an excellent idea that whitening modern DNN is often complicated by the need of feeding the inputs of neural networks can achieve a fast such a behemoth with millions of data entries. Developing convergence speed. Given the well-known fact novel techniques to increase training efficiency of DNNs is that independent components must be whitened, a highly active research topics. In this work, we propose a we introduce a novel Independent-Component novel training technique by combining two commonly used (IC) layer before each weight layer, whose in- ones, Batch Normalization (BatchNorm) (Ioffe & Szegedy, puts would be made more independent. However, 2015) and Dropout (Srivastava et al., 2014), for a purpose determining independent components is a compu- (making independent inputs to neural networks) that is not tationally intensive task. To overcome this chal- possibly achieved by either technique alone. This marriage lenge, we propose to implement an IC layer by of techniques endows a new perspective on how Dropout combining two popular techniques, Batch Nor- could be used for training DNNs and achieve the original malization and Dropout, in a new manner that we goal of whitening inputs of every layer (Le Cun et al., 1991; can rigorously prove that Dropout can quadrati- Ioffe & Szegedy, 2015) that inspired the BatchNorm work cally reduce the mutual information and linearly (but did not succeed).
    [Show full text]