Article

# Deep Neural Network Acceleration Based on Low-Rank Approximated Channel Pruning

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## Abstract

Acceleration and compression on deep Convolutional Neural Networks (CNNs) have become a critical problem to develop intelligence on resource-constrained devices. Previous channel pruning can be easily deployed and accelerated without specialized hardware and software. However, weight-level redundancy is not well explored in channel pruning, which results in a relatively low compression ratio. In this work, we propose a Low-rank Approximated channel Pruning (LAP) framework to tackle this problem with two targeted steps. First, we utilize low-rank approximation to eliminate the redundancy within filter. This step achieves acceleration, especially in shallow layers, and also converts filters into smaller compact ones. Then, we apply channel pruning on the approximated network in a global way and obtain further benefits, especially in deep layers. In addition, we propose a spectral norm based indicator to coordinate these two steps better. Moreover, inspired by the integral idea adopted in video coding, we propose an evaluator based on Integral of Decay Curve (IDC) to judge the efficiency of various acceleration and compression algorithms. Ablation experiments and IDC evaluator prove that LAP can significantly improve channel pruning. To further demonstrate the hardware compatibility, the network produced by LAP obtains impressive speedup efficiency on the FPGA.

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... Consequently, often reduced precision is used for implementing these CNNs on a FPGA platform. For example, in [16,[28][29][30][31][32], researchers were using VGG-16 as the targeted CNN model for FPGA implementation which has 30.76 billion operations. Mei et al. reduce the precision of the data from single precision floating point to half precision point in [28]. ...
... Lian et al. use 8-bit block floating point (BFP) instead of regular floating point data types [29]. In other research such as [16,[30][31][32], authors take one step further by using fixed points data types. J. Wang et al. proposed an equal distance quantization method to adopt various bits depth up to 8-bit on different layers in [31], while Z. Chen et al. tested different quantization methods in [32]. ...
... In other research such as [16,[30][31][32], authors take one step further by using fixed points data types. J. Wang et al. proposed an equal distance quantization method to adopt various bits depth up to 8-bit on different layers in [31], while Z. Chen et al. tested different quantization methods in [32]. Unlike AlexNet or VGG-16, the Ultra-CNN has only 1.93 million operations. ...
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... In the actual power system, with the new development of the internet of things (IoT) platform and the deployment of large number of edge devices, the need to collect data on the edge devices of IoT and make prediction at the edge becomes more urgent [16]. This requires us to develop methods with fewer parameters and a lower computational cost to apply to resource-constrained devices [17,18]. It is obvious that PQD signals exactly have time series characteristics, and as a special type of deep learning model, recurrent network contains a hidden layer to process time series data. ...
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Deep learning is a promising approach for extracting accurate information from raw sensor data from IoT devices deployed in complex environments. Because of its multilayer structure, deep learning is also appropriate for the edge computing environment. Therefore, in this article, we first introduce deep learning for IoTs into the edge computing environment. Since existing edge nodes have limited processing capability, we also design a novel offloading strategy to optimize the performance of IoT deep learning applications with edge computing. In the performance evaluation, we test the performance of executing multiple deep learning tasks in an edge computing environment with our strategy. The evaluation results show that our method outperforms other optimization solutions on deep learning for IoT.
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In recent years, deep neural networks (DNNs) have received increased attention, have been applied to different applications, and achieved dramatic accuracy improvements in many tasks. These works rely on deep networks with millions or even billions of parameters, and the availability of graphics processing units (GPUs) with very high computation capability plays a key role in their success. For example, Krizhevsky et al. [1] achieved breakthrough results in the 2012 ImageNet Challenge using a network containing 60 million parameters with five convolutional layers and three fully connected layers. Usually, it takes two to three days to train the whole model on the ImagetNet data set with an NVIDIA K40 machine. In another example, the top face-verification results from the Labeled Faces in the Wild (LFW) data set were obtained with networks containing hundreds of millions of parameters, using a mix of convolutional, locally connected, and fully connected layers [2], [3]. It is also very time-consuming to train such a model to obtain a reasonable performance. In architectures that only rely on fully connected layers, the number of parameters can grow to billions [4].
Conference Paper
Along with the recent development of Convolutional Neural Network (CNN) and its multilayering, it is important to reduce the amount of computation and the amount of data associated with convolution processing. Some compression methods of convolutional filters using low-rank approximation have been studied. The common goal of these studies is to accelerate the computation wherever possible while maintaining the accuracy of image recognition. In this paper, we investigate the trade-off between the compression error by low-rank approximation and the computational complexity for the state-of-the-arts CNN model.
Conference Paper
The state-of-the-art face recognition systems are built on deep convolutional neural networks (CNNs). However, these CNNs contain millions of parameters, leading to the deployment difficulties on mobile and embedded devices. One solution is to reduce the size of the trained CNNs by model compression. In this work, we propose an entropy-based prune metric to reduce the size of intermediate activations so as to accelerate and compress CNN models both in training and inference stages. First the importance of each filter in each layer is evaluated by our entropy-based method. Then some unimportant filters are removed according to a predefined compressing rate. Finally, we fine-tune the pruned model to improve its discrimination ability. Experiments conducted on LFW face dataset shows the effectiveness of our entropy-based method. We achieve $$1.92\times$$ compression and $$1.88\times$$ speed-up on VGG-16 model, $$2\times$$ compression and $$1.74\times$$ speed-up on WebFace model, both with only about 1% accuracy decrease evaluated on LFW.
Conference Paper
Neural networks are both computationally intensive and memory intensive, making them difficult to deploy on embedded systems with limited hardware resources. To address this limitation, We introduce a three stage pipeline: pruning, quantization and Huffman encoding, that work together to reduce the storage requirement of neural networks by 35x to 49x without affecting their accuracy. Our method first prunes the network by learning only the important connections. Next, we quantize the weights to enforce weight sharing, finally, we apply Huffman encoding. After the first two steps we retrain the network to fine tune the remaining connections and the quantized centroids. Pruning, reduces the number of connections by 9x to 13x; Quantization then reduces the number of bits that represent each connection from 32 to 5. On the ImageNet dataset, our method reduced the storage required by AlexNet by 35x from 240MB to 6.9MB, without loss of accuracy. Our method reduced the size of VGG16 by 49x from 552MB to 11.3MB, again with no loss of accuracy. This allows fitting the model into on-chip SRAM cache rather than off-chip DRAM memory, which has 180x less access energy.
Conference Paper
While depth tends to improve network performances, it also makes gradient-based training more difficult since deeper networks tend to be more non-linear. The recently proposed knowledge distillation approach is aimed at obtaining small and fast-to-execute models, and it has shown that a student network could imitate the soft output of a larger teacher network or ensemble of networks. In this paper, we extend this idea to allow the training of a student that is deeper and thinner than the teacher, using not only the outputs but also the intermediate representations learned by the teacher as hints to improve the training process and final performance of the student. Because the student intermediate hidden layer will generally be smaller than the teacher's intermediate hidden layer, additional parameters are introduced to map the student hidden layer to the prediction of the teacher hidden layer. This allows one to train deeper students that can generalize better or run faster, a trade-off that is controlled by the chosen student capacity. For example, on CIFAR-10, a deep student network with almost 10.4 times less parameters outperforms a larger, state-of-the-art teacher network.
Conference Paper
We trained a large, deep convolutional neural network to classify the 1.2 million high-resolution images in the ImageNet LSVRC-2010 contest into the 1000 dif- ferent classes. On the test data, we achieved top-1 and top-5 error rates of 37.5% and 17.0% which is considerably better than the previous state-of-the-art. The neural network, which has 60 million parameters and 650,000 neurons, consists of five convolutional layers, some of which are followed by max-pooling layers, and three fully-connected layers with a final 1000-way softmax. To make training faster, we used non-saturating neurons and a very efficient GPU implemen- tation of the convolution operation. To reduce overfitting in the fully-connected layers we employed a recently-developed regularization method called dropout that proved to be very effective. We also entered a variant of this model in the ILSVRC-2012 competition and achieved a winning top-5 test error rate of 15.3%, compared to 26.2% achieved by the second-best entry
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High demand for computation resources severely hinders deployment of large-scale Deep Neural Networks (DNN) in resource constrained devices. In this work, we propose a Structured Sparsity Learning (SSL) method to regularize the structures (i.e., filters, channels, filter shapes, and layer depth) of DNNs. SSL can: (1) learn a compact structure from a bigger DNN to reduce computation cost; (2) obtain a hardware-friendly structured sparsity of DNN to efficiently accelerate the DNNs evaluation. Experimental results show that SSL achieves on average 5.1x and 3.1x speedups of convolutional layer computation of AlexNet against CPU and GPU, respectively, with off-the-shelf libraries. These speedups are about twice speedups of non-structured sparsity; (3) regularize the DNN structure to improve classification accuracy. The results show that for CIFAR-10, regularization on layer depth can reduce 20 layers of a Deep Residual Network (ResNet) to 18 layers while improve the accuracy from 91.25% to 92.60%, which is still slightly higher than that of original ResNet with 32 layers. For AlexNet, structure regularization by SSL also reduces the error by around ~1%. Open source code is in https://github.com/wenwei202/caffe/tree/scnn.
Article
We propose an efficient and unified framework, namely ThiNet, to simultaneously accelerate and compress CNN models in both training and inference stages. We focus on the filter level pruning, i.e., the whole filter would be discarded if it is less important. Our method does not change the original network structure, thus it can be perfectly supported by any off-the-shelf deep learning libraries. We formally establish filter pruning as an optimization problem, and reveal that we need to prune filters based on statistics information computed from its next layer, not the current layer, which differentiates ThiNet from existing methods. Experimental results demonstrate the effectiveness of this strategy, which has advanced the state-of-the-art. We also show the performance of ThiNet on ILSVRC-12 benchmark. ThiNet achieves 3.31$\times$ FLOPs reduction and 16.63$\times$ compression on VGG-16, with only 0.52$\%$ top-5 accuracy drop. Similar experiments with ResNet-50 reveal that even for a compact network, ThiNet can also reduce more than half of the parameters and FLOPs, at the cost of roughly 1$\%$ top-5 accuracy drop. Moreover, the original VGG-16 model can be further pruned into a very small model with only 5.05MB model size, preserving AlexNet level accuracy but showing much stronger generalization ability.
Article
We propose a new framework for pruning convolutional kernels in neural networks to enable efficient inference, focusing on transfer learning where large and potentially unwieldy pretrained networks are adapted to specialized tasks. We interleave greedy criteria-based pruning with fine-tuning by backpropagation - a computationally efficient procedure that maintains good generalization in the pruned network. We propose a new criterion based on an efficient first-order Taylor expansion to approximate the absolute change in training cost induced by pruning a network component. After normalization, the proposed criterion scales appropriately across all layers of a deep CNN, eliminating the need for per-layer sensitivity analysis. The proposed criterion demonstrates superior performance compared to other criteria, such as the norm of kernel weights or average feature map activation.
Conference Paper
We propose two efficient approximations to standard convolutional neural networks: Binary-Weight-Networks and XNOR-Networks. In Binary-Weight-Networks, the filters are approximated with binary values resulting in 32$$\times$$ memory saving. In XNOR-Networks, both the filters and the input to convolutional layers are binary. XNOR-Networks approximate convolutions using primarily binary operations. This results in 58$$\times$$ faster convolutional operations (in terms of number of the high precision operations) and 32$$\times$$ memory savings. XNOR-Nets offer the possibility of running state-of-the-art networks on CPUs (rather than GPUs) in real-time. Our binary networks are simple, accurate, efficient, and work on challenging visual tasks. We evaluate our approach on the ImageNet classification task. The classification accuracy with a Binary-Weight-Network version of AlexNet is the same as the full-precision AlexNet. We compare our method with recent network binarization methods, BinaryConnect and BinaryNets, and outperform these methods by large margins on ImageNet, more than $$16\,\%$$ in top-1 accuracy. Our code is available at: http:// allenai. org/ plato/ xnornet.
Article
State-of-the-art neural networks are getting deeper and wider. While their performance increases with the increasing number of layers and neurons, it is crucial to design an efficient deep architecture in order to reduce computational and memory costs. Designing an efficient neural network, however, is labor intensive requiring many experiments, and fine-tunings. In this paper, we introduce network trimming which iteratively optimizes the network by pruning unimportant neurons based on analysis of their outputs on a large dataset. Our algorithm is inspired by an observation that the outputs of a significant portion of neurons in a large network are mostly zero, regardless of what inputs the network received. These zero activation neurons are redundant, and can be removed without affecting the overall accuracy of the network. After pruning the zero activation neurons, we retrain the network using the weights before pruning as initialization. We alternate the pruning and retraining to further reduce zero activations in a network. Our experiments on the LeNet and VGG-16 show that we can achieve high compression ratio of parameters without losing or even achieving higher accuracy than the original network.
Article
State-of-the-art deep neural networks (DNNs) have hundreds of millions of connections and are both computationally and memory intensive, making them difficult to deploy on embedded systems with limited hardware resources and power budgets. While custom hardware helps the computation, fetching weights from DRAM is two orders of magnitude more expensive than ALU operations, and dominates the required power. Previously proposed 'Deep Compression' makes it possible to fit large DNNs (AlexNet and VGGNet) fully in on-chip SRAM. This compression is achieved by pruning the redundant connections and having multiple connections share the same weight. We propose an energy efficient inference engine (EIE) that performs inference on this compressed network model and accelerates the resulting sparse matrix-vector multiplication with weight sharing. Going from DRAM to SRAM gives EIE 120× energy saving; Exploiting sparsity saves 10×; Weight sharing gives 8×; Skipping zero activations from ReLU saves another 3×. Evaluated on nine DNN benchmarks, EIE is 189× and 13× faster when compared to CPU and GPU implementations of the same DNN without compression. EIE has a processing power of 102 GOPS working directly on a compressed network, corresponding to 3 TOPS on an uncompressed network, and processes FC layers of AlexNet at 1.88×10⁴ frames/sec with a power dissipation of only 600mW. It is 24,000× and 3,400× more energy efficient than a CPU and GPU respectively. Compared with DaDianNao, EIE has 2.9×, 19× and 3× better throughput, energy efficiency and area efficiency.
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Deep convolutional neural networks (DCNNs) have become a very powerful tool in visual perception. DCNNs have applications in autonomous robots, security systems, mobile phones, and automobiles, where high throughput of the feedforward evaluation phase and power efficiency are important. Because of this increased usage, many field-programmable gate array (FPGA)-based accelerators have been proposed. In this paper, we present an optimized streaming method for DCNNs' hardware accelerator on an embedded platform. The streaming method acts as a compiler, transforming a high-level representation of DCNNs into operation codes to execute applications in a hardware accelerator. The proposed method utilizes maximum computational resources available based on a novel-scheduled routing topology that combines data reuse and data concatenation. It is tested with a hardware accelerator implemented on the Xilinx Kintex-7 XC7K325T FPGA. The system fully explores weight-level and node-level parallelizations of DCNNs and achieves a peak performance of 247 G-ops while consuming less than 4 W of power. We test our system with applications on object classification and object detection in real-world scenarios. Our results indicate high-performance efficiency, outperforming all other presented platforms while running these applications.
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Deeper neural networks are more difficult to train. We present a residual learning framework to ease the training of networks that are substantially deeper than those used previously. We explicitly reformulate the layers as learning residual functions with reference to the layer inputs, instead of learning unreferenced functions. We provide comprehensive empirical evidence showing that these residual networks are easier to optimize, and can gain accuracy from considerably increased depth. On the ImageNet dataset we evaluate residual nets with a depth of up to 152 layers---8x deeper than VGG nets but still having lower complexity. An ensemble of these residual nets achieves 3.57% error on the ImageNet test set. This result won the 1st place on the ILSVRC 2015 classification task. We also present analysis on CIFAR-10 with 100 and 1000 layers. The depth of representations is of central importance for many visual recognition tasks. Solely due to our extremely deep representations, we obtain a 28% relative improvement on the COCO object detection dataset. Deep residual nets are foundations of our submissions to ILSVRC & COCO 2015 competitions, where we also won the 1st places on the tasks of ImageNet detection, ImageNet localization, COCO detection, and COCO segmentation.
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Although the latest high-end smartphone has powerful CPU and GPU, running deeper convolutional neural networks (CNNs) for complex tasks such as ImageNet classification on mobile devices is challenging. To deploy deep CNNs on mobile devices, we present a simple and effective scheme to compress the entire CNN, which we call one-shot whole network compression. The proposed scheme consists of three steps: (1) rank selection with variational Bayesian matrix factorization, (2) Tucker decomposition on kernel tensor, and (3) fine-tuning to recover accumulated loss of accuracy, and each step can be easily implemented using publicly available tools. We demonstrate the effectiveness of the proposed scheme by testing the performance of various compressed CNNs (AlexNet, VGGS, GoogLeNet, and VGG-16) on the smartphone. Significant reductions in model size, runtime, and energy consumption are obtained, at the cost of small loss in accuracy. In addition, we address the important implementation level issue on 1?1 convolution, which is a key operation of inception module of GoogLeNet as well as CNNs compressed by our proposed scheme.
Article
Large CNNs have delivered impressive performance in various computer vision applications. But the storage and computation requirements make it problematic for deploying these models on mobile devices. Recently, tensor decompositions have been used for speeding up CNNs. In this paper, we further develop the tensor decomposition technique. We propose a new algorithm for computing the low-rank tensor decomposition for removing the redundancy in the convolution kernels. The algorithm finds the exact global optimizer of the decomposition and is more effective than iterative methods. Based on the decomposition, we further propose a new method for training low-rank constrained CNNs from scratch. Interestingly, while achieving a significant speedup, sometimes the low-rank constrained CNNs delivers significantly better performance than their non-constrained counterparts. On the CIFAR-10 dataset, the proposed low-rank NIN model achieves $91.31\%$ accuracy, which also improves upon state-of-the-art result. We evaluated the proposed method on CIFAR-10 and ILSVRC12 datasets for a variety of modern CNNs, including AlexNet, NIN, VGG and GoogleNet with success. For example, the forward time of VGG-16 is reduced by half while the performance is still comparable. Empirical success suggests that low-rank tensor decompositions can be a very useful tool for speeding up large CNNs.
Article
Neural networks are both computationally intensive and memory intensive, making them difficult to deploy on embedded systems. Also, conventional networks fix the architecture before training starts; as a result, training cannot improve the architecture. To address these limitations, we describe a method to reduce the storage and computation required by neural networks by an order of magnitude without affecting their accuracy, by learning only the important connections. Our method prunes redundant connections using a three-step method. First, we train the network to learn which connections are important. Next, we prune the unimportant connections. Finally, we retrain the network to fine tune the weights of the remaining connections. On the ImageNet dataset, our method reduced the number of parameters of AlexNet by a factor of 9x, from 61 million to 6.7 million, without incurring accuracy loss. Similar experiments with VGG16 found that the network as a whole can be reduced 6.8x just by pruning the fully-connected layers, again with no loss of accuracy.
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State-of-the-art object detection networks depend on region proposal algorithms to hypothesize object locations. Advances like SPPnet and Fast R-CNN have reduced the running time of these detection networks, exposing region proposal computation as a bottleneck. In this work, we introduce a Region Proposal Network (RPN) that shares full-image convolutional features with the detection network, thus enabling nearly cost-free region proposals. An RPN is a fully-convolutional network that simultaneously predicts object bounds and objectness scores at each position. RPNs are trained end-to-end to generate high-quality region proposals, which are used by Fast R-CNN for detection. With a simple alternating optimization, RPN and Fast R-CNN can be trained to share convolutional features. For the very deep VGG-16 model, our detection system has a frame rate of 5fps (including all steps) on a GPU, while achieving state-of-the-art object detection accuracy on PASCAL VOC 2007 (73.2% mAP) and 2012 (70.4% mAP) using 300 proposals per image. The code will be released.
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This paper aims to accelerate the test-time computation of convolutional neural networks (CNNs), especially very deep CNNs that have substantially impacted the computer vision community. Unlike existing methods that are designed for approximating linear filters or linear responses, our method takes the nonlinear units into account. We develop an effective solution to the resulting nonlinear optimization problem without the need of stochastic gradient descent (SGD). More importantly, while current methods mainly focus on optimizing one or two layers, our nonlinear method enables an asymmetric reconstruction that reduces the rapidly accumulated error when multiple (e.g., >=10) layers are approximated. For the widely used very deep VGG-16 model, our method achieves a whole-model speedup of 4x with merely a 0.3% increase of top-5 error in ImageNet classification. Our 4x accelerated VGG-16 model also shows a graceful accuracy degradation for object detection when plugged into the latest Fast R-CNN detector.
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A very simple way to improve the performance of almost any machine learning algorithm is to train many different models on the same data and then to average their predictions. Unfortunately, making predictions using a whole ensemble of models is cumbersome and may be too computationally expensive to allow deployment to a large number of users, especially if the individual models are large neural nets. Caruana and his collaborators have shown that it is possible to compress the knowledge in an ensemble into a single model which is much easier to deploy and we develop this approach further using a different compression technique. We achieve some surprising results on MNIST and we show that we can significantly improve the acoustic model of a heavily used commercial system by distilling the knowledge in an ensemble of models into a single model. We also introduce a new type of ensemble composed of one or more full models and many specialist models which learn to distinguish fine-grained classes that the full models confuse. Unlike a mixture of experts, these specialist models can be trained rapidly and in parallel.
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In this work we investigate the effect of the convolutional network depth on its accuracy in the large-scale image recognition setting. Our main contribution is a thorough evaluation of networks of increasing depth, which shows that a significant improvement on the prior-art configurations can be achieved by pushing the depth to 16-19 weight layers. These findings were the basis of our ImageNet Challenge 2014 submission, where our team secured the first and the second places in the localisation and classification tracks respectively.
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The focus of this paper is speeding up the evaluation of convolutional neural networks. While delivering impressive results across a range of computer vision and machine learning tasks, these networks are computationally demanding, limiting their deployability. Convolutional layers generally consume the bulk of the processing time, and so in this work we present two simple schemes for drastically speeding up these layers. This is achieved by exploiting cross-channel or filter redundancy to construct a low rank basis of filters that are rank-1 in the spatial domain. Our methods are architecture agnostic, and can be easily applied to existing CPU and GPU convolutional frameworks for tuneable speedup performance. We demonstrate this with a real world network designed for scene text character recognition, showing a possible 2.5x speedup with no loss in accuracy, and 4.5x speedup with less than 1% drop in accuracy, still achieving state-of-the-art on standard benchmarks.
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Treatment of the predictive aspect of statistical mechanics as a form of statistical inference is extended to the density-matrix formalism and applied to a discussion of the relation between irreversibility and information loss. A principle of "statistical complementarity" is pointed out, according to which the empirically verifiable probabilities of statistical mechanics necessarily correspond to incomplete predictions. A preliminary discussion is given of the second law of thermodynamics and of a certain class of irreversible processes, in an approximation equivalent to that of the semiclassical theory of radiation. It is shown that a density matrix does not in general contain all the information about a system that is relevant for predicting its behavior. In the case of a system perturbed by random fluctuating fields, the density matrix cannot satisfy any differential equation because rho&dot;(t) does not depend only on rho(t), but also on past conditions The rigorous theory involves stochastic equations in the type rho(t)=G(t, 0)rho(0), where the operator G is a functional of conditions during the entire interval (0-->t). Therefore a general theory of irreversible processes cannot be based on differential rate equations corresponding to time-proportional transition probabilities. However, such equations often represent useful approximations.
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H.264/AVC is newest video coding standard of the ITU-T Video Coding Experts Group and the ISO/IEC Moving Picture Experts Group. The main goals of the H.264/AVC standardization effort have been enhanced compression performance and provision of a "network-friendly" video representation addressing "conversational" (video telephony) and "nonconversational" (storage, broadcast, or streaming) applications. H.264/AVC has achieved a significant improvement in rate-distortion efficiency relative to existing standards. This article provides an overview of the technical features of H.264/AVC, describes profiles and applications for the standard, and outlines the history of the standardization process.