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Szegedy, Christian, Liu, Wei, Jia, Yangqing, Sermanet, Pierre, Reed, Scott, This work investigates the effect of the convolutional network depth on its accuracy in the large-scale image recognition setting using an architecture with very small convolution filters, which shows that a significant improvement on the prior-art configurations can be achieved by pushing the depth to 16-19 weight layers. In particular, we consider using singular-value decomposition (SVD) to factorize the parameter matrix. Simply applying k-means clustering to the weights or conducting Almost all of the above mentioned works focus on making the prediction speed of CNN faster; little work has been specifically devoted to making CNN models smaller. In particular, we have found in terms of compressing the most storage . This work shows that a compressed network can be created by starting with a model pre-trained for the task of visual place recognition and then fine-tuning it via trained pruning and quantization, and resulting compressed networks have sizes of around 30MB and 65MB which makes them easily usable in memory constrained devices. Compressing Deep Convolutional Networks using Vector Quantization Quantized Convolutional Neural Networks for Mobile Devices Song HanICLR 2016best paper w [i] [j]0trick huffman From the results in Figure 1, we see that by using more centers k and smaller segment size s, we were able to obtain smaller classification error. (2013), in that we are able to compress the parameters about 20 times with little decrease of performance. For RQ, we found it was not able to achieve a very high compression rate, mainly because the codebook size was too big. web pages sshrviz, weixin_45201708: Dynamic Capacity Networks; ResNeXt: Aggregated Residual Transformations for Deep Neural Networks; . Due to a planned power outage on Friday, 1/14, between 8am-1pm PST, some services may be impacted. 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition. There have been other attempts to reduce the number of parameters of neural networks by replacing the fully connected layer with global average pooling. small-dense model size10.28MBLarge-sparse Model size 9.04MBLarge-sparse Modelsmall-dense model, https://blog.csdn.net/liujianlin01/article/details/80861406, Pruning Filters for Efficient ConvNets, To prune, or not to prune: exploring the efficacy of pruning for model compression, NISP: Pruning Networks using Neuron Importance Score Propagation. Denil, Misha, Shakibi, Babak, Dinh, Laurent, Ranzato, Marcaurelio, and The bottleneck comes from model storage and testing speed. Freitas, NandoD. In Burges, C.j.c., Bottou, L., Welling, M., Ghahramani, Z., and The convolutional neural network we used, from Zeiler & Fergus (2013), contains 5 convolutional layers and 3 dense connected layers. abs/1412.6115, 2014. As mentioned in section 3.2.3, we were able to perform PQ for either the x-axis or the y-axis and therefore show results for both cases. In particular, our paper can be viewed as a compression realization of the parameter prediction results reported in Denil etal. For example, if we use k=256 centers, only need 8 bits are needed per cluster index. , : (2011), who explored the properties of CPU to speed up the execution of CNN, particularly focused on the aligning of memory and SIMD operations to boost matrix operations. These results motivate us to apply vector quantization methods to explore the redundancy in parameter space. A deep neural network model compression framework based on weight pruning, weight quantization and knowledge distillation is constructed, which shows that the combination of three algorithms can compress 80% FLOPs and reduce the accuracy by only 1%. All of the input images were first resized to minimal dimensions of 257, after which we performed random cropping to 225225, patches. Gokhale, V., Jin, Jonghoon, Dundar, A., Martini, B., and Culurciello, E. A 240 g-ops/s mobile coprocessor for deep neural networks. It has also been applied to image retrieval, with impressive results. It is designed for production environments and is optimized for speed and accuracy on a small number of training images. Compressing all three layers together usually led to larger error, especially when the compression rate was high. What follows is a huge demand for machine computing power, CNN usually occupies a lot of memory space, and the computing cost is high [1, 2].High-performance computing resources generally mean high prices, which hinders the application of deep learning to edge devices with low . Therefore, this method is also a good choice when the goal is to compress data very aggressively. The comparison among KM, PQ, and RQ suggests some interesting insights. Our method operates by pruning the unimportant connections, quantizing the network using weight sharing, and then applying Huffman coding. The nonlinear function we used here was RELU. (2013) that the useful parameters in a CNN are about 5% (we were able to compress them about 20 times). methods. We first consider matrix factorization methods, which have been widely used to speed up CNN (Denton etal., 2014) as well as for compressing parameters in linear models (Denton etal., 2014), . To address this limitation, we introduce "deep compression", a three stage pipeline: pruning, trained quantization and Huffman coding, that work together to reduce the storage requirement of neural networks by 35x to 49x without affecting . Improving the speed of neural networks on cpus. (eds.). This article proposes a space efficient quantization scheme which uses eight or less bits to represent the original 32-bit weights and adopts singular value decomposition (SVD) method to decrease the parameter size of fully-connected layers for further compression. Deep convolutional neural network (DCNN) based image codecs, consisting of encoder, quantizer and decoder, have achieved promising image compression results. Mathieu etal. The most closely related one, Denton etal. Han [2]DNN AlexNet35 [3] With the great progress in this area, the state-of-the-art image classifier can achieve 94% top five accuracy on the ILSVRC2014 dataset with 1000 object classes, and is already very close human performance. In this paper, we tackle this model storage issue by investigating information theoretical vector quantization methods for compressing the parameters of CNNs. 2:while Bt> do 3: for each network layer jL do The results are reported in Figure 4 (for accuracy@1 only). We performed experiments on the Holidays dataset (Jegou etal., 2008). Deep convolutional neural networks (CNN) has become the most promising method for object recognition, repeatedly demonstrating record breaking results for image classification and object detection in recent years. In our experiments, we evaluated both cases. The goal was either to achieve higher compression rate with same accuracy or higher accuracy with same compression rate. For example, in Figure 1, the red curve always has much smaller classification error than other methods. Somewhat surprisingly, we have found very similar results to those of Denil etal. Sermanet, Pierre, Eigen, David, Zhang, Xiang, Mathieu, Michael, Fergus, Rob, 2.1. To achieve this goal, we present "deep compression": a three-stage pipeline (Figure 1) to reduce the storage required by neural network in a manner that preserves the original accuracy. Download Citation | Quantization Adaptor for Bit-Level Deep Learning-Based Massive MIMO CSI Feedback | In massive multiple-input multiple-output (MIMO) systems, the user equipment (UE) needs to . only 1. Tzeng, Eric, and Darrell, Trevor. Denton, Emily, Zaremba, Wojciech, Bruna, Joan, LeCun, Yann, and Fergus, Rob. This work shows that a compressed network can be created by starting with a model pre-trained for the task of visual place recognition and then fine-tuning it via trained pruning and quantization, and resulting compressed networks have sizes of around 30MB and 65MB which makes them easily usable in memory constrained devices. Applying PQ works even better, which means that there are very meaningful sub-vector local structures in these weight matrices. for object recognition, repeatedly demonstrating record breaking results for Compressing deep convolutional networks using vector quantization. Published in: 2022 17th Canadian Workshop on Information Theory (CWIT) Article #: Date of Conference: 05-08 June 2022 Date Added to IEEE Xplore: 14 July 2022 ISBN Information: For example, we consider binarizing the parameters, scalar quantization using. Handwritten digit recognition with a back-propagation network. In this work, instead of the traditional matrix factorization methods considered in (Denton etal., 2014; Jaderberg etal., 2014), we mainly consider a series of information theoretical vector quantization methods (Jegou etal., 2011; Chen etal., 2010), for compressing dense connected layers. arkiver2 small-dense model size10.28MBLarge-sparse Model size 9.04MBLarge-sparse Modelsmall-dense model, PQ-girl: It focuses on reducing the number of bits to represent each parame-ter. [Paper] 2. This prohibits the usage of convolutional networks. We shall compare different PQ methods when we align the segment size, and also compare them with the aligned compression rate. However, a very deep CNN generally involves many layers with millions of parameters, making the storage of the network model to be extremely large. The two low-rank matrices ^U and ^V, as well as the eigenvalues, must be stored. There Is No Preview Available For This Item, This item does not appear to have any files that can be experienced on Archive.org. image search. Gong, Yunchao, Lazebnik, Svetlana, Gordo, Albert, and Perronnin, Florent. During the prediction, we can directly look up the values for each wij in c. Thus, the reconstructed matrix is: For this approach, we only need to store the indexes and the codebook as the parameters. Please download files in this item to interact with them on your computer. This paper proposes a version of the state-of-the-art Fisher vector image encoding that can be stacked in multiple layers, and significantly improves on standard Fisher vectors, and obtains competitive results with deep convolutional networks at a smaller computational learning cost. Another simple method is to perform scalar quantization to the parameters. This prohibits the usage of deep CNNs on resource limited hardware, especially cell phones or other embedded devices. A method for compressing the structure of deep neural networks by applying clustering analysis to find similar neurons in each layer of the original network, and merge them and the corresponding connections is proposed. However, when we took the size of the codebook into account and measured the accuracy for the same compression rate, as in Figure 2, we found using more centers is not always helpful because they will aggressively increase the codebook size. For each fixed k, we show results for different segment dimension (column) sizes s=1,2,3,4, which changed the compression rate from lower to higher. These over-sized models contain a large amount of filters in the convolutional layers, which are responsible for almost 99% of the computation. Fixed-point feedforward deep neural network design using weights +1, 0, and- 1. In particular, because the W is learned on a set of outputs of different filters, grouping together output from specific filters or grouping together specific dimensions from different filters might be interesting. Another interesting implication of this paper is that our empirical results confirmed the finding in Denil etal. For kmeans (KM), we varied the number of clusters from 1 to 32 to achieve a compression rate between 32 and 1. CNN features off-the-shelf: an astounding baseline for recognition. We used a different number of clusters k=4,8,16 (corresponds to 2,3,4 bits) for each segment. (2013). [1412.6115] Compressing Deep Convolutional Networks using Vector Quantization It will be interesting to investigate what kinds of redundancies are present in the behavior of the learned parameters Abstract: Deep convolutional neural networks (CNN) has become the most promising method for object recognition, repeatedly demonstrating record . deep CNNs on resource limited hardware, especially cell phones or other The performance of RQ was unsatisfactory; here, we report results only for 256 centers with t=2,3 iterations. By removing . [1] Gong et al., 2014, [Compressing deep convolutional networks using vector quantization] ( Compressing Deep Convolutional Networks using Vector Quantization) #### 2.1.1 Pruning 1. Culurciello, Eugenio, Dundar, Aysegul, Jin, Jonghoon, Gokhale, Vinayak, and By compressing the parameters more than 20 times, we addressed the problem of applying state-of-the art CNNs in embedded devices. Papers With Code is a free resource with all data licensed under. We used cosine distance to measure the similarities among image features. Somewhat surprisingly, we found that by simply performing a scalar quantization to the parameter values using kmeans, we were able to obtain 8-16 compression rate of the parameters without sacrificing top-five accuracy in more than 0.5% of the compressions. 2016StanfordNVIDIADeep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Codingweightcodebookweight sharingweight VQVector quantizationDcodebookcodewordcodeword quantizer Semantic Scholar is a free, AI-powered research tool for scientific literature, based at the Allen Institute for AI. Neural networks are both computationally intensive and memory intensive, making them difficult to deploy on embedded systems with limited hardware resources. By removing . Deep convolutional neural networks (CNN) has become the most promising method for object recognition, repeatedly demonstrating record breaking results for image classification and object. Jaderberg, M., Vedaldi, A., and Zisserman, A. Given the parameter, where URmm and VRnn are two dense orthogonal matrices and SRmn is a diagonal matrix. Given the k centers, we only need log2(k) bits to encode the centers. Whereas this paper mainly focused on compressing dense connected layers, it will be interesting to investigate if we can apply the same vector quantization methods to compress convolutional layers. task. Large-sparse Model To evaluate the different methods, we used the classification accuracy on the validation set as the evaluation protocol. We were able to achieve a 4-8 times compression rate with KM while keeping the accuracy loss within 1%. Two simple schemes for drastically speeding up convolutional neural networks are presented, achieved by exploiting cross-channel or filter redundancy to construct a low rank basis of filters that are rank-1 in the spatial domain. on June 30, 2018. In particular, we have found in terms of compressing the most storage demanding dense connected layers, vector quantization methods have a clear gain over existing matrix factorization methods. In this article we mainly consider compressing CNNs for computer vision tasks. Section 3 below contains a comparison of all of the quantization methods we introduce herein. Here, we are taking a more aggressive approach by turning each neuron on if it is positive and turning it off when it is negative. Simply applying k-means clustering to the weights or conducting product quantization can lead to a very good balance between model size and recognition accuracy. The results for accuracy@1 are reported in Figure 1 and Figure 2 for different axis alignments. Vanhoucke etal. However, a very deep CNN generally involves many layers with millions of parameters . Andrew. Compressing Deep Convolutional Networks using Vector Quantization, Advanced embedding details, examples, and help, http://arxiv.org/licenses/nonexclusive-distrib/1.0/, Terms of Service (last updated 12/31/2014). View 3 excerpts, references methods and background. on the Internet. A blog about Compressive Sensing, Computational Imaging, Machine Learning. . 1. Compressing Deep Convolutional Networks using Vector Quantization,ICLR,2015 ; Deep Learning with Limited Numerical Precision, ICML, . Almost all of the recent successful recognition systems (Jia, 2013; Donahue etal., 2013; Simonyan etal., 2013; Sermanet etal., 2013; Zeiler & Fergus, 2013; Gong etal., 2014) are built on top of this architecture. It also has a validation set of 20,000 images, in categories that contain 20 images each. The learning rate started at 0.02 and halved every 5-10 epochs; the weight decay was set to 0.0005; and momentum was set to 0.9. However, a very deep This difference is because the codebook itself is using too much storage space and and makes the compression rate very low. Networks, A High-Performance Adaptive Quantization Approach for Edge CNN This work introduces Tensor Ring Networks (TR-Nets), which significantly compress both the fully connected layers and the convolutional layers of deep neural networks, and shows promise in scientific computing and deep learning, especially for emerging resource-constrained devices such as smartphones, wearables and IoT devices. This prohibits the usage of deep . Jegou, Herve, Douze, Matthijs, and Schmid, Cordelia. A simple but effective scheme called multi-scale orderless pooling (MOP-CNN), which extracts CNN activations for local patches at multiple scale levels, performs orderless VLAD pooling of these activations at each level separately, and concatenates the result. Abstract: In this paper, we present a novel vector quantization technique, VQLC, for the compression of convolutional neural networks. We start with the simplest way to quantize the parameter matrices. In this section, we consider two classes of methods for compressing the parameters in dense connected layers. , 1.1:1 2.VIPC, Compressing Deep Convolutional Networks using Vector Quantization , https://arxiv.org/abs/1412.611590%, For example, when we used k=16 centers, the classification error was clearly not lower than when we used fewer number of clusters (e.g. Then the images were fed into 5 different convolutional layers with respective filter sizes of 7, 5, 3, 3, and 3. From a geometric point of view, assuming that dense connected layers are a set of hyperplanes, we are actually rounding each hyperplane to its nearest coordinate. Show all files, Uploaded by Due to its assumption that the vectors in each subspace are heavily redundant and by performing quantization in each subspace, we are able to better explore the redundancy structure. [Paper] 4. These results suggests that there is considerable redundancy between each single neuron. Weinberger, K.q. In particular, we have found in terms of compressing the most storage . We used both the accuracy@1 and accuracy@5 to evaluate different parameter compression methods. LeCun, Y., Boser, B., Denker, J.S., Henderson, D., Howard, R.E., Hubbard, W., After the clustering, each value in w is assigned a cluster index, and a codebook can be formed of c1k the cluster centers. Y. Gong, L. Liu, M. Yang, and L. D. Bourdev, "Compressing deep convolutional networks using vector quantization," CoRR, vol. Next, we compute the residual r1z between wz and c1j for all the data points and recursively quantize the residual vectors r1z into k different code words c2j. This difference is mainly because the two factorized matrices still need to be stored for SVD, which is not optimized for saving storage. Part II: quantization-A Survey of Model Compression and Acceleration for Deep Neural Networks; Structure. Somewhat surprisingly, kmeans, despite its simplicity, works well for this task. Large-sparse Model In this paper, we tackle this model storage issue by investigating information theoretical vector quantization methods for compressing the parameters of CNNs. Deep convolutional neural networks (CNN) has become the most promising method for object recognition, repeatedly demonstrating record breaking results for image classification and object detection in recent years. In this paper, we proposed a DCNN architecture for image compression . One surprising finding was that k, means with 2 centers (1 bit) gave high resultseven higher than the original feature (we also verified the variance as 0.1%). Deep convolutional neural networks (CNN) has become the most promising method for object recognition, repeatedly demonstrating record breaking results for image classification and object detection in recent years. The basic idea of PQ is to partition the For the 1000-category classification task in the ImageNet challenge, we are able to achieve 16-24 times compression of the network with only 1% loss of classification accuracy using the state-of-the-art CNN. vector space into many disjoint subspaces, and perform quantization in each subspace. Deep convolutional neural networks (CNN) has become the most promising method for object recognition, repeatedly demonstrating record breaking results for image classification and object detection in recent years. For example, a typical CNN. The key question here arises: Do we really need all those filters? For PQ, we used 8 centers per segment and varied the dimension (from 1 to 4) of each segment to achieve different compression rates. Weiss, Yair, Torralba, Antonio, and Fergus, Rob. This section presents an application of the compressed CNN to image retrieval, in order to verify the generalization ability of the compressed networks. This prohibits the usage of deep CNNs on resource limited hardware, especially cell phones or other embedded devices. more than 200M bytes), which limits the applicability of such models on the embedded platform.
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