(2013). Given the same compression rate, its accuracy was also much worse than the other methods. Compressing all three layers together usually led to larger error, especially when the compression rate was high. For binary quantization, which has no parameter to tune, the compression rate was 32. Edit social preview. As a result, the deployment of such models is not possible when only small amounts . This work studies quantization, coding, pruning and weight sharing techniques for reducing model size for the instance retrieval problem, providing the most comprehensive study on this topic. Freitas, NandoD. In Burges, C.j.c., Bottou, L., Welling, M., Ghahramani, Z., and 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. (2013) that the useful parameters in a CNN are about 5% (we were able to compress them about 20 times). Addeddate 2018-06-30 10:29:19 External-identifier urn:arXiv:1412.6115 Identifier arxiv-1412.6115 Scanner Deep convolutional neural networks (Krizhevsky etal., 2012; LeCun etal., 1990; Szegedy etal., 2014; Simonyan & Zisserman, 2014) has recently achieved significant progress and have become the gold standard for object recognition, image classification, and retrieval. Girshick, Ross, Donahue, Jeff, Darrell, Trevor, and Malik, Jitendra. 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%). 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition. View 6 excerpts, references background and methods. Large-sparse Model In particular, SVD achieves impressive results for compressing and speeding up convolutional layers (Denton etal., 2014) but does not work well for compressing dense connected layers. Martini, Berin. 1 PDF There have been other attempts to reduce the number of parameters of neural networks by replacing the fully connected layer with global average pooling. In particular, we have found in terms of [1] Gong et al., 2014, [Compressing deep convolutional networks using vector quantization] ( Compressing Deep Convolutional Networks using Vector Quantization) #### 2.1.1 Pruning 1. Many learning-based binarization or product quantization methods are available, such as Spectral Hashing (Weiss etal., 2008), Iterative Quantization (Gong etal., 2012), and Catesian kmeans (Norouzi & Fleet, 2013), among others. Exploiting linear structure within convolutional networks for efficient evaluation. Two very recent works by Denton etal. Motivated by the hypothesis that better quantization codebooks exist beyond the neighbourhood of a pretrained model, we depart from the conventional strategy in which a codebook is constructed from a pretrained model and then fine tuned. Please download files in this item to interact with them on your computer. Using priors to avoid the curse of dimensionality arising in Big Data. For WRmn, we can collect all its scalar values as wR1mn, and perform kmeans clustering to the values: where w and c are both scalars. abs/1412.6115, 2014. 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. Applications, Do More Dropouts in Pool5 Feature Maps for Better Object Detection. Somewhat surprisingly, we have found very similar results to those of Denil etal. For the 1000-category classification task in the ImageNet 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. Add a . 2.1. The nonlinear function we used here was RELU. CNNCNNCNNCNN CVMLFacebook R http://blog.csdn.net/shuzfan/article/details/51678499 We also conducted additional analysis on the classification error rate for compressing each single layer while fixing other layers as uncompressed. Denton, Emily, Zaremba, Wojciech, Bruna, Joan, LeCun, Yann, and Fergus, Rob. on the Internet. For example, CNN has already been applied to object classification, scene classification, and indoor scene classification. However, a very deep In particular, we consider the use of product quantization (PQ) (Jegou etal., 2011), which explores the redundancy of structures in vector space. These results motivate us to apply vector quantization methods to explore the redundancy in parameter space. This prohibits the usage of deep CNNs on resource limited hardware, especially cell phones or other embedded devices. This prohibits the usage of deep CNNs on resource limited hardware, especially cell phones or other embedded devices. It will also be interesting to apply fine-tuning to the compressed layers to improve performance. 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. So the compression rate given m, n, and k is computed as mn/k(m+n+1). Similarly to the above sections, we present the classification errors with respect to the compression rate. This prohibits the usage of deep CNNs on resource limited hardware, especially cell phones or other embedded devices. This prohibits the usage of Such learning models exploit recent results in the field of deep learning, typically leading to highly performing, yet very large neural networks with (at least) millions of parameters. image search. Compressing Deep Convolutional Networks using Vector Quantization Authors: Yunchao Gong Liu Liu Ming Yang Meta Lubomir Bourdev Abstract Deep convolutional neural networks (CNN) has become. Jaderberg, M., Vedaldi, A., and Zisserman, A. The approximation of SVD is controlled by the decay along the eigenvalues in S. The SVD method is optimal in the sense of a Frobenius norm, which minimizes the MSE error between the approximated matrix ^W and original W. programmable logic. The use of vector quantization methods to compress CNN parameters is mainly inspired by the work of Denil etal. codes for large-scale image retrieval. Given the parameter W, we take the sign of the matrix: This method is mainly inspired by Dropconnect (Wan etal., 2013). Let t=0 . methods. This paper uses speech recognition as an example task, and shows that a real-time hybrid hidden Markov model / neural network (HMM/NN) large vocabulary system can be built with a 10 speedup over an unoptimized baseline and a 4 speed up over an aggressively optimized floating-point baseline at no cost in accuracy. 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. A large, deep convolutional neural network was trained to classify the 1.2 million high-resolution images in the ImageNet LSVRC-2010 contest into the 1000 different classes and employed a recently developed regularization method called "dropout" that proved to be very effective. compressing the parameters of CNNs. Search the history of over 752 billion In this paper, we tackle this model storage issue by investigating information theoretical vector quantization methods for compressing the parameters of CNNs. features. First, KM works reasonably well and can achieve a descent compression rate without sacrificing performance. Gong, Yunchao, Wang, Liwei, Guo, Ruiqi, and Lazebnik, Svetlana. Both methods studied only the fully connected layer , ignoring the convolutional layers. 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. These over-sized models contain a large amount of filters in the convolutional layers, which are responsible for almost 99% of the computation. Using large state-of-the-art models, this work demonstrates speedups of convolutional layers on both CPU and GPU by a factor of 2 x, while keeping the accuracy within 1% of the original model. All of the input images were first resized to minimal dimensions of 257, after which we performed random cropping to 225225, patches. Somewhat surprisingly, kmeans, despite its simplicity, works well for this task. Thus, in order to apply neural network methods to embedded platforms, one important research problem is how to compress parameters to reduce storage requirements. ). convolutional networks. Sermanet, Pierre, Eigen, David, Zhang, Xiang, Mathieu, Michael, Fergus, Rob, Full-precision weights, activations and even gradients in networks can be quantized to 16-bit floating point numbers, 8-bit integers, or . However, a very deep CNN generally involves many layers with millions of parameters, making the storage of the network model to be extremely large. This result is consistent with previous observations for PQ (i.e., that using more centers in each segment can usually obtain a lower rate of quantization error). First, we prune the networking by removing the redundant connections, keeping only the most informative connections. RQ works extremely poorly for such a task, which probably means there are few global structures in these weight vectors. Iterative quantization: A Procrustean approach to learning binary 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. By compressing the parameters more than 20 times, we addressed the problem of applying state-of-the art CNNs in embedded devices. 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 . We used a different number of clusters k=4,8,16 (corresponds to 2,3,4 bits) for each segment. Show all files, Uploaded by 2016StanfordNVIDIADeep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Codingweightcodebookweight sharingweight VQVector quantizationDcodebookcodewordcodeword quantizer Part II: quantization-A Survey of Model Compression and Acceleration for Deep Neural Networks; Structure. We shall compare different PQ methods when we align the segment size, and also compare them with the aligned compression rate. In conclusion, we found that vector quantized CNNs can be safely applied to problems other than image classification. For example, a typical CNN. The compression rate is m/(tk+log2(k)tn). For each sub-vector wiz, we need only to store its corresponding cluster index and the codebooks. storage of the network model to be extremely large. The most closely related one, Denton etal. We highlight our experiments on AlexNet which reduced the weight storage by 35 without loss of accuracy. We were able to achieve a 4-8 times compression rate with KM while keeping the accuracy loss within 1%. It is especially useful when the bandwidth is limited or photos are not allowed to be sent to servers. Papers With Code is a free resource with all data licensed under. and Jackel, L.D. 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. Applying PQ works even better, which means that there are very meaningful sub-vector local structures in these weight matrices. vector space into many disjoint subspaces, and perform quantization in each subspace. Product Quantization for Nearest Neighbor Search,TPAMI,2011 ; Compressing Deep Convolutional Networks using Vector Quantization,ICLR,2015 ; Deep Learning with Limited Numerical Precision, ICML, 2015 ; Ristretto: Hardware-Oriented Approximation of Convolutional Neural Networks, ArXiv, 2016 ; Fixed Point Quantization of Deep Convolutional . For this reason, we do not consider the other methods in this paper. Gong et al. Deep fisher networks for large-scale image classification. Networks, A High-Performance Adaptive Quantization Approach for Edge CNN Given a state-of-the-art model with about 200MB of parameters, we were able to reduce them to less than 10MB, which enabled us to easily deploy such models. embedded devices. , which randomly sets part of the parameters (neurons) to 0 during training. The abovementioned (KM, PQ, and RQ) are three different kinds of vector quantization methods for compressing matrices. Regularization of neural networks using dropconnect. 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 particular, we have found in terms of compressing the most storage . Capture a web page as it appears now for use as a trusted citation in the future. Therefore, this method is also a good choice when the goal is to compress data very aggressively. Denil, Misha, Shakibi, Babak, Dinh, Laurent, Ranzato, Marcaurelio, and Accelerating deep neural networks on mobile processor with embedded Our main interest is quantization techniques, which compress networks by reducing the precision of parameters. 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. . Large-sparse Model This paper makes the following contributions: 1) We are among the first to systematically explore vector quantization methods for compressing the dense connected layers of deep CNNs to reduce storage; 2) We have performed a comprehensive evaluation of different vector quantization methods, which has shown in particular that structured quantization such as product quantization works significantly better than other methods; 3) We have performed experiments on other tasks such as image retrieval, to verify the generalization ability of the compressed model. We used cosine distance to measure the similarities among image features. We need to store all the codebooks for each iteration, which potentially needs large a amount of memory. 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. These researchers showed that by exploring the linear structure of CNN parameters (in particular, convolutional layers), CNN testing time can be sped up by as much as 200% while keeping the accuracy within 1% of the original model. It will be interesting to investigate what kinds of redundancies are present in the behavior of the learned parameters. Finally, a vector can be reconstructed by adding its corresponding centers at each stage: given we have recursively performed t iterations. This prohibits the usage of deep CNNs on resource limited hardware, especially cell phones or other embedded devices. The basic idea is to first quantize the vectors into k centers and then to recursively quantize the residuals. A few early works on compressing CNNs have been published; however, their focus is different from ours. There are no reviews yet. (2013), in that we are able to compress the parameters about 20 times with little decrease of performance. Then the images were fed into 5 different convolutional layers with respective filter sizes of 7, 5, 3, 3, and 3. Handwritten digit recognition with a back-propagation network. The success of the convolutional neural network (CNN) comes with a tremendous growth of diverse CNN structures, making it hard to deploy on limited-resource platforms. deep CNNs on resource limited hardware, especially cell phones or other However, the size of the CNN models are typically very large (e.g. 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. For example, if we use k=256 centers, only need 8 bits are needed per cluster index. 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.
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