Accelerating deep neural networks (DNNs) has been attracting increasing attention as it can benefit a wide range of applications, e.g., enabling mobile systems with limited computing resources to own powerful visual recognition ability. A practical strategy to this goal usually relies on a two-stage process: operating on the trained DNNs (e.g., approximating the convolutional filters with tensor decomposition) and fine-tuning the amended network, leading to difficulty in balancing the trade-off between acceleration and maintaining recognition performance. In this work, aiming at a general and comprehensive way for neural network acceleration, we develop a Wavelet-like Auto-Encoder (WAE) that decomposes the original input image into two low-resolution channels (sub-images) and incorporate the WAE into the classification neural networks for joint training. The two decomposed channels, in particular, are encoded to carry the low-frequency information (e.g., image profiles) and high-frequency (e.g., image details or noises), respectively, and enable reconstructing the original input image through the decoding process. Then, we feed the low-frequency channel into a standard classification network such as VGG or ResNet and employ a very lightweight network to fuse with the high-frequency channel to obtain the classification result. Compared to existing DNN acceleration solutions, our framework has the following advantages: i) it is tolerant to any existing convolutional neural networks for classification without amending their structures; ii) the WAE provides an interpretable way to preserve the main components of the input image for classification.
works explore more optimal network structures for efficient training and inference. @cite_18 develop a low-dimensional embedding method to reduce the number and size of the filters. @cite_10 show that stacked filters with small spatial dimensions (e.g., @math ) could operate in the same receptive field of larger filters (e.g., @math ) with less computational complexity. @cite_17 further replace some @math filters with @math filters, and decrease the number of input channels to @math filters to simultaneously speed up and compress the deep networks.
@cite_18 @cite_10 @cite_17
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Conventional convolutional neural networks use either a linear or a nonlinear filter to extract features from an image patch (region) of spatial size @math (typically, @math is small and is equal to @math , e.g., @math is 5 or 7). Generally, the size of the filter is equal to the size @math of the input patch. We argue that the representational ability of equal-size strategy is not strong enough. To overcome the drawback, we propose to use subpatch filter whose spatial size @math is smaller than @math . The proposed subpatch filter consists of two subsequent filters. The first one is a linear filter of spatial size @math and is aimed at extracting features from spatial domain. The second one is of spatial size @math and is used for strengthening the connection between different input feature channels and for reducing the number of parameters. The subpatch filter convolves with the input patch and the resulting network is called a subpatch network. Taking the output of one subpatch network as input, we further repeat constructing subpatch networks until the output contains only one neuron in spatial domain. These subpatch networks form a new network called the cascaded subpatch network (CSNet). The feature layer generated by CSNet is called the csconv layer. For the whole input image, we construct a deep neural network by stacking a sequence of csconv layers. Experimental results on five benchmark data sets demonstrate the effectiveness and compactness of the proposed CSNet. For example, our CSNet reaches a test error of 5.68 on the CIFAR10 data set without model averaging. To the best of our knowledge, this is the best result ever obtained on the CIFAR10 data set. In recent years considerable research efforts have been devoted to compression techniques of convolutional neural networks (CNNs). Many works so far have focused on CNN connection pruning methods which produce sparse parameter tensors in convolutional or fully-connected layers. It has been demonstrated in several studies that even simple methods can effectively eliminate connections of a CNN. However, since these methods make parameter tensors just sparser but no smaller, the compression may not transfer directly to acceleration without support from specially designed hardware. In this paper, we propose an iterative approach named Auto-balanced Filter Pruning, where we pre-train the network in an innovative auto-balanced way to transfer the representational capacity of its convolutional layers to a fraction of the filters, prune the redundant ones, then re-train it to restore the accuracy. In this way, a smaller version of the original network is learned and the floating-point operations (FLOPs) are reduced. By applying this method on several common CNNs, we show that a large portion of the filters can be discarded without obvious accuracy drop, leading to significant reduction of computational burdens. Concretely, we reduce the inference cost of LeNet-5 on MNIST, VGG-16 and ResNet-56 on CIFAR-10 by 95.1 , 79.7 and 60.9 , respectively. Copyright © 2018, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. One of recent trends [31, 32, 14] in network architecture design is stacking small filters (e.g., 1x1 or 3x3) in the entire network because the stacked small filters is more efficient than a large kernel, given the same computational complexity. However, in the field of semantic segmentation, where we need to perform dense per-pixel prediction, we find that the large kernel (and effective receptive field) plays an important role when we have to perform the classification and localization tasks simultaneously. Following our design principle, we propose a Global Convolutional Network to address both the classification and localization issues for the semantic segmentation. We also suggest a residual-based boundary refinement to further refine the object boundaries. Our approach achieves state-of-art performance on two public benchmarks and significantly outperforms previous results, 82.2 (vs 80.2 ) on PASCAL VOC 2012 dataset and 76.9 (vs 71.8 ) on Cityscapes dataset. We propose a new method for creating computationally efficient convolutional neural networks (CNNs) by using low-rank representations of convolutional filters. Rather than approximating filters in previously-trained networks with more efficient versions, we learn a set of small basis filters from scratch; during training, the network learns to combine these basis filters into more complex filters that are discriminative for image classification. To train such networks, a novel weight initialization scheme is used. This allows effective initialization of connection weights in convolutional layers composed of groups of differently-shaped filters. We validate our approach by applying it to several existing CNN architectures and training these networks from scratch using the CIFAR, ILSVRC and MIT Places datasets. Our results show similar or higher accuracy than conventional CNNs with much less compute. Applying our method to an improved version of VGG-11 network using global max-pooling, we achieve comparable validation accuracy using 41 less compute and only 24 of the original VGG-11 model parameters; another variant of our method gives a 1 percentage point increase in accuracy over our improved VGG-11 model, giving a top-5 center-crop validation accuracy of 89.7 while reducing computation by 16 relative to the original VGG-11 model. Applying our method to the GoogLeNet architecture for ILSVRC, we achieved comparable accuracy with 26 less compute and 41 fewer model parameters. Applying our method to a near state-of-the-art network for CIFAR, we achieved comparable accuracy with 46 less compute and 55 fewer parameters. This paper describes a novel approach of packing sparse convolutional neural networks for their efficient systolic array implementations. By combining subsets of columns in the original filter matrix associated with a convolutional layer, we increase the utilization efficiency of the systolic array substantially (e.g., 4x) due to the increased density of nonzeros in the resulting packed filter matrix. In combining columns, for each row, all filter weights but one with the largest magnitude are pruned. We retrain the remaining weights to preserve high accuracy. We demonstrate that in mitigating data privacy concerns the retraining can be accomplished with only fractions of the original dataset (e.g., 10 for CIFAR-10). We study the effectiveness of this joint optimization for both high utilization and classification accuracy with ASIC and FPGA designs based on efficient bit-serial implementations of multiplier-accumulators. We present analysis and empirical evidence on the superior performance of our column combining approach against prior arts under metrics such as energy efficiency (3x) and inference latency (12x). In this paper we propose a novel decomposition method based on filter group approximation, which can significantly reduce the redundancy of deep convolutional neural networks (CNNs) while maintaining the majority of feature representation. Unlike other low-rank decomposition algorithms which operate on spatial or channel dimension of filters, our proposed method mainly focuses on exploiting the filter group structure for each layer. For several commonly used CNN models, including VGG and ResNet, our method can reduce over 80 floating-point operations (FLOPs) with less accuracy drop than state-of-the-art methods on various image classification datasets. Besides, experiments demonstrate that our method is conducive to alleviating degeneracy of the compressed network, which hurts the convergence and performance of the network. We propose an unsupervised method for learning multi-stage hierarchies of sparse convolutional features. While sparse coding has become an increasingly popular method for learning visual features, it is most often trained at the patch level. Applying the resulting filters convolutionally results in highly redundant codes because overlapping patches are encoded in isolation. By training convolutionally over large image windows, our method reduces the redudancy between feature vectors at neighboring locations and improves the efficiency of the overall representation. In addition to a linear decoder that reconstructs the image from sparse features, our method trains an efficient feed-forward encoder that predicts quasi-sparse features from the input. While patch-based training rarely produces anything but oriented edge detectors, we show that convolutional training produces highly diverse filters, including center-surround filters, corner detectors, cross detectors, and oriented grating detectors. We show that using these filters in multistage convolutional network architecture improves performance on a number of visual recognition and detection tasks. Abstract We develop a technique to test the hypothesis that multilayered, feed-forward networks with few units on the first hidden layer generalize better than networks with many units in the first layer. Large networks are trained to perform a classification task and the redundant units are removed (“pruning”) to produce the smallest network capable of performing the task. A technique for inserting layers where pruning has introduced linear inseparability is also described. Two tests of ability to generalize are used—the ability to classify training inputs corrupted by noise and the ability to classify new patterns from each class. The hypothesis is found to be false for networks trained with noisy inputs. Pruning to the minimum number of units in the first layer produces networks which correctly classify the training set but generalize poorly compared with larger networks. In this paper, we consider numerous low-level vision problems (e.g., edge-preserving filtering and denoising) as recursive image filtering via a hybrid neural network. The network contains several spatially variant recurrent neural networks (RNN) as equivalents of a group of distinct recursive filters for each pixel, and a deep convolutional neural network (CNN) that learns the weights of RNNs. The deep CNN can learn regulations of recurrent propagation for various tasks and effectively guides recurrent propagation over an entire image. The proposed model does not need a large number of convolutional channels nor big kernels to learn features for low-level vision filters. It is significantly smaller and faster in comparison with a deep CNN based image filter. Experimental results show that many low-level vision tasks can be effectively learned and carried out in real-time by the proposed algorithm. Two-dimensional spatial linear filters are constrained by general uncertainty relations that limit their attainable information resolution for orientation, spatial frequency, and two-dimensional (2D) spatial position. The theoretical lower limit for the joint entropy, or uncertainty, of these variables is achieved by an optimal 2D filter family whose spatial weighting functions are generated by exponentiated bivariate second-order polynomials with complex coefficients, the elliptic generalization of the one-dimensional elementary functions proposed in Gabor’s famous theory of communication [ J. Inst. Electr. Eng.93, 429 ( 1946)]. The set includes filters with various orientation bandwidths, spatial-frequency bandwidths, and spatial dimensions, favoring the extraction of various kinds of information from an image. Each such filter occupies an irreducible quantal volume (corresponding to an independent datum) in a four-dimensional information hyperspace whose axes are interpretable as 2D visual space, orientation, and spatial frequency, and thus such a filter set could subserve an optimally efficient sampling of these variables. Evidence is presented that the 2D receptive-field profiles of simple cells in mammalian visual cortex are well described by members of this optimal 2D filter family, and thus such visual neurons could be said to optimize the general uncertainty relations for joint 2D-spatial–2D-spectral information resolution. The variety of their receptive-field dimensions and orientation and spatial-frequency bandwidths, and the correlations among these, reveal several underlying constraints, particularly in width length aspect ratio and principal axis organization, suggesting a polar division of labor in occupying the quantal volumes of information hyperspace. Such an ensemble of 2D neural receptive fields in visual cortex could locally embed coarse polar mappings of the orientation–frequency plane piecewise within the global retinotopic mapping of visual space, thus efficiently representing 2D spatial visual information by localized 2D spectral signatures. One of recent trends [30, 31, 14] in network architec- ture design is stacking small filters (e.g., 1x1 or 3x3) in the entire network because the stacked small filters is more ef- ficient than a large kernel, given the same computational complexity. However, in the field of semantic segmenta- tion, where we need to perform dense per-pixel prediction, we find that the large kernel (and effective receptive field) plays an important role when we have to perform the clas- sification and localization tasks simultaneously. Following our design principle, we propose a Global Convolutional Network to address both the classification and localization issues for the semantic segmentation. We also suggest a residual-based boundary refinement to further refine the ob- ject boundaries. Our approach achieves state-of-art perfor- mance on two public benchmarks and significantly outper- forms previous results, 82.2 (vs 80.2 ) on PASCAL VOC 2012 dataset and 76.9 (vs 71.8 ) on Cityscapes dataset. The success of CNNs in various applications is accompanied by a significant increase in the computation and parameter storage costs. Recent efforts toward reducing these overheads involve pruning and compressing the weights of various layers without hurting original accuracy. However, magnitude-based pruning of weights reduces a significant number of parameters from the fully connected layers and may not adequately reduce the computation costs in the convolutional layers due to irregular sparsity in the pruned networks. We present an acceleration method for CNNs, where we prune filters from CNNs that are identified as having a small effect on the output accuracy. By removing whole filters in the network together with their connecting feature maps, the computation costs are reduced significantly. In contrast to pruning weights, this approach does not result in sparse connectivity patterns. Hence, it does not need the support of sparse convolution libraries and can work with existing efficient BLAS libraries for dense matrix multiplications. We show that even simple filter pruning techniques can reduce inference costs for VGG-16 by up to 34 and ResNet-110 by up to 38 on CIFAR10 while regaining close to the original accuracy by retraining the networks. The success of CNNs in various applications is accompanied by a significant increase in the computation and parameter storage costs. Recent efforts toward reducing these overheads involve pruning and compressing the weights of various layers without hurting original accuracy. However, magnitude-based pruning of weights reduces a significant number of parameters from the fully connected layers and may not adequately reduce the computation costs in the convolutional layers due to irregular sparsity in the pruned networks. We present an acceleration method for CNNs, where we prune filters from CNNs that are identified as having a small effect on the output accuracy. By removing whole filters in the network together with their connecting feature maps, the computation costs are reduced significantly. In contrast to pruning weights, this approach does not result in sparse connectivity patterns. Hence, it does not need the support of sparse convolution libraries and can work with existing efficient BLAS libraries for dense matrix multiplications. We show that even simple filter pruning techniques can reduce inference costs for VGG-16 by up to 34 and ResNet-110 by up to 38 on CIFAR10 while regaining close to the original accuracy by retraining the networks. Deep Convolutional Neural Networks (CNNs) offer remarkable performance of classifications and regressions in many high-dimensional problems and have been widely utilized in real-word cognitive applications. However, high computational cost of CNNs greatly hinder their deployment in resource-constrained applications, real-time systems and edge computing platforms. To overcome this challenge, we propose a novel filter-pruning framework, two-phase filter pruning based on conditional entropy, namely , to compress the CNN models and reduce the inference time with marginal performance degradation. In our proposed method, we formulate filter pruning process as an optimization problem and propose a novel filter selection criteria measured by conditional entropy. Based on the assumption that the representation of neurons shall be evenly distributed, we also develop a maximum-entropy filter freeze technique that can reduce over fitting. Two filter pruning strategies -- global and layer-wise strategies, are compared. Our experiment result shows that combining these two strategies can achieve a higher neural network compression ratio than applying only one of them under the same accuracy drop threshold. Two-phase pruning, that is, combining both global and layer-wise strategies, achieves 10 X FLOPs reduction and 46 inference time reduction on VGG-16, with 2 accuracy drop. 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 @math FLOPs reduction and 16.63 @math compression on VGG-16, with only 0.52 @math 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 @math 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. Recently there has been a lot of work on pruning filters from deep convolutional neural networks (CNNs) with the intention of reducing computations. The key idea is to rank the filters based on a certain criterion (say, l1-norm, average percentage of zeros, etc) and retain only the top ranked filters. Once the low scoring filters are pruned away the remainder of the network is fine tuned and is shown to give performance comparable to the original unpruned network. In this work, we report experiments which suggest that the comparable performance of the pruned network is not due to the specific criterion chosen but due to the inherent plasticity of deep neural networks which allows them to recover from the loss of pruned filters once the rest of the filters are fine-tuned. Specifically, we show counter-intuitive results wherein by randomly pruning 25-50 filters from deep CNNs we are able to obtain the same performance as obtained by using state of the art pruning methods. We empirically validate our claims by doing an exhaustive evaluation with VGG-16 and ResNet-50. Further, we also evaluate a real world scenario where a CNN trained on all 1000 ImageNet classes needs to be tested on only a small set of classes at test time (say, only animals). We create a new benchmark dataset from ImageNet to evaluate such class specific pruning and show that even here a random pruning strategy gives close to state of the art performance. Lastly, unlike existing approaches which mainly focus on the task of image classification, in this work we also report results on object detection. We show that using a simple random pruning strategy we can achieve significant speed up in object detection (74 improvement in fps) while retaining the same accuracy as that of the original Faster RCNN model. This paper explores the complexity of deep feedforward networks with linear pre-synaptic couplings and rectified linear activations. This is a contribution to the growing body of work contrasting the representational power of deep and shallow network architectures. In particular, we offer a framework for comparing deep and shallow models that belong to the family of piecewise linear functions based on computational geometry. We look at a deep rectifier multi-layer perceptron (MLP) with linear outputs units and compare it with a single layer version of the model. In the asymptotic regime, when the number of inputs stays constant, if the shallow model has @math hidden units and @math inputs, then the number of linear regions is @math . For a @math layer model with @math hidden units on each layer it is @math . The number @math grows faster than @math when @math tends to infinity or when @math tends to infinity and @math . Additionally, even when @math is small, if we restrict @math to be @math , we can show that a deep model has considerably more linear regions that a shallow one. We consider this as a first step towards understanding the complexity of these models and specifically towards providing suitable mathematical tools for future analysis. In many machine learning tasks it is desirable that a model's prediction transforms in an equivariant way under transformations of its input. Convolutional neural networks (CNNs) implement translational equivariance by construction; for other transformations, however, they are compelled to learn the proper mapping. In this work, we develop Steerable Filter CNNs (SFCNNs) which achieve joint equivariance under translations and rotations by design. The proposed architecture employs steerable filters to efficiently compute orientation dependent responses for many orientations without suffering interpolation artifacts from filter rotation. We utilize group convolutions which guarantee an equivariant mapping. In addition, we generalize He's weight initialization scheme to filters which are defined as a linear combination of a system of atomic filters. Numerical experiments show a substantial enhancement of the sample complexity with a growing number of sampled filter orientations and confirm that the network generalizes learned patterns over orientations. The proposed approach achieves state-of-the-art on the rotated MNIST benchmark and on the ISBI 2012 2D EM segmentation challenge. In a traditional convolutional layer, the learned filters stay fixed after training. In contrast, we introduce a new framework, the Dynamic Filter Network, where filters are generated dynamically conditioned on an input. We show that this architecture is a powerful one, with increased flexibility thanks to its adaptive nature, yet without an excessive increase in the number of model parameters. A wide variety of filtering operations can be learned this way, including local spatial transformations, but also others like selective (de)blurring or adaptive feature extraction. Moreover, multiple such layers can be combined, e.g. in a recurrent architecture. We demonstrate the effectiveness of the dynamic filter network on the tasks of video and stereo prediction, and reach state-of-the-art performance on the moving MNIST dataset with a much smaller model. By visualizing the learned filters, we illustrate that the network has picked up flow information by only looking at unlabelled training data. This suggests that the network can be used to pretrain networks for various supervised tasks in an unsupervised way, like optical flow and depth estimation. In a traditional convolutional layer, the learned filters stay fixed after training. In contrast, we introduce a new framework, the Dynamic Filter Network, where filters are generated dynamically conditioned on an input. We show that this architecture is a powerful one, with increased flexibility thanks to its adaptive nature, yet without an excessive increase in the number of model parameters. A wide variety of filtering operations can be learned this way, including local spatial transformations, but also others like selective (de)blurring or adaptive feature extraction. Moreover, multiple such layers can be combined, e.g. in a recurrent architecture. We demonstrate the effectiveness of the dynamic filter network on the tasks of video and stereo prediction, and reach state-of-the-art performance on the moving MNIST dataset with a much smaller model. By visualizing the learned filters, we illustrate that the network has picked up flow information by only looking at unlabelled training data. This suggests that the network can be used to pretrain networks for various supervised tasks in an unsupervised way, like optical flow and depth estimation.