Previous works utilized ''smaller-norm-less-important'' criterion to prune filters with smaller norm values in a convolutional neural network. In this paper, we analyze this norm-based criterion and point out that its effectiveness depends on two requirements that are not always met: (1) the norm deviation of the filters should be large; (2) the minimum norm of the filters should be small. To solve this problem, we propose a novel filter pruning method, namely Filter Pruning via Geometric Median (FPGM), to compress the model regardless of those two requirements. Unlike previous methods, FPGM compresses CNN models by pruning filters with redundancy, rather than those with ''relatively less'' importance. When applied to two image classification benchmarks, our method validates its usefulness and strengths. Notably, on CIFAR-10, FPGM reduces more than 52 FLOPs on ResNet-110 with even 2.69 relative accuracy improvement. Moreover, on ILSVRC-2012, FPGM reduces more than 42 FLOPs on ResNet-101 without top-5 accuracy drop, which has advanced the state-of-the-art. Code is publicly available on GitHub: this https URL
Most previous works on accelerating CNNs can be roughly divided into three categories, namely, @cite_1 @cite_2 , @cite_20 @cite_32 , and . -based approaches aim to remove the unnecessary connections of the neural network @cite_8 @cite_17 . Essentially, always results in unstructured models, which makes it hard to deploy the existing efficient BLAS library, while not only reduces the storage usage on devices but also decreases computation cost to accelerate the inference. We could roughly divide the filter pruning methods into two categories by whether the training data is utilized to determine the pruned filters, that is, and filter pruning. Data independent method is more efficient than data dependent method as the ultimating of training data is computation consuming.
@cite_8 @cite_1 @cite_32 @cite_2 @cite_20 @cite_17
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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. 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. Convolutional neural networks (CNNs) have state-of-the-art performance on many problems in machine vision. However, networks with superior performance often have millions of weights so that it is difficult or impossible to use CNNs on computationally limited devices or to humanly interpret them. A myriad of CNN compression approaches have been proposed and they involve pruning and compressing the weights and filters. In this article, we introduce a greedy structural compression scheme that prunes filters in a trained CNN. We define a filter importance index equal to the classification accuracy reduction (CAR) of the network after pruning that filter (similarly defined as RAR for regression). We then iteratively prune filters based on the CAR index. This algorithm achieves substantially higher classification accuracy in AlexNet compared to other structural compression schemes that prune filters. Pruning half of the filters in the first or second layer of AlexNet, our CAR algorithm achieves 26 and 20 higher classification accuracies respectively, compared to the best benchmark filter pruning scheme. Our CAR algorithm, combined with further weight pruning and compressing, reduces the size of first or second convolutional layer in AlexNet by a factor of 42, while achieving close to original classification accuracy through retraining (or fine-tuning) network. Finally, we demonstrate the interpretability of CAR-compressed CNNs by showing that our algorithm prunes filters with visually redundant functionalities. In fact, out of top 20 CAR-pruned filters in AlexNet, 17 of them in the first layer and 14 of them in the second layer are color-selective filters as opposed to shape-selective filters. To our knowledge, this is the first reported result on the connection between compression and interpretability of CNNs. 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 aims to simultaneously accelerate and compress off-the-shelf CNN models via filter pruning strategy. The importance of each filter is evaluated by the proposed entropy-based method first. Then several unimportant filters are discarded to get a smaller CNN model. Finally, fine-tuning is adopted to recover its generalization ability which is damaged during filter pruning. Our method can reduce the size of intermediate activations, which would dominate most memory footprint during model training stage but is less concerned in previous compression methods. Experiments on the ILSVRC-12 benchmark demonstrate the effectiveness of our method. Compared with previous filter importance evaluation criteria, our entropy-based method obtains better performance. We achieve 3.3x speed-up and 16.64x compression on VGG-16, 1.54x acceleration and 1.47x compression on ResNet-50, both with about 1 top-5 accuracy decrease. Convolutional Neural Network (CNN) image classifiers are traditionally designed to have sequential convolutional layers with a single output layer. This is based on the assumption that all target classes should be treated equally and exclusively. However, some classes can be more difficult to distinguish than others, and classes may be organized in a hierarchy of categories. At the same time, a CNN is designed to learn internal representations that abstract from the input data based on its hierarchical layered structure. So it is natural to ask if an inverse of this idea can be applied to learn a model that can predict over a classification hierarchy using multiple output layers in decreasing order of class abstraction. In this paper, we introduce a variant of the traditional CNN model named the Branch Convolutional Neural Network (B-CNN). A B-CNN model outputs multiple predictions ordered from coarse to fine along the concatenated convolutional layers corresponding to the hierarchical structure of the target classes, which can be regarded as a form of prior knowledge on the output. To learn with B-CNNs a novel training strategy, named the Branch Training strategy (BT-strategy), is introduced which balances the strictness of the prior with the freedom to adjust parameters on the output layers to minimize the loss. In this way we show that CNN based models can be forced to learn successively coarse to fine concepts in the internal layers at the output stage, and that hierarchical prior knowledge can be adopted to boost CNN models' classification performance. Our models are evaluated to show that the B-CNN extensions improve over the corresponding baseline CNN on the benchmark datasets MNIST, CIFAR-10 and CIFAR-100. While the research on convolutional neural networks (CNNs) is progressing quickly, the real-world deployment of these models is often limited by computing resources and memory constraints. In this paper, we address this issue by proposing a novel filter pruning method to compress and accelerate CNNs. Our work is based on the linear relationship identified in different feature map subspaces via visualization of feature maps. Such linear relationship implies that the information in CNNs is redundant. Our method eliminates the redundancy in convolutional filters by applying subspace clustering to feature maps. In this way, most of the representative information in the network can be retained in each cluster. Therefore, our method provides an effective solution to filter pruning for which most existing methods directly remove filters based on simple heuristics. The proposed method is independent of the network structure, thus it can be adopted by any off-the-shelf deep learning libraries. Experiments on different networks and tasks show that our method outperforms existing techniques before fine-tuning, and achieves the state-of-the-art results after fine-tuning. 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. Network pruning is an effective way to accelerate Convolutional Neural Networks (CNNs). In recent years, structured pruning methods are proposed in favor of unstructured methods as they have shown greater speedup in practical use. Existing structured methods does pruning along two main dimensions: 3D-filter wise, i.e., remove a 3D-fllter as a whole, and filter-shape wise, i.e., remove a same position from all 3D-filters. In this work, we propose a new group-wise 2D-fllter pruning approach that is orthogonal and complementary to the existing methods. The proposed approach removes a portion of 2D-fllters from each 3D-filter according to the pruning patterns learned from the data, and leads to compressed models that do not require sophisticated implementation of convolution operations. A fine-tuning process is followed to recover the accuracy. The knowledge distillation (KD) framework is explored in the fine-tuning process to improve the performance. We present our method for learning the pruning pattens as well as the fine-tuning strategy based on knowledge distillation. The proposed approach is validated on two representative CNN models — ZF and VGG16, pre-trained on ILSVRC12. Experimental results demonstrate the effectiveness of our approach. In VGG16, we get even higher accuracy after speeding-up the network by 4 times. We introduce a model-based image reconstruction framework with a convolution neural network (CNN) based regularization prior. The proposed formulation provides a systematic approach for deriving deep architectures for inverse problems with the arbitrary structure. Since the forward model is explicitly accounted for, a smaller network with fewer parameters is sufficient to capture the image information compared to black-box deep learning approaches, thus reducing the demand for training data and training time. Since we rely on end-to-end training, the CNN weights are customized to the forward model, thus offering improved performance over approaches that rely on pre-trained denoisers. The main difference of the framework from existing end-to-end training strategies is the sharing of the network weights across iterations and channels. Our experiments show that the decoupling of the number of iterations from the network complexity offered by this approach provides benefits including lower demand for training data, reduced risk of overfitting, and implementations with significantly reduced memory footprint. We propose to enforce data-consistency by using numerical optimization blocks such as conjugate gradients algorithm within the network; this approach offers faster convergence per iteration, compared to methods that rely on proximal gradients steps to enforce data consistency. Our experiments show that the faster convergence translates to improved performance, especially when the available GPU memory restricts the number of iterations. Accelerating Convolutional Neural Networks (CNNs) on GPUs usually involves two stages: training and inference. Traditionally, this two-stage process is deployed on high-end GPU-equipped servers. Driven by the increase in compute power of desktop and mobile GPUs, there is growing interest in performing inference on various kinds of platforms. In contrast to the requirements of high throughput and accuracy during the training stage, end-users will face diverse requirements related to inference tasks. To address this emerging trend and new requirements, we propose Pervasive CNN (P-CNN), a user satisfaction-aware CNN inference framework. P-CNN is composed of two phases: cross-platform offline compilation and run-time management. Based on users' requirements, offline compilation generates the optimal kernel using architecture-independent techniques, such as adaptive batch size selection and coordinated fine-tuning. The runtime management phase consists of accuracy tuning, execution, and calibration. First, accuracy tuning dynamically identifies the fastest kernels with acceptable accuracy. Next, the run-time kernel scheduler partitions the optimal computing resource for each layer and schedules the GPU thread blocks. If its accuracy is not acceptable to the end-user, the calibration stage selects a slower but more precise kernel to improve the accuracy. Finally, we design a user satisfaction metric for CNNs to evaluate ourPervasive deign. Our evaluation results show P-CNN can provide the best user satisfaction for different inference tasks. Deep Convolutional Neural Networks (CNNs) perform billions of operations for classifying a single input. To reduce these computations, this paper offers a solution that leverages a combination of runtime information and the algorithmic structure of CNNs. Specifically, in numerous modern CNNs, the outputs of compute-heavy convolution operations are fed to activation units that output zero if their input is negative. By exploiting this unique algorithmic property, we propose a predictive early activation technique, dubbed SnaPEA. This technique cuts the computation of convolution operations short if it determines that the output will be negative. SnaPEA can operate in two distinct modes, exact and predictive. In the exact mode, with no loss in classification accuracy, SnaPEA statically re-orders the weights based on their signs and periodically performs a single-bit sign check on the partial sum. Once the partial sum drops below zero, the rest of computations can simply be ignored, since the output value will be zero in any case. In the predictive mode, which trades the classification accuracy for larger savings, SnaPEA speculatively cuts the computation short even earlier than the exact mode. To control the accuracy, we develop a multi-variable optimization algorithm that thresholds the degree of speculation. As such, the proposed algorithm exposes a knob to gracefully navigate the trade-offs between the classification accuracy and computation reduction. Compared to a state-of-the-art CNN accelerator, SnaPEA in the exact mode, yields, on average, 28 speedup and 16 energy reduction in various modern CNNs without affecting their classification accuracy. With 3 loss in classification accuracy, on average, 67.8 of the convolutional layers can operate in the predictive mode. The average speedup and energy saving of these layers are 2.02x and 1.89x, respectively. The benefits grow to a maximum of 3.59x speedup and 3.14x energy reduction. Compared to static pruning approaches, which are complimentary to the dynamic approach of SnaPEA, our proposed technique offers up to 63 speedup and 49 energy reduction across the convolution layers with no loss in classification accuracy. Deep learning methods such as convolutional neural networks (CNNs) can deliver highly accurate classification results when provided with large enough data sets and respective labels. However, using CNNs along with limited labeled data can be problematic, as this leads to extensive overfitting. In this letter, we propose a novel method by considering a pretrained CNN designed for tackling an entirely different classification problem, namely, the ImageNet challenge, and exploit it to extract an initial set of representations. The derived representations are then transferred into a supervised CNN classifier, along with their class labels, effectively training the system. Through this two-stage framework, we successfully deal with the limited-data problem in an end-to-end processing scheme. Comparative results over the UC Merced Land Use benchmark prove that our method significantly outperforms the previously best stated results, improving the overall accuracy from 83.1 up to 92.4 . Apart from statistical improvements, our method introduces a novel feature fusion algorithm that effectively tackles the large data dimensionality by using a simple and computationally efficient approach. Convolutional neural networks (CNNs) have achieved great success on grid-like data such as images, but face tremendous challenges in learning from more generic data such as graphs. In CNNs, the trainable local filters enable the automatic extraction of high-level features. The computation with filters requires a fixed number of ordered units in the receptive fields. However, the number of neighboring units is neither fixed nor are they ordered in generic graphs, thereby hindering the applications of convolutional operations. Here, we address these challenges by proposing the learnable graph convolutional layer (LGCL). LGCL automatically selects a fixed number of neighboring nodes for each feature based on value ranking in order to transform graph data into grid-like structures in 1-D format, thereby enabling the use of regular convolutional operations on generic graphs. To enable model training on large-scale graphs, we propose a sub-graph training method to reduce the excessive memory and computational resource requirements suffered by prior methods on graph convolutions. Our experimental results on node classification tasks in both transductive and inductive learning settings demonstrate that our methods can achieve consistently better performance on the Cora, Citeseer, Pubmed citation network, and protein-protein interaction network datasets. Our results also indicate that the proposed methods using sub-graph training strategy are more efficient as compared to prior approaches. Recently, neuron activations extracted from a pre-trained convolutional neural network (CNN) show promising performance in various visual tasks. However, due to the domain and task bias, using the features generated from the model pre-trained for image classification as image representations for instance retrieval is problematic. In this paper, we propose quartet-net learning to improve the discriminative power of CNN features for instance retrieval. The general idea is to map the features into a space where the image similarity can be better evaluated. Our network differs from the traditional Siamese-net in two ways. First, we adopt a double-margin contrastive loss with a dynamic margin tuning strategy to train the network which leads to more robust performance. Second, we introduce in the mimic learning regularization to improve the generalization ability of the network by preventing it from overfitting to the training data. Catering for the network learning, we collect a large-scale dataset, namely GeoPair, which consists of 68k matching image pairs and 63k non-matching pairs. Experiments on several standard instance retrieval datasets demonstrate the effectiveness of our method. In this work, we investigate the use of sparsity-inducing regularizers during training of Convolution Neural Networks (CNNs). These regularizers encourage that fewer connections in the convolution and fully connected layers take non-zero values and in effect result in sparse connectivity between hidden units in the deep network. This in turn reduces the memory and runtime cost involved in deploying the learned CNNs. We show that training with such regularization can still be performed using stochastic gradient descent implying that it can be used easily in existing codebases. Experimental evaluation of our approach on MNIST, CIFAR, and ImageNet datasets shows that our regularizers can result in dramatic reductions in memory requirements. For instance, when applied on AlexNet, our method can reduce the memory consumption by a factor of four with minimal loss in accuracy. Convolutional neural networks (CNN) have achieved impressive performance on the wide variety of tasks (classification, detection, etc.) across multiple domains at the cost of high computational and memory requirements. Thus, leveraging CNNs for real-time applications necessitates model compression approaches that not only reduce the total number of parameters but reduce the overall computation as well. In this work, we present a stability-based approach for filter-level pruning of CNNs. We evaluate our proposed approach on different architectures (LeNet, VGG-16, ResNet, and Faster RCNN) and datasets and demonstrate its generalizability through extensive experiments. Moreover, our compressed models can be used at run-time without requiring any special libraries or hardware. Our model compression method reduces the number of FLOPS by an impressive factor of 6.03X and GPU memory footprint by more than 17X, significantly outperforming other state-of-the-art filter pruning methods. Recent years have witnessed the great success of convolutional neural networks (CNNs) in many related fields. However, its huge model size and computation complexity bring in difficulty when deploying CNNs in some scenarios, like embedded system with low computation power. To address this issue, many works have been proposed to prune filters in CNNs to reduce computation. However, they mainly focus on seeking which filters are unimportant in a layer and then prune filters layer by layer or globally. In this paper, we argue that the pruning order is also very significant for model pruning. We propose a novel approach to figure out which layers should be pruned in each step. First, we utilize a long short-term memory (LSTM) to learn the hierarchical characteristics of a network and generate a pruning decision for each layer, which is the main difference from previous works. Next, a channel-based method is adopted to evaluate the importance of filters in a to-be-pruned layer, followed by an accelerated recovery step. Experimental results demonstrate that our approach is capable of reducing 70.1 FLOPs for VGG and 47.5 for Resnet-56 with comparable accuracy. Also, the learning results seem to reveal the sensitivity of each network layer. The deployment of deep convolutional neural networks (CNNs) in many real world applications is largely hindered by their high computational cost. In this paper, we propose a novel learning scheme for CNNs to simultaneously 1) reduce the model size; 2) decrease the run-time memory footprint; and 3) lower the number of computing operations, without compromising accuracy. This is achieved by enforcing channel-level sparsity in the network in a simple but effective way. Different from many existing approaches, the proposed method directly applies to modern CNN architectures, introduces minimum overhead to the training process, and requires no special software hardware accelerators for the resulting models. We call our approach network slimming, which takes wide and large networks as input models, but during training insignificant channels are automatically identified and pruned afterwards, yielding thin and compact models with comparable accuracy. We empirically demonstrate the effectiveness of our approach with several state-of-the-art CNN models, including VGGNet, ResNet and DenseNet, on various image classification datasets. For VGGNet, a multi-pass version of network slimming gives a 20x reduction in model size and a 5x reduction in computing operations.