Deep neural networks (DNNs) although achieving human-level performance in many domains, have very large model size that hinders their broader applications on edge computing devices. Extensive research work have been conducted on DNN model compression or pruning. However, most of the previous work took heuristic approaches. This work proposes a progressive weight pruning approach based on ADMM (Alternating Direction Method of Multipliers), a powerful technique to deal with non-convex optimization problems with potentially combinatorial constraints. Motivated by dynamic programming, the proposed method reaches extremely high pruning rate by using partial prunings with moderate pruning rates. Therefore, it resolves the accuracy degradation and long convergence time problems when pursuing extremely high pruning ratios. It achieves up to 34 times pruning rate for ImageNet dataset and 167 times pruning rate for MNIST dataset, significantly higher than those reached by the literature work. Under the same number of epochs, the proposed method also achieves faster convergence and higher compression rates. The codes and pruned DNN models are released in the link bit.ly/2zxdlss
The enormous size of modern deep neural networks makes it challenging to deploy those models in memory and communication limited scenarios. Thus, compressing a trained model without a significant loss in performance has become an increasingly important task. Tremendous advances has been made recently, where the main technical building blocks are parameter pruning, parameter sharing (quantization), and low-rank factorization. In this paper, we propose principled approaches to improve upon the common heuristics used in those building blocks, namely pruning and quantization. We first study the fundamental limit for model compression via the rate distortion theory. We bring the rate distortion function from data compression to model compression to quantify this fundamental limit. We prove a lower bound for the rate distortion function and prove its achievability for linear models. Although this achievable compression scheme is intractable in practice, this analysis motivates a novel model compression framework. This framework provides a new objective function in model compression, which can be applied together with other classes of model compressor such as pruning or quantization. Theoretically, we prove that the proposed scheme is optimal for compressing one-hidden-layer ReLU neural networks. Empirically, we show that the proposed scheme improves upon the baseline in the compression-accuracy tradeoff.
Making deep convolutional neural networks more accurate typically comes at the cost of increased computational and memory resources. In this paper, we reduce this cost by exploiting the fact that the importance of features computed by convolutional layers is highly input-dependent, and propose feature boosting and suppression (FBS), a new method to predictively amplify salient convolutional channels and skip unimportant ones at run-time. FBS introduces small auxiliary connections to existing convolutional layers. In contrast to channel pruning methods which permanently remove channels, it preserves the full network structures and accelerates convolution by dynamically skipping unimportant input and output channels. FBS-augmented networks are trained with conventional stochastic gradient descent, making it readily available for many state-of-the-art CNNs. We compare FBS to a range of existing channel pruning and dynamic execution schemes and demonstrate large improvements on ImageNet classification. Experiments show that FBS can respectively provide $5\times$ and $2\times$ savings in compute on VGG-16 and ResNet-18, both with less than $0.6\%$ top-5 accuracy loss.
Knowledge distillation (KD) is a popular method for reducing the computational overhead of deep network inference, in which the output of a teacher model is used to train a smaller, faster student model. Hint training (i.e., FitNets) extends KD by regressing a student model's intermediate representation to a teacher model's intermediate representation. In this work, we introduce bLock-wise Intermediate representation Training (LIT), a novel model compression technique that extends the use of intermediate representations in deep network compression, outperforming KD and hint training. LIT has two key ideas: 1) LIT trains a student of the same width (but shallower depth) as the teacher by directly comparing the intermediate representations, and 2) LIT uses the intermediate representation from the previous block in the teacher model as an input to the current student block during training, avoiding unstable intermediate representations in the student network. We show that LIT provides substantial reductions in network depth without loss in accuracy -- for example, LIT can compress a ResNeXt-110 to a ResNeXt-20 (5.5x) on CIFAR10 and a VDCNN-29 to a VDCNN-9 (3.2x) on Amazon Reviews without loss in accuracy, outperforming KD and hint training in network size for a given accuracy. We also show that applying LIT to identical student/teacher architectures increases the accuracy of the student model above the teacher model, outperforming the recently-proposed Born Again Networks procedure on ResNet, ResNeXt, and VDCNN. Finally, we show that LIT can effectively compress GAN generators, which are not supported in the KD framework because GANs output pixels as opposed to probabilities.
Compression techniques for deep neural network models are becoming very important for the efficient execution of high-performance deep learning systems on edge-computing devices. The concept of model compression is also important for analyzing the generalization error of deep learning, known as the compression-based error bound. However, there is still huge gap between a practically effective compression method and its rigorous background of statistical learning theory. To resolve this issue, we develop a new theoretical framework for model compression and propose a new pruning method called {\it spectral pruning} based on this framework. We define the ``degrees of freedom'' to quantify the intrinsic dimensionality of a model by using the eigenvalue distribution of the covariance matrix across the internal nodes and show that the compression ability is essentially controlled by this quantity. Moreover, we present a sharp generalization error bound of the compressed model and characterize the bias--variance tradeoff induced by the compression procedure. We apply our method to several datasets to justify our theoretical analyses and show the superiority of the the proposed method.
Spectral mixture (SM) kernels comprise a powerful class of generalized kernels for Gaussian processes (GPs) to describe complex patterns. This paper introduces model compression and time- and phase (TP) modulated dependency structures to the original (SM) kernel for improved generalization of GPs. Specifically, by adopting Bienaym\'es identity, we generalize the dependency structure through cross-covariance between the SM components. Then, we propose a novel SM kernel with a dependency structure (SMD) by using cross-convolution between the SM components. Furthermore, we ameliorate the expressiveness of the dependency structure by parameterizing it with time and phase delays. The dependency structure has clear interpretations in terms of spectral density, covariance behavior, and sampling path. To enrich the SMD with effective hyperparameter initialization, compressible SM kernel components, and sparse dependency structures, we introduce a novel structure adaptation (SA) algorithm in the end. A thorough comparative analysis of the SMD on both synthetic and real-life applications corroborates its efficacy.
Deep neural networks have achieved increasingly accurate results on a wide variety of complex tasks. However, much of this improvement is due to the growing use and availability of computational resources (e.g use of GPUs, more layers, more parameters, etc). Most state-of-the-art deep networks, despite performing well, over-parameterize approximate functions and take a significant amount of time to train. With increased focus on deploying deep neural networks on resource constrained devices like smart phones, there has been a push to evaluate why these models are so resource hungry and how they can be made more efficient. This work evaluates and compares three distinct methods for deep model compression and acceleration: weight pruning, low rank factorization, and knowledge distillation. Comparisons on VGG nets trained on CIFAR10 show that each of the models on their own are effective, but that the true power lies in combining them. We show that by combining pruning and knowledge distillation methods we can create a compressed network 85 times smaller than the original, all while retaining 96% of the original model's accuracy.
Weight pruning methods of DNNs have been demonstrated to achieve a good model pruning rate without loss of accuracy, thereby alleviating the significant computation/storage requirements of large-scale DNNs. Structured weight pruning methods have been proposed to overcome the limitation of irregular network structure and demonstrated actual GPU acceleration. However, in prior work the pruning rate (degree of sparsity) and GPU acceleration are limited (to less than 50%) when accuracy needs to be maintained. In this work,we overcome these limitations by proposing a unified, systematic framework of structured weight pruning for DNNs. It is a framework that can be used to induce different types of structured sparsity, such as filter-wise, channel-wise, and shape-wise sparsity, as well non-structured sparsity. The proposed framework incorporates stochastic gradient descent with ADMM, and can be understood as a dynamic regularization method in which the regularization target is analytically updated in each iteration. Without loss of accuracy on the AlexNet model, we achieve 2.58X and 3.65X average measured speedup on two GPUs, clearly outperforming the prior work. The average speedups reach 3.15X and 8.52X when allowing a moderate ac-curacy loss of 2%. In this case the model compression for convolutional layers is 15.0X, corresponding to 11.93X measured CPU speedup. Our experiments on ResNet model and on other data sets like UCF101 and CIFAR-10 demonstrate the consistently higher performance of our framework.
Deep neural networks (DNNs) have achieved significant success in a variety of real world applications, i.e., image classification. However, tons of parameters in the networks restrict the efficiency of neural networks due to the large model size and the intensive computation. To address this issue, various approximation techniques have been investigated, which seek for a light weighted network with little performance degradation in exchange of smaller model size or faster inference. Both low-rankness and sparsity are appealing properties for the network approximation. In this paper we propose a unified framework to compress the convolutional neural networks (CNNs) by combining these two properties, while taking the nonlinear activation into consideration. Each layer in the network is approximated by the sum of a structured sparse component and a low-rank component, which is formulated as an optimization problem. Then, an extended version of alternating direction method of multipliers (ADMM) with guaranteed convergence is presented to solve the relaxed optimization problem. Experiments are carried out on VGG-16, AlexNet and GoogLeNet with large image classification datasets. The results outperform previous work in terms of accuracy degradation, compression rate and speedup ratio. The proposed method is able to remarkably compress the model (with up to 4.9x reduction of parameters) at a cost of little loss or without loss on accuracy.
Deep convolution neural network has achieved great success in many artificial intelligence applications. However, its enormous model size and massive computation cost have become the main obstacle for deployment of such powerful algorithm in the low power and resource-limited embedded systems. As the countermeasure to this problem, in this work, we propose statistical weight scaling and residual expansion methods to reduce the bit-width of the whole network weight parameters to ternary values (i.e. -1, 0, +1), with the objectives to greatly reduce model size, computation cost and accuracy degradation caused by the model compression. With about 16x model compression rate, our ternarized ResNet-32/44/56 could outperform full-precision counterparts by 0.12%, 0.24% and 0.18% on CIFAR- 10 dataset. We also test our ternarization method with AlexNet and ResNet-18 on ImageNet dataset, which both achieve the best top-1 accuracy compared to recent similar works, with the same 16x compression rate. If further incorporating our residual expansion method, compared to the full-precision counterpart, our ternarized ResNet-18 even improves the top-5 accuracy by 0.61% and merely degrades the top-1 accuracy only by 0.42% for the ImageNet dataset, with 8x model compression rate. It outperforms the recent ABC-Net by 1.03% in top-1 accuracy and 1.78% in top-5 accuracy, with around 1.25x higher compression rate and more than 6x computation reduction due to the weight sparsity.
In this paper we investigate statistical model compression applied to natural language understanding (NLU) models. Small-footprint NLU models are important for enabling offline systems on hardware restricted devices, and for decreasing on-demand model loading latency in cloud-based systems. To compress NLU models, we present two main techniques, parameter quantization and perfect feature hashing. These techniques are complementary to existing model pruning strategies such as L1 regularization. We performed experiments on a large scale NLU system. The results show that our approach achieves 14-fold reduction in memory usage compared to the original models with minimal predictive performance impact.
Deep neural networks (DNNs) have been proven to have many redundancies. Hence, many efforts have been made to compress DNNs. However, the existing model compression methods treat all the input samples equally while ignoring the fact that the difficulties of various input samples being correctly classified are different. To address this problem, DNNs with adaptive dropping mechanism are well explored in this work. To inform the DNNs how difficult the input samples can be classified, a guideline that contains the information of input samples is introduced to improve the performance. Based on the developed guideline and adaptive dropping mechanism, an innovative soft-guided adaptively-dropped (SGAD) neural network is proposed in this paper. Compared with the 32 layers residual neural networks, the presented SGAD can reduce the FLOPs by 77% with less than 1% drop in accuracy on CIFAR-10.
Model compression is essential for serving large deep neural nets on devices with limited resources or applications that require real-time responses. As a case study, a state-of-the-art neural language model usually consists of one or more recurrent layers sandwiched between an embedding layer used for representing input tokens and a softmax layer for generating output tokens. For problems with a very large vocabulary size, the embedding and the softmax matrices can account for more than half of the model size. For instance, the bigLSTM model achieves state-of- the-art performance on the One-Billion-Word (OBW) dataset with around 800k vocabulary, and its word embedding and softmax matrices use more than 6GBytes space, and are responsible for over 90% of the model parameters. In this paper, we propose GroupReduce, a novel compression method for neural language models, based on vocabulary-partition (block) based low-rank matrix approximation and the inherent frequency distribution of tokens (the power-law distribution of words). The experimental results show our method can significantly outperform traditional compression methods such as low-rank approximation and pruning. On the OBW dataset, our method achieved 6.6 times compression rate for the embedding and softmax matrices, and when combined with quantization, our method can achieve 26 times compression rate, which translates to a factor of 12.8 times compression for the entire model with very little degradation in perplexity.
The focus of this paper is speeding up the evaluation of convolutional neural networks. While delivering impressive results across a range of computer vision and machine learning tasks, these networks are computationally demanding, limiting their deployability. Convolutional layers generally consume the bulk of the processing time, and so in this work we present two simple schemes for drastically speeding up these layers. This is achieved by exploiting cross-channel or filter redundancy to construct a low rank basis of filters that are rank-1 in the spatial domain. Our methods are architecture agnostic, and can be easily applied to existing CPU and GPU convolutional frameworks for tuneable speedup performance. We demonstrate this with a real world network designed for scene text character recognition, showing a possible 2.5x speedup with no loss in accuracy, and 4.5x speedup with less than 1% drop in accuracy, still achieving state-of-the-art on standard benchmarks.
In order to achieve high efficiency of classification in intrusion detection, a compressed model is proposed in this paper which combines horizontal compression with vertical compression. OneR is utilized as horizontal com-pression for attribute reduction, and affinity propagation is employed as vertical compression to select small representative exemplars from large training data. As to be able to computationally compress the larger volume of training data with scalability, MapReduce based parallelization approach is then implemented and evaluated for each step of the model compression process abovementioned, on which common but efficient classification methods can be directly used. Experimental application study on two publicly available datasets of intrusion detection, KDD99 and CMDC2012, demonstrates that the classification using the compressed model proposed can effectively speed up the detection procedure at up to 184 times, most importantly at the cost of a minimal accuracy difference with less than 1% on average.
Recently, multilayer bootstrap network (MBN) has demonstrated promising performance in unsupervised dimensionality reduction. It can learn compact representations in standard data sets, i.e. MNIST and RCV1. However, as a bootstrap method, the prediction complexity of MBN is high. In this paper, we propose an unsupervised model compression framework for this general problem of unsupervised bootstrap methods. The framework compresses a large unsupervised bootstrap model into a small model by taking the bootstrap model and its application together as a black box and learning a mapping function from the input of the bootstrap model to the output of the application by a supervised learner. To specialize the framework, we propose a new technique, named compressive MBN. It takes MBN as the unsupervised bootstrap model and deep neural network (DNN) as the supervised learner. Our initial result on MNIST showed that compressive MBN not only maintains the high prediction accuracy of MBN but also is over thousands of times faster than MBN at the prediction stage. Our result suggests that the new technique integrates the effectiveness of MBN on unsupervised learning and the effectiveness and efficiency of DNN on supervised learning together for the effectiveness and efficiency of compressive MBN on unsupervised learning.
Corrupting the input and hidden layers of deep neural networks (DNNs) with multiplicative noise, often drawn from the Bernoulli distribution (or 'dropout'), provides regularization that has significantly contributed to deep learning's success. However, understanding how multiplicative corruptions prevent overfitting has been difficult due to the complexity of a DNN's functional form. In this paper, we show that when a Gaussian prior is placed on a DNN's weights, applying multiplicative noise induces a Gaussian scale mixture, which can be reparameterized to circumvent the problematic likelihood function. Analysis can then proceed by using a type-II maximum likelihood procedure to derive a closed-form expression revealing how regularization evolves as a function of the network's weights. Results show that multiplicative noise forces weights to become either sparse or invariant to rescaling. We find our analysis has implications for model compression as it naturally reveals a weight pruning rule that starkly contrasts with the commonly used signal-to-noise ratio (SNR). While the SNR prunes weights with large variances, seeing them as noisy, our approach recognizes their robustness and retains them. We empirically demonstrate our approach has a strong advantage over the SNR heuristic and is competitive to retraining with soft targets produced from a teacher model.
Augmented reality (AR) displays become more and more popular recently, because of its high intuitiveness for humans and high-quality head-mounted display have rapidly developed. To achieve such displays with augmented information, highly accurate image registration or ego-positioning are required, but little attention have been paid for out-door environments. This paper presents a method for ego-positioning in outdoor environments with low cost monocular cameras. To reduce the computational and memory requirements as well as the communication overheads, we formulate the model compression algorithm as a weighted k-cover problem for better preserving model structures. Specifically for real-world vision-based positioning applications, we consider the issues with large scene change and propose a model update algorithm to tackle these problems. A long- term positioning dataset with more than one month, 106 sessions, and 14,275 images is constructed. Based on both local and up-to-date models constructed in our approach, extensive experimental results show that high positioning accuracy (mean ~ 30.9cm, stdev. ~ 15.4cm) can be achieved, which outperforms existing vision-based algorithms.
As font is one of the core design concepts, automatic font identification and similar font suggestion from an image or photo has been on the wish list of many designers. We study the Visual Font Recognition (VFR) problem, and advance the state-of-the-art remarkably by developing the DeepFont system. First of all, we build up the first available large-scale VFR dataset, named AdobeVFR, consisting of both labeled synthetic data and partially labeled real-world data. Next, to combat the domain mismatch between available training and testing data, we introduce a Convolutional Neural Network (CNN) decomposition approach, using a domain adaptation technique based on a Stacked Convolutional Auto-Encoder (SCAE) that exploits a large corpus of unlabeled real-world text images combined with synthetic data preprocessed in a specific way. Moreover, we study a novel learning-based model compression approach, in order to reduce the DeepFont model size without sacrificing its performance. The DeepFont system achieves an accuracy of higher than 80% (top-5) on our collected dataset, and also produces a good font similarity measure for font selection and suggestion. We also achieve around 6 times compression of the model without any visible loss of recognition accuracy.
Top-performing machine learning systems, such as deep neural networks, large ensembles and complex probabilistic graphical models, can be expensive to store, slow to evaluate and hard to integrate into larger systems. Ideally, we would like to replace such cumbersome models with simpler models that perform equally well. In this thesis, we study knowledge distillation, the idea of extracting the knowledge contained in a complex model and injecting it into a more convenient model. We present a general framework for knowledge distillation, whereby a convenient model of our choosing learns how to mimic a complex model, by observing the latter's behaviour and being penalized whenever it fails to reproduce it. We develop our framework within the context of three distinct machine learning applications: (a) model compression, where we compress large discriminative models, such as ensembles of neural networks, into models of much smaller size; (b) compact predictive distributions for Bayesian inference, where we distil large bags of MCMC samples into compact predictive distributions in closed form; (c) intractable generative models, where we distil unnormalizable models such as RBMs into tractable models such as NADEs. We contribute to the state of the art with novel techniques and ideas. In model compression, we describe and implement derivative matching, which allows for better distillation when data is scarce. In compact predictive distributions, we introduce online distillation, which allows for significant savings in memory. Finally, in intractable generative models, we show how to use distilled models to robustly estimate intractable quantities of the original model, such as its intractable partition function.