Quantization based model compression serves as high performing and fast approach for inference that yields models which are highly compressed when compared to their full-precision floating point counterparts. The most extreme quantization is a 1-bit representation of parameters such that they have only two possible values, typically -1(0) or +1, enabling efficient implementation of the ubiquitous dot product using only additions. The main contribution of this work is the introduction of a method to smooth the combinatorial problem of determining a binary vector of weights to minimize the expected loss for a given objective by means of empirical risk minimization with backpropagation. This is achieved by approximating a multivariate binary state over the weights utilizing a deterministic and differentiable transformation of real-valued, continuous parameters. The proposed method adds little overhead in training, can be readily applied without any substantial modifications to the original architecture, does not introduce additional saturating nonlinearities or auxiliary losses, and does not prohibit applying other methods for binarizing the activations. Contrary to common assertions made in the literature, it is demonstrated that binary weighted networks can train well with the same standard optimization techniques and similar hyperparameter settings as their full-precision counterparts, specifically momentum SGD with large learning rates and $L_2$ regularization. To conclude experiments demonstrate the method performs remarkably well across a number of inductive image classification tasks with various architectures compared to their full-precision counterparts. The source code is publicly available at https://bitbucket.org/YanivShu/binary_weighted_networks_public.
Deep Learning has revolutionized the fields of computer vision, natural language understanding, speech recognition, information retrieval and more. However, with the progressive improvements in deep learning models, their number of parameters, latency, resources required to train, etc. have all have increased significantly. Consequently, it has become important to pay attention to these footprint metrics of a model as well, not just its quality. We present and motivate the problem of efficiency in deep learning, followed by a thorough survey of the five core areas of model efficiency (spanning modeling techniques, infrastructure, and hardware) and the seminal work there. We also present an experiment-based guide along with code, for practitioners to optimize their model training and deployment. We believe this is the first comprehensive survey in the efficient deep learning space that covers the landscape of model efficiency from modeling techniques to hardware support. Our hope is that this survey would provide the reader with the mental model and the necessary understanding of the field to apply generic efficiency techniques to immediately get significant improvements, and also equip them with ideas for further research and experimentation to achieve additional gains.
Compressing Deep Neural Network (DNN) models to alleviate the storage and computation requirements is essential for practical applications, especially for resource limited devices. Although capable of reducing a reasonable amount of model parameters, previous unstructured or structured weight pruning methods can hardly truly accelerate inference, either due to the poor hardware compatibility of the unstructured sparsity or due to the low sparse rate of the structurally pruned network. Aiming at reducing both storage and computation, as well as preserving the original task performance, we propose a generalized weight unification framework at a hardware compatible micro-structured level to achieve high amount of compression and acceleration. Weight coefficients of a selected micro-structured block are unified to reduce the storage and computation of the block without changing the neuron connections, which turns to a micro-structured pruning special case when all unified coefficients are set to zero, where neuron connections (hence storage and computation) are completely removed. In addition, we developed an effective training framework based on the alternating direction method of multipliers (ADMM), which converts our complex constrained optimization into separately solvable subproblems. Through iteratively optimizing the subproblems, the desired micro-structure can be ensured with high compression ratio and low performance degradation. We extensively evaluated our method using a variety of benchmark models and datasets for different applications. Experimental results demonstrate state-of-the-art performance.
Neural network compression techniques have become increasingly popular as they can drastically reduce the storage and computation requirements for very large networks. Recent empirical studies have illustrated that even simple pruning strategies can be surprisingly effective, and several theoretical studies have shown that compressible networks (in specific senses) should achieve a low generalization error. Yet, a theoretical characterization of the underlying cause that makes the networks amenable to such simple compression schemes is still missing. In this study, we address this fundamental question and reveal that the dynamics of the training algorithm has a key role in obtaining such compressible networks. Focusing our attention on stochastic gradient descent (SGD), our main contribution is to link compressibility to two recently established properties of SGD: (i) as the network size goes to infinity, the system can converge to a mean-field limit, where the network weights behave independently, (ii) for a large step-size/batch-size ratio, the SGD iterates can converge to a heavy-tailed stationary distribution. In the case where these two phenomena occur simultaneously, we prove that the networks are guaranteed to be '$\ell_p$-compressible', and the compression errors of different pruning techniques (magnitude, singular value, or node pruning) become arbitrarily small as the network size increases. We further prove generalization bounds adapted to our theoretical framework, which indeed confirm that the generalization error will be lower for more compressible networks. Our theory and numerical study on various neural networks show that large step-size/batch-size ratios introduce heavy-tails, which, in combination with overparametrization, result in compressibility.
Channel pruning and tensor decomposition have received extensive attention in convolutional neural network compression. However, these two techniques are traditionally deployed in an isolated manner, leading to significant accuracy drop when pursuing high compression rates. In this paper, we propose a Collaborative Compression (CC) scheme, which joints channel pruning and tensor decomposition to compress CNN models by simultaneously learning the model sparsity and low-rankness. Specifically, we first investigate the compression sensitivity of each layer in the network, and then propose a Global Compression Rate Optimization that transforms the decision problem of compression rate into an optimization problem. After that, we propose multi-step heuristic compression to remove redundant compression units step-by-step, which fully considers the effect of the remaining compression space (i.e., unremoved compression units). Our method demonstrates superior performance gains over previous ones on various datasets and backbone architectures. For example, we achieve 52.9% FLOPs reduction by removing 48.4% parameters on ResNet-50 with only a Top-1 accuracy drop of 0.56% on ImageNet 2012.
Knowledge distillation (KD) has proved to be an effective approach for deep neural network compression, which learns a compact network (student) by transferring the knowledge from a pre-trained, over-parameterized network (teacher). In traditional KD, the transferred knowledge is usually obtained by feeding training samples to the teacher network to obtain the class probabilities. However, the original training dataset is not always available due to storage costs or privacy issues. In this study, we propose a novel data-free KD approach by modeling the intermediate feature space of the teacher with a multivariate normal distribution and leveraging the soft targeted labels generated by the distribution to synthesize pseudo samples as the transfer set. Several student networks trained with these synthesized transfer sets present competitive performance compared to the networks trained with the original training set and other data-free KD approaches.
As the complexity of Deep Neural Network (DNN) models increases, their deployment on mobile devices becomes increasingly challenging, especially in complex vision tasks such as image classification. Many of recent contributions aim either to produce compact models matching the limited computing capabilities of mobile devices or to offload the execution of such burdensome models to a compute-capable device at the network edge - the edge servers. In this paper, we propose to modify the structure and training process of DNN models for complex image classification tasks to achieve in-network compression in the early network layers. Our training process stems from knowledge distillation, a technique that has been traditionally used to build small - student - models mimicking the output of larger - teacher - models. Here, we adopt this idea to obtain aggressive compression while preserving accuracy. Our results demonstrate that our approach is effective for state-of-the-art models trained over complex datasets, and can extend the parameter region in which edge computing is a viable and advantageous option. Additionally, we demonstrate that in many settings of practical interest we reduce the inference time with respect to specialized models such as MobileNet v2 executed at the mobile device, while improving accuracy.
Offloading the execution of complex Deep Neural Networks (DNNs) models to compute-capable devices at the network edge, that is, edge servers, can significantly reduce capture-to-output delay. However, the communication link between the mobile devices and edge servers can become the bottleneck when channel conditions are poor. We propose a framework to split DNNs for image processing and minimize capture-to-output delay in a wide range of network conditions and computing parameters. The core idea is to split the DNN models into head and tail models, where the two sections are deployed at the mobile device and edge server, respectively. Different from prior literature presenting DNN splitting frameworks, we distill the architecture of the head DNN to reduce its computational complexity and introduce a bottleneck, thus minimizing processing load at the mobile device as well as the amount of wirelessly transferred data. Our results show 98% reduction in used bandwidth and 85% in computation load compared to straightforward splitting.
We study low-rank parameterizations of weight matrices with embedded spectral properties in the Deep Learning context. The low-rank property leads to parameter efficiency and permits taking computational shortcuts when computing mappings. Spectral properties are often subject to constraints in optimization problems, leading to better models and stability of optimization. We start by looking at the compact SVD parameterization of weight matrices and identifying redundancy sources in the parameterization. We further apply the Tensor Train (TT) decomposition to the compact SVD components, and propose a non-redundant differentiable parameterization of fixed TT-rank tensor manifolds, termed the Spectral Tensor Train Parameterization (STTP). We demonstrate the effects of neural network compression in the image classification setting and both compression and improved training stability in the generative adversarial training setting.
We can compress a rectifier network while exactly preserving its underlying functionality with respect to a given input domain if some of its neurons are stable. However, current approaches to determine the stability of neurons with Rectified Linear Unit (ReLU) activations require solving or finding a good approximation to multiple discrete optimization problems. In this work, we introduce an algorithm based on solving a single optimization problem to identify all stable neurons. Our approach is on median 183 times faster than the state-of-art method on CIFAR-10, which allows us to explore exact compression on deeper (5 x 100) and wider (2 x 800) networks within minutes. For classifiers trained under an amount of L1 regularization that does not worsen accuracy, we can remove up to 56% of the connections on the CIFAR-10 dataset. The code is available at the following link, https://github.com/yuxwind/ExactCompression.
Learning convolutional neural networks (CNNs) with low bitwidth is challenging because performance may drop significantly after quantization. Prior arts often discretize the network weights by carefully tuning hyper-parameters of quantization (e.g. non-uniform stepsize and layer-wise bitwidths), which are complicated and sub-optimal because the full-precision and low-precision models have a large discrepancy. This work presents a novel quantization pipeline, Frequency-Aware Transformation (FAT), which has several appealing benefits. (1) Rather than designing complicated quantizers like existing works, FAT learns to transform network weights in the frequency domain before quantization, making them more amenable to training in low bitwidth. (2) With FAT, CNNs can be easily trained in low precision using simple standard quantizers without tedious hyper-parameter tuning. Theoretical analysis shows that FAT improves both uniform and non-uniform quantizers. (3) FAT can be easily plugged into many CNN architectures. When training ResNet-18 and MobileNet-V2 in 4 bits, FAT plus a simple rounding operation already achieves 70.5% and 69.2% top-1 accuracy on ImageNet without bells and whistles, outperforming recent state-of-the-art by reducing 54.9X and 45.7X computations against full-precision models. We hope FAT provides a novel perspective for model quantization. Code is available at \url{https://github.com/ChaofanTao/FAT_Quantization}.
Compression and efficient storage of neural network (NN) parameters is critical for applications that run on resource-constrained devices. Despite the significant progress in NN model compression, there has been considerably less investigation in the actual \textit{physical} storage of NN parameters. Conventionally, model compression and physical storage are decoupled, as digital storage media with error-correcting codes (ECCs) provide robust error-free storage. However, this decoupled approach is inefficient as it ignores the overparameterization present in most NNs and forces the memory device to allocate the same amount of resources to every bit of information regardless of its importance. In this work, we investigate analog memory devices as an alternative to digital media -- one that naturally provides a way to add more protection for significant bits unlike its counterpart, but is noisy and may compromise the stored model's performance if used naively. We develop a variety of robust coding strategies for NN weight storage on analog devices, and propose an approach to jointly optimize model compression and memory resource allocation. We then demonstrate the efficacy of our approach on models trained on MNIST, CIFAR-10 and ImageNet datasets for existing compression techniques. Compared to conventional error-free digital storage, our method reduces the memory footprint by up to one order of magnitude, without significantly compromising the stored model's accuracy.
Modern Neural Networks are eminent in achieving state of the art performance on tasks under Computer Vision, Natural Language Processing and related verticals. However, they are notorious for their voracious memory and compute appetite which further obstructs their deployment on resource limited edge devices. In order to achieve edge deployment, researchers have developed pruning and quantization algorithms to compress such networks without compromising their efficacy. Such compression algorithms are broadly experimented on standalone CNN and RNN architectures while in this work, we present an unconventional end to end compression pipeline of a CNN-LSTM based Image Captioning model. The model is trained using VGG16 or ResNet50 as an encoder and an LSTM decoder on the flickr8k dataset. We then examine the effects of different compression architectures on the model and design a compression architecture that achieves a 73.1% reduction in model size, 71.3% reduction in inference time and a 7.7% increase in BLEU score as compared to its uncompressed counterpart.
Neural network compression methods like pruning and quantization are very effective at efficiently deploying Deep Neural Networks (DNNs) on edge devices. However, DNNs remain vulnerable to adversarial examples-inconspicuous inputs that are specifically designed to fool these models. In particular, Universal Adversarial Perturbations (UAPs), are a powerful class of adversarial attacks which create adversarial perturbations that can generalize across a large set of inputs. In this work, we analyze the effect of various compression techniques to UAP attacks, including different forms of pruning and quantization. We test the robustness of compressed models to white-box and transfer attacks, comparing them with their uncompressed counterparts on CIFAR-10 and SVHN datasets. Our evaluations reveal clear differences between pruning methods, including Soft Filter and Post-training Pruning. We observe that UAP transfer attacks between pruned and full models are limited, suggesting that the systemic vulnerabilities across these models are different. This finding has practical implications as using different compression techniques can blunt the effectiveness of black-box transfer attacks. We show that, in some scenarios, quantization can produce gradient-masking, giving a false sense of security. Finally, our results suggest that conclusions about the robustness of compressed models to UAP attacks is application dependent, observing different phenomena in the two datasets used in our experiments.
Deep neural networks (DNNs) have been extremely successful in solving many challenging AI tasks in natural language processing, speech recognition, and computer vision nowadays. However, DNNs are typically computation intensive, memory demanding, and power hungry, which significantly limits their usage on platforms with constrained resources. Therefore, a variety of compression techniques (e.g. quantization, pruning, and knowledge distillation) have been proposed to reduce the size and power consumption of DNNs. Blockwise knowledge distillation is one of the compression techniques that can effectively reduce the size of a highly complex DNN. However, it is not widely adopted due to its long training time. In this paper, we propose a novel parallel blockwise distillation algorithm to accelerate the distillation process of sophisticated DNNs. Our algorithm leverages local information to conduct independent blockwise distillation, utilizes depthwise separable layers as the efficient replacement block architecture, and properly addresses limiting factors (e.g. dependency, synchronization, and load balancing) that affect parallelism. The experimental results running on an AMD server with four Geforce RTX 2080Ti GPUs show that our algorithm can achieve 3x speedup plus 19% energy savings on VGG distillation, and 3.5x speedup plus 29% energy savings on ResNet distillation, both with negligible accuracy loss. The speedup of ResNet distillation can be further improved to 3.87 when using four RTX6000 GPUs in a distributed cluster.
Several methods of knowledge distillation have been developed for neural network compression. While they all use the KL divergence loss to align the soft outputs of the student model more closely with that of the teacher, the various methods differ in how the intermediate features of the student are encouraged to match those of the teacher. In this paper, we propose a simple-to-implement method using auxiliary classifiers at intermediate layers for matching features, which we refer to as multi-head knowledge distillation (MHKD). We add loss terms for training the student that measure the dissimilarity between student and teacher outputs of the auxiliary classifiers. At the same time, the proposed method also provides a natural way to measure differences at the intermediate layers even though the dimensions of the internal teacher and student features may be different. Through several experiments in image classification on multiple datasets we show that the proposed method outperforms prior relevant approaches presented in the literature.
While knowledge distillation (transfer) has been attracting attentions from the research community, the recent development in the fields has heightened the need for reproducible studies and highly generalized frameworks to lower barriers to such high-quality, reproducible deep learning research. Several researchers voluntarily published frameworks used in their knowledge distillation studies to help other interested researchers reproduce their original work. Such frameworks, however, are usually neither well generalized nor maintained, thus researchers are still required to write a lot of code to refactor/build on the frameworks for introducing new methods, models, datasets and designing experiments. In this paper, we present our developed open-source framework built on PyTorch and dedicated for knowledge distillation studies. The framework is designed to enable users to design experiments by declarative PyYAML configuration files, and helps researchers complete the recently proposed ML Code Completeness Checklist. Using the developed framework, we demonstrate its various efficient training strategies, and implement a variety of knowledge distillation methods. We also reproduce some of their original experimental results on the ImageNet and COCO datasets presented at major machine learning conferences such as ICLR, NeurIPS, CVPR and ECCV, including recent state-of-the-art methods. All the source code, configurations, log files and trained model weights are publicly available at https://github.com/yoshitomo-matsubara/torchdistill .
We introduce Dirichlet pruning, a novel post-processing technique to transform a large neural network model into a compressed one. Dirichlet pruning is a form of structured pruning that assigns the Dirichlet distribution over each layer's channels in convolutional layers (or neurons in fully-connected layers) and estimates the parameters of the distribution over these units using variational inference. The learned distribution allows us to remove unimportant units, resulting in a compact architecture containing only crucial features for a task at hand. The number of newly introduced Dirichlet parameters is only linear in the number of channels, which allows for rapid training, requiring as little as one epoch to converge. We perform extensive experiments, in particular on larger architectures such as VGG and ResNet (45% and 58% compression rate, respectively) where our method achieves the state-of-the-art compression performance and provides interpretable features as a by-product.
The compression of deep neural networks (DNNs) to reduce inference cost becomes increasingly important to meet realistic deployment requirements of various applications. There have been a significant amount of work regarding network compression, while most of them are heuristic rule-based or typically not friendly to be incorporated into varying scenarios. On the other hand, sparse optimization yielding sparse solutions naturally fits the compression requirement, but due to the limited study of sparse optimization in stochastic learning, its extension and application onto model compression is rarely well explored. In this work, we propose a model compression framework based on the recent progress on sparse stochastic optimization. Compared to existing model compression techniques, our method is effective and requires fewer extra engineering efforts to incorporate with varying applications, and has been numerically demonstrated on benchmark compression tasks. Particularly, we achieve up to 7.2 and 2.9 times FLOPs reduction with the same level of evaluation accuracy on VGG16 for CIFAR10 and ResNet50 for ImageNet compared to the baseline heavy models, respectively.
Deep Neural Network (DNN) has gained unprecedented performance due to its automated feature extraction capability. This high order performance leads to significant incorporation of DNN models in different Internet of Things (IoT) applications in the past decade. However, the colossal requirement of computation, energy, and storage of DNN models make their deployment prohibitive on resource constraint IoT devices. Therefore, several compression techniques were proposed in recent years for reducing the storage and computation requirements of the DNN model. These techniques on DNN compression have utilized a different perspective for compressing DNN with minimal accuracy compromise. It encourages us to make a comprehensive overview of the DNN compression techniques. In this paper, we present a comprehensive review of existing literature on compressing DNN model that reduces both storage and computation requirements. We divide the existing approaches into five broad categories, i.e., network pruning, sparse representation, bits precision, knowledge distillation, and miscellaneous, based upon the mechanism incorporated for compressing the DNN model. The paper also discussed the challenges associated with each category of DNN compression techniques. Finally, we provide a quick summary of existing work under each category with the future direction in DNN compression.