We present a differentiable joint pruning and quantization (DJPQ) scheme. We frame neural network compression as a joint gradient-based optimization problem, trading off between model pruning and quantization automatically for hardware efficiency. DJPQ incorporates variational information bottleneck based structured pruning and mixed-bit precision quantization into a single differentiable loss function. In contrast to previous works which consider pruning and quantization separately, our method enables users to find the optimal trade-off between both in a single training procedure. To utilize the method for more efficient hardware inference, we extend DJPQ to integrate structured pruning with power-of-two bit-restricted quantization. We show that DJPQ significantly reduces the number of Bit-Operations (BOPs) for several networks while maintaining the top-1 accuracy of original floating-point models (e.g., 53x BOPs reduction in ResNet18 on ImageNet, 43x in MobileNetV2). Compared to the conventional two-stage approach, which optimizes pruning and quantization independently, our scheme outperforms in terms of both accuracy and BOPs. Even when considering bit-restricted quantization, DJPQ achieves larger compression ratios and better accuracy than the two-stage approach.
Fermi National Accelerator Laboratory（费米国家加速器实验室）；University of California San Diego（加州大学圣地亚哥分校）；Xilinx Research（赛灵思研究院）；Northwestern University（西北大学）
Efficient machine learning implementations optimized for inference in hardware have wide-ranging benefits, depending on the application, from lower inference latency to higher data throughput and reduced energy consumption. Two popular techniques for reducing computation in neural networks are pruning, removing insignificant synapses, and quantization, reducing the precision of the calculations. In this work, we explore the interplay between pruning and quantization during the training of neural networks for ultra low latency applications targeting high energy physics use cases. Techniques dev…
Qualcomm Technologies, Inc.（高通技术公司）；Qualcomm AI Research（高通人工智能研究院）
As edge devices become prevalent, deploying Deep Neural Networks (DNN) on edge devices has become a critical issue. However, DNN requires a high computational resource which is rarely available for edge devices. To handle this, we propose a novel model compression method for the devices with limited computational resources, called PQK consisting of pruning, quantization, and knowledge distillation (KD) processes. Unlike traditional pruning and KD, PQK makes use of unimportant weights pruned in the pruning process to make a teacher network for training a better student network without pre-train…
In recent years, the growing size of neural networks has led to a vast amount of research concerning compression techniques to mitigate the drawbacks of such large sizes. Most of these research works can be categorized into three broad families : Knowledge Distillation, Pruning, and Quantization. While there has been steady research in this domain, adoption and commercial usage of the proposed techniques has not quite progressed at the rate. We present KD-Lib, an open-source PyTorch based library, which contains state-of-the-art modular implementations of algorithms from the three families on …
Modern neural network architectures typically have many millions of parameters and can be pruned significantly without substantial loss in effectiveness which demonstrates they are over-parameterized. The contribution of this work is two-fold. The first is a method for approximating a multivariate Bernoulli random variable by means of a deterministic and differentiable transformation of any real-valued multivariate random variable. The second is a method for model selection by element-wise multiplication of parameters with approximate binary gates that may be computed deterministically or stoc…
University of Cambridge（剑桥大学）；Samsung AI Centre Cambridge（三星剑桥人工智能中心）
Embedded and personal IoT devices are powered by microcontroller units (MCUs), whose extreme resource scarcity is a major obstacle for applications relying on on-device deep learning inference. Orders of magnitude less storage, memory and computational capacity, compared to what is typically required to execute neural networks, impose strict structural constraints on the network architecture and call for specialist model compression methodology. In this work, we present a differentiable structured network pruning method for convolutional neural networks, which integrates a model's MCU-specific…
University of California, Irvine（加利福尼亚大学尔湾分校）；Department of Mathematics（数学系）
We propose an adaptive projection-gradient descent-shrinkage-splitting method (APGDSSM) to integrate penalty based channel pruning into quantization-aware training (QAT). APGDSSM concurrently searches weights in both the quantized subspace and the sparse subspace. APGDSSM uses shrinkage operator and a splitting technique to create sparse weights, as well as the Group Lasso penalty to push the weight sparsity into channel sparsity. In addition, we propose a novel complementary transformed l1 penalty to stabilize the training for extreme compression.
The Chinese University of Hong Kong（香港中文大学）；SenseBrain, Ltd（SenseBrain有限公司）；Shanghai AI Lab（上海人工智能实验室）；The University of Hong Kong（香港大学）
Model quantization is challenging due to many tedious hyper-parameters such as precision (bitwidth), dynamic range (minimum and maximum discrete values) and stepsize (interval between discrete values). Unlike prior arts that carefully tune these values, we present a fully differentiable approach to learn all of them, named Differentiable Dynamic Quantization (DDQ), which has several benefits. (1) DDQ is able to quantize challenging lightweight architectures like MobileNets, where different layers prefer different quantization parameters. (2) DDQ is hardware-friendly and can be easily implement…
We propose the position-based scaled gradient (PSG) that scales the gradient depending on the position of a weight vector to make it more compression-friendly. First, we theoretically show that applying PSG to the standard gradient descent (GD), which is called PSGD, is equivalent to the GD in the warped weight space, a space made by warping the original weight space via an appropriately designed invertible function. Second, we empirically show that PSG acting as a regularizer to a weight vector is favorable for model compression domains such as quantization and pruning. PSG reduces the gap be…
Large deep neural network (DNN) models pose the key challenge to energy efficiency due to the significantly higher energy consumption of off-chip DRAM accesses than arithmetic or SRAM operations. It motivates the intensive research on model compression with two main approaches. Weight pruning leverages the redundancy in the number of weights and can be performed in a non-structured, which has higher flexibility and pruning rate but incurs index accesses due to irregular weights, or structured manner, which preserves the full matrix structure with lower pruning rate. Weight quantization leverag…
Ningxia University（宁夏大学）；Collaborative Innovation Center for Ningxia Big Data and Artificial Intelligence co-founded by Ningxia Municipality and Ministry of Education（宁夏大数据与人工智能省部共建协同创新中心）
Existing differentiable channel pruning methods often attach scaling factors or masks behind channels to prune filters with less importance, and implicitly assume uniform contribution of input samples to filter importance. Specifically, the effects of instance complexity on pruning performance are not yet fully investigated in static network pruning. In this paper, we propose a simple yet effective differentiable network pruning method CWP based on instance complexity weighted filter importance scores. We define instance complexity related weight for each instance by giving higher weights to h…
Facebook AI Research（脸书人工智能研究院）；Brown University（布朗大学）
In order to contrast the explosion in size of state-of-the-art machine learning models that can be attributed to the empirical advantages of over-parametrization, and due to the necessity of deploying fast, sustainable, and private on-device models on resource-constrained devices, the community has focused on techniques such as pruning, quantization, and distillation as central strategies for model compression. Towards the goal of facilitating the adoption of a common interface for neural network pruning in PyTorch, this contribution describes the recent addition of the PyTorch torch.nn.utils.…
University of Toronto（多伦多大学）；York University（约克大学）
In this work, PRUNIX, a framework for training and pruning convolutional neural networks is proposed for deployment on memristor crossbar based accelerators. PRUNIX takes into account the numerous non-ideal effects of memristor crossbars including weight quantization, state-drift, aging and stuck-at-faults. PRUNIX utilises a novel Group Sawtooth Regularization intended to improve non-ideality tolerance as well as sparsity, and a novel Adaptive Pruning Algorithm (APA) intended to minimise accuracy loss by considering the sensitivity of different layers of a CNN to pruning. We compare our regula…
Hong Kong University of Science and Technology（香港科技大学）；Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）；Jockey Club Institute for Advanced Study, HKUST（香港科技大学赛马会高等研究院）；Reality Labs, Meta Inc（Meta公司现实实验室）；ACCESS - AI Chip Center for Emerging Smart Systems（新兴智能系统AI芯片中心（ACCESS））；Carnegie Mellon University（卡内基梅隆大学）
In order to deploy deep models in a computationally efficient manner, model quantization approaches have been frequently used. In addition, as new hardware that supports mixed bitwidth arithmetic operations, recent research on mixed precision quantization (MPQ) begins to fully leverage the capacity of representation by searching optimized bitwidths for different layers and modules in a network. However, previous studies mainly search the MPQ strategy in a costly scheme using reinforcement learning, neural architecture search, etc., or simply utilize partial prior knowledge for bitwidth assignm…
HESTIA: A Hessian-Guided Differentiable Quantization-Aware Training Framework for Extremely Low-Bit LLMs
School of Software and Microelectronics, Peking University, Beijing, China（软件与微电子学院，北京大学，北京，中国）；School of Computer Science, Peking University, Beijing, China（计算机科学学院，北京大学，北京，中国）
This paper describes a channel-selection approach for simplifying deep neural networks. Specifically, we propose a new type of generic network layer, called pruning layer, to seamlessly augment a given pre-trained model for compression. Each pruning layer, comprising $1 \times 1$ depth-wise kernels, is represented with a dual format: one is real-valued and the other is binary. The former enables a two-phase optimization process of network pruning to operate with an end-to-end differentiable network, and the latter yields the mask information for channel selection. Our method progressively perf…
Pruning is one of the most effective model reduction techniques. Deep networks require massive computation and such models need to be compressed to bring them on edge devices. Most existing pruning techniques are focused on vision-based models like convolutional networks, while text-based models are still evolving. The emergence of multi-modal multi-task learning calls for a general method that works on vision and text architectures simultaneously. We introduce a \emph{differentiable mask}, that induces sparsity on various granularity to fill this gap. We apply our method successfully to prune…
Unstructured neural network pruning algorithms have achieved impressive compression rates. However, the resulting - typically irregular - sparse matrices hamper efficient hardware implementations, leading to additional memory usage and complex control logic that diminishes the benefits of unstructured pruning. This has spurred structured coarse-grained pruning solutions that prune entire filters or even layers, enabling efficient implementation at the expense of reduced flexibility. Here we propose a flexible new pruning mechanism that facilitates pruning at different granularities (weights, k…
Camera-based Deep Learning algorithms are increasingly needed for perception in Automated Driving systems. However, constraints from the automotive industry challenge the deployment of CNNs by imposing embedded systems with limited computational resources. In this paper, we propose an approach to embed a multi-task CNN network under such conditions on a commercial prototype platform, i.e. a low power System on Chip (SoC) processing four surround-view fisheye cameras at 10 FPS. The first focus is on designing an efficient and compact multi-task network architecture. Secondly, a pruning method i…
Budgeted pruning is the problem of pruning under resource constraints. In budgeted pruning, how to distribute the resources across layers (i.e., sparsity allocation) is the key problem. Traditional methods solve it by discretely searching for the layer-wise pruning ratios, which lacks efficiency. In this paper, we propose Differentiable Sparsity Allocation (DSA), an efficient end-to-end budgeted pruning flow. Utilizing a novel differentiable pruning process, DSA finds the layer-wise pruning ratios with gradient-based optimization. It allocates sparsity in continuous space, which is more effici…
Equivariant-Aware Structured Pruning for Efficient Edge Deployment: A Comprehensive Framework with Adaptive Fine-Tuning
Faculty of Computers and Information Technology, University of Tabuk（计算机与信息科技学院，塔布克大学）；Artificial Intelligence and Sensing Technologies (AIST) Research Center, University of Tabuk（人工智能与传感技术（AIST）研究中心，塔布克大学）
Inference time, model size, and accuracy are critical for deploying deep neural network models. Numerous research efforts have been made to compress neural network models with faster inference and higher accuracy. Pruning and quantization are mainstream methods to this end. During model quantization, converting individual float values of layer weights to low-precision ones can substantially reduce the computational overhead and improve the inference speed. Many quantization methods have been studied, for example, vector quantization, low-bit quantization, and binary/ternary quantization. This …
Pruning and quantization are proven methods for improving the performance and storage efficiency of convolutional neural networks (CNNs). Pruning removes near-zero weights in tensors and masks weak connections between neurons in neighbouring layers. Quantization reduces the precision of weights by replacing them with numerically similar values that require less storage. In this paper, we identify another form of redundancy in CNN weight tensors, in the form of repeated patterns of similar values. We observe that pruning and quantization both tend to drastically increase the number of repeated …
We propose a simple but effective data-driven channel pruning algorithm, which compresses deep neural networks in a differentiable way by exploiting the characteristics of operations. The proposed approach makes a joint consideration of batch normalization (BN) and rectified linear unit (ReLU) for channel pruning; it estimates how likely the two successive operations deactivate each feature map and prunes the channels with high probabilities. To this end, we learn differentiable masks for individual channels and make soft decisions throughout the optimization procedure, which facilitates to ex…
Model compression techniques, such as pruning and quantization, are becoming increasingly important to reduce the memory footprints and the amount of computations. Despite model size reduction, achieving performance enhancement on devices is, however, still challenging mainly due to the irregular representations of sparse matrix formats. This paper proposes a new weight representation scheme for Sparse Quantized Neural Networks, specifically achieved by fine-grained and unstructured pruning method. The representation is encrypted in a structured regular format, which can be efficiently decoded…
Recent works imply that the channel pruning can be regarded as searching optimal sub-structure from unpruned networks. However, existing works based on this observation require training and evaluating a large number of structures, which limits their application. In this paper, we propose a novel differentiable method for channel pruning, named Differentiable Markov Channel Pruning (DMCP), to efficiently search the optimal sub-structure. Our method is differentiable and can be directly optimized by gradient descent with respect to standard task loss and budget regularization (e.g. FLOPs constra…
We propose a new gradient-based approach for extracting sub-architectures from a given large model. Contrarily to existing pruning methods, which are unable to disentangle the network architecture and the corresponding weights, our architecture-pruning scheme produces transferable new structures that can be successfully retrained to solve different tasks. We focus on a transfer-learning setup where architectures can be trained on a large data set but very few data points are available for fine-tuning them on new tasks. We define a new gradient-based algorithm that trains architectures of arbit…
Energy efficient implementations and deployments of Spiking neural networks (SNNs) have been of great interest due to the possibility of developing artificial systems that can achieve the computational powers and energy efficiency of the biological brain. Efficient implementations of SNNs on modern digital hardware are also inspired by advances in machine learning and deep neural networks (DNNs). Two techniques widely employed in the efficient deployment of DNNs -- the quantization and pruning of parameters, can both compress the model size, reduce memory footprints, and facilitate low-latency…
We introduce Bayesian Bits, a practical method for joint mixed precision quantization and pruning through gradient based optimization. Bayesian Bits employs a novel decomposition of the quantization operation, which sequentially considers doubling the bit width. At each new bit width, the residual error between the full precision value and the previously rounded value is quantized. We then decide whether or not to add this quantized residual error for a higher effective bit width and lower quantization noise. By starting with a power-of-two bit width, this decomposition will always produce har…
The convolutional neural network has achieved great success in fulfilling computer vision tasks despite large computation overhead against efficient deployment. Structured (channel) pruning is usually applied to reduce the model redundancy while preserving the network structure, such that the pruned network can be easily deployed in practice. However, existing structured pruning methods require hand-crafted rules which may lead to tremendous pruning space. In this paper, we introduce Differentiable Annealing Indicator Search (DAIS) that leverages the strength of neural architecture search in t…
IST Austria（奥地利科学技术研究所）；ETH Zurich（苏黎世联邦理工学院）；Neural Magic（神经魔法公司）
We consider the problem of model compression for deep neural networks (DNNs) in the challenging one-shot/post-training setting, in which we are given an accurate trained model, and must compress it without any retraining, based only on a small amount of calibration input data. This problem has become popular in view of the emerging software and hardware support for executing models compressed via pruning and/or quantization with speedup, and well-performing solutions have been proposed independently for both compression approaches. In this paper, we introduce a new compression framework which …
We propose a simple and easy to implement neural network compression algorithm that achieves results competitive with more complicated state-of-the-art methods. The key idea is to modify the original optimization problem by adding K independent Gaussian priors (corresponding to the k-means objective) over the network parameters to achieve parameter quantization, as well as an L1 penalty to achieve pruning. Unlike many existing quantization-based methods, our method uses hard clustering assignments of network parameters, which adds minimal change or overhead to standard network training. We als…
Quantization and pruning are core techniques used to reduce the inference costs of deep neural networks. State-of-the-art quantization techniques are currently applied to both the weights and activations; however, pruning is most often applied to only the weights of the network. In this work, we jointly apply novel uniform quantization and unstructured pruning methods to both the weights and activations of deep neural networks during training. Using our methods, we empirically evaluate the currently accepted prune-then-quantize paradigm across a wide range of computer vision tasks and observe …
ETH Zürich（苏黎世联邦理工学院）；The University of Sydney（悉尼大学）；KU Leuven（鲁汶大学）
Network pruning has been the driving force for the acceleration of neural networks and the alleviation of model storage/transmission burden. With the advent of AutoML and neural architecture search (NAS), pruning has become topical with automatic mechanism and searching based architecture optimization. Yet, current automatic designs rely on either reinforcement learning or evolutionary algorithm. Due to the non-differentiability of those algorithms, the pruning algorithm needs a long searching stage before reaching the convergence. To circumvent this problem, this paper introduces a differenti…
Syracuse University（雪城大学）；Peking University（北京大学）；MIT-IBM Watson AI Lab, IBM Research（IBM研究院麻省理工学院-IBM沃森人工智能实验室）；Northeastern University（东北大学）
Many model compression techniques of Deep Neural Networks (DNNs) have been investigated, including weight pruning, weight clustering and quantization, etc. Weight pruning leverages the redundancy in the number of weights in DNNs, while weight clustering/quantization leverages the redundancy in the number of bit representations of weights. They can be effectively combined in order to exploit the maximum degree of redundancy. However, there lacks a systematic investigation in literature towards this direction. In this paper, we fill this void and develop a unified, systematic framework of DNN we…
When large scale training data is available, one can obtain compact and accurate networks to be deployed in resource-constrained environments effectively through quantization and pruning. However, training data are often protected due to privacy concerns and it is challenging to obtain compact networks without data. We study data-free quantization and pruning by transferring knowledge from trained large networks to compact networks. Auxiliary generators are simultaneously and adversarially trained with the targeted compact networks to generate synthetic inputs that maximize the discrepancy bet…
We propose DiffQ a differentiable method for model compression for quantizing model parameters without gradient approximations (e.g., Straight Through Estimator). We suggest adding independent pseudo quantization noise to model parameters during training to approximate the effect of a quantization operator. DiffQ is differentiable both with respect to the unquantized weights and the number of bits used. Given a single hyper-parameter balancing between the quantized model size and accuracy, DiffQ optimizes the number of bits used per individual weight or groups of weights, in end-to-end trainin…
