Network quantization is an effective compression method to reduce the model size and computational cost. Despite the high compression ratio, training a low-precision model is difficult due to the discrete and non-differentiable nature of quantization, resulting in considerable performance degradation. Recently, Sharpness-Aware Minimization (SAM) is proposed to improve the generalization performance of the models by simultaneously minimizing the loss value and the loss curvature. In this paper, we devise a Sharpness-Aware Quantization (SAQ) method to train quantized models, leading to better generalization performance. Moreover, since each layer contributes differently to the loss value and the loss sharpness of a network, we further devise an effective method that learns a configuration generator to automatically determine the bitwidth configurations of each layer, encouraging lower bits for flat regions and vice versa for sharp landscapes, while simultaneously promoting the flatness of minima to enable more aggressive quantization. Extensive experiments on CIFAR-100 and ImageNet show the superior performance of the proposed methods. For example, our quantized ResNet-18 with 55.1x Bit-Operation (BOP) reduction even outperforms the full-precision one by 0.7% in terms of the Top-1 accuracy. Code is available at //github.com/zhuang-group/SAQ.
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We study the performance of a phase-noise impaired double reconfigurable intelligent surface (RIS)-aided multiuser (MU) multiple-input single-output (MISO) system under spatial correlation at both RISs and base-station (BS). The downlink achievable rate is derived in closed-form under maximum ratio transmission (MRT) precoding. In addition, we obtain the optimal phase-shift design at both RISs in closed-form for the considered channel and phase-noise models. Numerical results validate the analytical expressions, and highlight the effects of different system parameters on the achievable rate. In particular, it is demonstrated that while phase-noise at RISs and spatial correlation at BS are capacity limiting factors, the spatial correlation at both RISs is essential to obtain high achievable rates.
Efficiency of gradient propagation in intermediate layers of convolutional neural networks is of key importance for super-resolution task. To this end, we propose a deep architecture for single image super-resolution (SISR), which is built using efficient convolutional units we refer to as mixed-dense connection blocks (MDCB). The design of MDCB combines the strengths of both residual and dense connection strategies, while overcoming their limitations. To enable super-resolution for multiple factors, we propose a scale-recurrent framework which reutilizes the filters learnt for lower scale factors recursively for higher factors. This leads to improved performance and promotes parametric efficiency for higher factors. We train two versions of our network to enhance complementary image qualities using different loss configurations. We further employ our network for video super-resolution task, where our network learns to aggregate information from multiple frames and maintain spatio-temporal consistency. The proposed networks lead to qualitative and quantitative improvements over state-of-the-art techniques on image and video super-resolution benchmarks.
While neural networks have been remarkably successful in a wide array of applications, implementing them in resource-constrained hardware remains an area of intense research. By replacing the weights of a neural network with quantized (e.g., 4-bit, or binary) counterparts, massive savings in computation cost, memory, and power consumption are attained. We modify a post-training neural-network quantization method, GPFQ, that is based on a greedy path-following mechanism, and rigorously analyze its error. We prove that for quantizing a single-layer network, the relative square error essentially decays linearly in the number of weights -- i.e., level of over-parametrization. Our result holds across a range of input distributions and for both fully-connected and convolutional architectures. To empirically evaluate the method, we quantize several common architectures with few bits per weight, and test them on ImageNet, showing only minor loss of accuracy. We also demonstrate that standard modifications, such as bias correction and mixed precision quantization, further improve accuracy.
Inference time, model size, and accuracy are three key factors in deep model compression. Most of the existing work addresses these three key factors separately as it is difficult to optimize them all at the same time. For example, low-bit quantization aims at obtaining a faster model; weight sharing quantization aims at improving compression ratio and accuracy; and mixed-precision quantization aims at balancing accuracy and inference time. To simultaneously optimize bit-width, model size, and accuracy, we propose pruning ternary quantization (PTQ): a simple, effective, symmetric ternary quantization method. We integrate L2 normalization, pruning, and the weight decay term to reduce the weight discrepancy in the gradient estimator during quantization, thus producing highly compressed ternary weights. Our method brings the highest test accuracy and the highest compression ratio. For example, it produces a 939kb (49$\times$) 2bit ternary ResNet-18 model with only 4\% accuracy drop on the ImageNet dataset. It compresses 170MB Mask R-CNN to 5MB (34$\times$) with only 2.8\% average precision drop. Our method is verified on image classification, object detection/segmentation tasks with different network structures such as ResNet-18, ResNet-50, and MobileNetV2.
Adder Neural Networks (ANNs) which only contain additions bring us a new way of developing deep neural networks with low energy consumption. Unfortunately, there is an accuracy drop when replacing all convolution filters by adder filters. The main reason here is the optimization difficulty of ANNs using $\ell_1$-norm, in which the estimation of gradient in back propagation is inaccurate. In this paper, we present a novel method for further improving the performance of ANNs without increasing the trainable parameters via a progressive kernel based knowledge distillation (PKKD) method. A convolutional neural network (CNN) with the same architecture is simultaneously initialized and trained as a teacher network, features and weights of ANN and CNN will be transformed to a new space to eliminate the accuracy drop. The similarity is conducted in a higher-dimensional space to disentangle the difference of their distributions using a kernel based method. Finally, the desired ANN is learned based on the information from both the ground-truth and teacher, progressively. The effectiveness of the proposed method for learning ANN with higher performance is then well-verified on several benchmarks. For instance, the ANN-50 trained using the proposed PKKD method obtains a 76.8\% top-1 accuracy on ImageNet dataset, which is 0.6\% higher than that of the ResNet-50.
Graph signals are signals with an irregular structure that can be described by a graph. Graph neural networks (GNNs) are information processing architectures tailored to these graph signals and made of stacked layers that compose graph convolutional filters with nonlinear activation functions. Graph convolutions endow GNNs with invariance to permutations of the graph nodes' labels. In this paper, we consider the design of trainable nonlinear activation functions that take into consideration the structure of the graph. This is accomplished by using graph median filters and graph max filters, which mimic linear graph convolutions and are shown to retain the permutation invariance of GNNs. We also discuss modifications to the backpropagation algorithm necessary to train local activation functions. The advantages of localized activation function architectures are demonstrated in four numerical experiments: source localization on synthetic graphs, authorship attribution of 19th century novels, movie recommender systems and scientific article classification. In all cases, localized activation functions are shown to improve model capacity.
Deep convolutional neural networks (CNNs) have recently achieved great success in many visual recognition tasks. However, existing deep neural network models are computationally expensive and memory intensive, hindering their deployment in devices with low memory resources or in applications with strict latency requirements. Therefore, a natural thought is to perform model compression and acceleration in deep networks without significantly decreasing the model performance. During the past few years, tremendous progress has been made in this area. In this paper, we survey the recent advanced techniques for compacting and accelerating CNNs model developed. These techniques are roughly categorized into four schemes: parameter pruning and sharing, low-rank factorization, transferred/compact convolutional filters, and knowledge distillation. Methods of parameter pruning and sharing will be described at the beginning, after that the other techniques will be introduced. For each scheme, we provide insightful analysis regarding the performance, related applications, advantages, and drawbacks etc. Then we will go through a few very recent additional successful methods, for example, dynamic capacity networks and stochastic depths networks. After that, we survey the evaluation matrix, the main datasets used for evaluating the model performance and recent benchmarking efforts. Finally, we conclude this paper, discuss remaining challenges and possible directions on this topic.
The central building block of convolutional neural networks (CNNs) is the convolution operator, which enables networks to construct informative features by fusing both spatial and channel-wise information within local receptive fields at each layer. A broad range of prior research has investigated the spatial component of this relationship, seeking to strengthen the representational power of a CNN by enhancing the quality of spatial encodings throughout its feature hierarchy. In this work, we focus instead on the channel relationship and propose a novel architectural unit, which we term the "Squeeze-and-Excitation" (SE) block, that adaptively recalibrates channel-wise feature responses by explicitly modelling interdependencies between channels. We show that these blocks can be stacked together to form SENet architectures that generalise extremely effectively across different datasets. We further demonstrate that SE blocks bring significant improvements in performance for existing state-of-the-art CNNs at minimal additional computational cost. Squeeze-and-Excitation Networks formed the foundation of our ILSVRC 2017 classification submission which won first place and reduced the top-5 error to 2.251%, surpassing the winning entry of 2016 by a relative improvement of ~25%. Models and code are available at //github.com/hujie-frank/SENet.
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.
We present an overview of techniques for quantizing convolutional neural networks for inference with integer weights and activations. Per-channel quantization of weights and per-layer quantization of activations to 8-bits of precision post-training produces classification accuracies within 2% of floating point networks for a wide variety of CNN architectures. Model sizes can be reduced by a factor of 4 by quantizing weights to 8-bits, even when 8-bit arithmetic is not supported. This can be achieved with simple, post training quantization of weights.We benchmark latencies of quantized networks on CPUs and DSPs and observe a speedup of 2x-3x for quantized implementations compared to floating point on CPUs. Speedups of up to 10x are observed on specialized processors with fixed point SIMD capabilities, like the Qualcomm QDSPs with HVX. Quantization-aware training can provide further improvements, reducing the gap to floating point to 1% at 8-bit precision. Quantization-aware training also allows for reducing the precision of weights to four bits with accuracy losses ranging from 2% to 10%, with higher accuracy drop for smaller networks.We introduce tools in TensorFlow and TensorFlowLite for quantizing convolutional networks and review best practices for quantization-aware training to obtain high accuracy with quantized weights and activations. We recommend that per-channel quantization of weights and per-layer quantization of activations be the preferred quantization scheme for hardware acceleration and kernel optimization. We also propose that future processors and hardware accelerators for optimized inference support precisions of 4, 8 and 16 bits.
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