Precision Highway for Ultra Low-Precision Quantization

Neural network quantization has an inherent problem called accumulated quantization error, which is the key obstacle towards ultra-low precision, e.g., 2- or 3-bit precision. To resolve this problem, we propose precision highway, which forms an end-to-end high-precision information flow while performing the ultra low-precision computation. First, we describe how the precision highway reduce the accumulated quantization error in both convolutional and recurrent neural networks. We also provide the quantitative analysis of the benefit of precision highway and evaluate the overhead on the state-of-the-art hardware accelerator. In the experiments, our proposed method outperforms the best existing quantization methods while offering 3-bit weight/activation quantization with no accuracy loss and 2-bit quantization with a 2.45 % top-1 accuracy loss in ResNet-50. We also report that the proposed method significantly outperforms the existing method in the 2-bit quantization of an LSTM for language modeling

A Survey on Methods and Theories of Quantized Neural Networks

Deep neural networks are the state-of-the-art methods for many real-world tasks, such as computer vision, natural language processing and speech recognition. For all its popularity, deep neural networks are also criticized for consuming a lot of memory and draining battery life of devices during training and inference. This makes it hard to deploy these models on mobile or embedded devices which have tight resource constraints. Quantization is recognized as one of the most effective approaches to satisfy the extreme memory requirements that deep neural network models demand. Instead of adopting 32-bit floating point format to represent weights, quantized representations store weights using more compact formats such as integers or even binary numbers. Despite a possible degradation in predictive performance, quantization provides a potential solution to greatly reduce the model size and the energy consumption. In this survey, we give a thorough review of different aspects of quantized neural networks. Current challenges and trends of quantized neural networks are also discussed.Comment: 17 pages, 8 figure

QGAN: Quantized Generative Adversarial Networks

The intensive computation and memory requirements of generative adversarial neural networks (GANs) hinder its real-world deployment on edge devices such as smartphones. Despite the success in model reduction of CNNs, neural network quantization methods have not yet been studied on GANs, which are mainly faced with the issues of both the effectiveness of quantization algorithms and the instability of training GAN models. In this paper, we start with an extensive study on applying existing successful methods to quantize GANs. Our observation reveals that none of them generates samples with reasonable quality because of the underrepresentation of quantized values in model weights, and the generator and discriminator networks show different sensitivities upon quantization methods. Motivated by these observations, we develop a novel quantization method for GANs based on EM algorithms, named as QGAN. We also propose a multi-precision algorithm to help find the optimal number of bits of quantized GAN models in conjunction with corresponding result qualities. Experiments on CIFAR-10 and CelebA show that QGAN can quantize GANs to even 1-bit or 2-bit representations with results of quality comparable to original models

Feature Map Transform Coding for Energy-Efficient CNN Inference

Convolutional neural networks (CNNs) achieve state-of-the-art accuracy in a variety of tasks in computer vision and beyond. One of the major obstacles hindering the ubiquitous use of CNNs for inference on low-power edge devices is their high computational complexity and memory bandwidth requirements. The latter often dominates the energy footprint on modern hardware. In this paper, we introduce a lossy transform coding approach, inspired by image and video compression, designed to reduce the memory bandwidth due to the storage of intermediate activation calculation results. Our method does not require fine-tuning the network weights and halves the data transfer volumes to the main memory by compressing feature maps, which are highly correlated, with variable length coding. Our method outperform previous approach in term of the number of bits per value with minor accuracy degradation on ResNet-34 and MobileNetV2. We analyze the performance of our approach on a variety of CNN architectures and demonstrate that FPGA implementation of ResNet-18 with our approach results in a reduction of around 40% in the memory energy footprint, compared to quantized network, with negligible impact on accuracy. When allowing accuracy degradation of up to 2%, the reduction of 60% is achieved. A reference implementation is available at https://github.com/CompressTeam/TransformCodingInferenc

Proximal Mean-field for Neural Network Quantization

Compressing large Neural Networks (NN) by quantizing the parameters, while maintaining the performance is highly desirable due to reduced memory and time complexity. In this work, we cast NN quantization as a discrete labelling problem, and by examining relaxations, we design an efficient iterative optimization procedure that involves stochastic gradient descent followed by a projection. We prove that our simple projected gradient descent approach is, in fact, equivalent to a proximal version of the well-known mean-field method. These findings would allow the decades-old and theoretically grounded research on MRF optimization to be used to design better network quantization schemes. Our experiments on standard classification datasets (MNIST, CIFAR10/100, TinyImageNet) with convolutional and residual architectures show that our algorithm obtains fully-quantized networks with accuracies very close to the floating-point reference networks

Memory-Driven Mixed Low Precision Quantization For Enabling Deep Network Inference On Microcontrollers

This paper presents a novel end-to-end methodology for enabling the deployment of low-error deep networks on microcontrollers. To fit the memory and computational limitations of resource-constrained edge-devices, we exploit mixed low-bitwidth compression, featuring 8, 4 or 2-bit uniform quantization, and we model the inference graph with integer-only operations. Our approach aims at determining the minimum bit precision of every activation and weight tensor given the memory constraints of a device. This is achieved through a rule-based iterative procedure, which cuts the number of bits of the most memory-demanding layers, aiming at meeting the memory constraints. After a quantization-aware retraining step, the fake-quantized graph is converted into an inference integer-only model by inserting the Integer Channel-Normalization (ICN) layers, which introduce a negligible loss as demonstrated on INT4 MobilenetV1 models. We report the latency-accuracy evaluation of mixed-precision MobilenetV1 family networks on a STM32H7 microcontroller. Our experimental results demonstrate an end-to-end deployment of an integer-only Mobilenet network with Top1 accuracy of 68% on a device with only 2MB of FLASH memory and 512kB of RAM, improving by 8% the Top1 accuracy with respect to previously published 8 bit implementations for microcontrollers.Comment: Submitted to NeurIPS 201

Entropy-Constrained Training of Deep Neural Networks

We propose a general framework for neural network compression that is motivated by the Minimum Description Length (MDL) principle. For that we first derive an expression for the entropy of a neural network, which measures its complexity explicitly in terms of its bit-size. Then, we formalize the problem of neural network compression as an entropy-constrained optimization objective. This objective generalizes many of the compression techniques proposed in the literature, in that pruning or reducing the cardinality of the weight elements of the network can be seen special cases of entropy-minimization techniques. Furthermore, we derive a continuous relaxation of the objective, which allows us to minimize it using gradient based optimization techniques. Finally, we show that we can reach state-of-the-art compression results on different network architectures and data sets, e.g. achieving x71 compression gains on a VGG-like architecture.Comment: 8 pages, 6 figure

Value-aware Quantization for Training and Inference of Neural Networks

We propose a novel value-aware quantization which applies aggressively reduced precision to the majority of data while separately handling a small amount of large data in high precision, which reduces total quantization errors under very low precision. We present new techniques to apply the proposed quantization to training and inference. The experiments show that our method with 3-bit activations (with 2% of large ones) can give the same training accuracy as full-precision one while offering significant (41.6% and 53.7%) reductions in the memory cost of activations in ResNet-152 and Inception-v3 compared with the state-of-the-art method. Our experiments also show that deep networks such as Inception-v3, ResNet-101 and DenseNet-121 can be quantized for inference with 4-bit weights and activations (with 1% 16-bit data) within 1% top-1 accuracy drop

Granger Causality Analysis Based on Quantized Minimum Error Entropy Criterion

Linear regression model (LRM) based on mean square error (MSE) criterion is widely used in Granger causality analysis (GCA), which is the most commonly used method to detect the causality between a pair of time series. However, when signals are seriously contaminated by non-Gaussian noises, the LRM coefficients will be inaccurately identified. This may cause the GCA to detect a wrong causal relationship. Minimum error entropy (MEE) criterion can be used to replace the MSE criterion to deal with the non-Gaussian noises. But its calculation requires a double summation operation, which brings computational bottlenecks to GCA especially when sizes of the signals are large. To address the aforementioned problems, in this study we propose a new method called GCA based on the quantized MEE (QMEE) criterion (GCA-QMEE), in which the QMEE criterion is applied to identify the LRM coefficients and the quantized error entropy is used to calculate the causality indexes. Compared with the traditional GCA, the proposed GCA-QMEE not only makes the results more discriminative, but also more robust. Its computational complexity is also not high because of the quantization operation. Illustrative examples on synthetic and EEG datasets are provided to verify the desirable performance and the availability of the GCA-QMEE.Comment: 5 pages, 2 figures, 3 table

ReLeQ: A Reinforcement Learning Approach for Deep Quantization of Neural Networks

Deep Neural Networks (DNNs) typically require massive amount of computation resource in inference tasks for computer vision applications. Quantization can significantly reduce DNN computation and storage by decreasing the bitwidth of network encodings. Recent research affirms that carefully selecting the quantization levels for each layer can preserve the accuracy while pushing the bitwidth below eight bits. However, without arduous manual effort, this deep quantization can lead to significant accuracy loss, leaving it in a position of questionable utility. As such, deep quantization opens a large hyper-parameter space (bitwidth of the layers), the exploration of which is a major challenge. We propose a systematic approach to tackle this problem, by automating the process of discovering the quantization levels through an end-to-end deep reinforcement learning framework (ReLeQ). We adapt policy optimization methods to the problem of quantization, and focus on finding the best design decisions in choosing the state and action spaces, network architecture and training framework, as well as the tuning of various hyperparamters. We show how ReLeQ can balance speed and quality, and provide an asymmetric general solution for quantization of a large variety of deep networks (AlexNet, CIFAR-10, LeNet, MobileNet-V1, ResNet-20, SVHN, and VGG-11) that virtually preserves the accuracy (=< 0.3% loss) while minimizing the computation and storage cost. With these DNNs, ReLeQ enables conventional hardware to achieve 2.2x speedup over 8-bit execution. Similarly, a custom DNN accelerator achieves 2.0x speedup and energy reduction compared to 8-bit runs. These encouraging results mark ReLeQ as the initial step towards automating the deep quantization of neural networks.Comment: Presented as a spotlight paper at NeurIPS Workshop on ML for Systems 201