Learning Accurate Low-Bit Deep Neural Networks with Stochastic Quantization

Low-bit deep neural networks (DNNs) become critical for embedded applications due to their low storage requirement and computing efficiency. However, they suffer much from the non-negligible accuracy drop. This paper proposes the stochastic quantization (SQ) algorithm for learning accurate low-bit DNNs. The motivation is due to the following observation. Existing training algorithms approximate the real-valued elements/filters with low-bit representation all together in each iteration. The quantization errors may be small for some elements/filters, while are remarkable for others, which lead to inappropriate gradient direction during training, and thus bring notable accuracy drop. Instead, SQ quantizes a portion of elements/filters to low-bit with a stochastic probability inversely proportional to the quantization error, while keeping the other portion unchanged with full-precision. The quantized and full-precision portions are updated with corresponding gradients separately in each iteration. The SQ ratio is gradually increased until the whole network is quantized. This procedure can greatly compensate the quantization error and thus yield better accuracy for low-bit DNNs. Experiments show that SQ can consistently and significantly improve the accuracy for different low-bit DNNs on various datasets and various network structures.Comment: BMVC 2017 Ora

Progressive Stochastic Binarization of Deep Networks

A plethora of recent research has focused on improving the memory footprint and inference speed of deep networks by reducing the complexity of (i) numerical representations (for example, by deterministic or stochastic quantization) and (ii) arithmetic operations (for example, by binarization of weights). We propose a stochastic binarization scheme for deep networks that allows for efficient inference on hardware by restricting itself to additions of small integers and fixed shifts. Unlike previous approaches, the underlying randomized approximation is progressive, thus permitting an adaptive control of the accuracy of each operation at run-time. In a low-precision setting, we match the accuracy of previous binarized approaches. Our representation is unbiased - it approaches continuous computation with increasing sample size. In a high-precision regime, the computational costs are competitive with previous quantization schemes. Progressive stochastic binarization also permits localized, dynamic accuracy control within a single network, thereby providing a new tool for adaptively focusing computational attention. We evaluate our method on networks of various architectures, already pretrained on ImageNet. With representational costs comparable to previous schemes, we obtain accuracies close to the original floating point implementation. This includes pruned networks, except the known special case of certain types of separated convolutions. By focusing computational attention using progressive sampling, we reduce inference costs on ImageNet further by a factor of up to 33% (before network pruning)

Mixed Precision Quantization of ConvNets via Differentiable Neural Architecture Search

Recent work in network quantization has substantially reduced the time and space complexity of neural network inference, enabling their deployment on embedded and mobile devices with limited computational and memory resources. However, existing quantization methods often represent all weights and activations with the same precision (bit-width). In this paper, we explore a new dimension of the design space: quantizing different layers with different bit-widths. We formulate this problem as a neural architecture search problem and propose a novel differentiable neural architecture search (DNAS) framework to efficiently explore its exponential search space with gradient-based optimization. Experiments show we surpass the state-of-the-art compression of ResNet on CIFAR-10 and ImageNet. Our quantized models with 21.1x smaller model size or 103.9x lower computational cost can still outperform baseline quantized or even full precision models

Scalable Methods for 8-bit Training of Neural Networks

Quantized Neural Networks (QNNs) are often used to improve network efficiency during the inference phase, i.e. after the network has been trained. Extensive research in the field suggests many different quantization schemes. Still, the number of bits required, as well as the best quantization scheme, are yet unknown. Our theoretical analysis suggests that most of the training process is robust to substantial precision reduction, and points to only a few specific operations that require higher precision. Armed with this knowledge, we quantize the model parameters, activations and layer gradients to 8-bit, leaving at a higher precision only the final step in the computation of the weight gradients. Additionally, as QNNs require batch-normalization to be trained at high precision, we introduce Range Batch-Normalization (BN) which has significantly higher tolerance to quantization noise and improved computational complexity. Our simulations show that Range BN is equivalent to the traditional batch norm if a precise scale adjustment, which can be approximated analytically, is applied. To the best of the authors' knowledge, this work is the first to quantize the weights, activations, as well as a substantial volume of the gradients stream, in all layers (including batch normalization) to 8-bit while showing state-of-the-art results over the ImageNet-1K dataset

DFTerNet: Towards 2-bit Dynamic Fusion Networks for Accurate Human Activity Recognition

Deep Convolutional Neural Networks (DCNNs) are currently popular in human activity recognition applications. However, in the face of modern artificial intelligence sensor-based games, many research achievements cannot be practically applied on portable devices. DCNNs are typically resource-intensive and too large to be deployed on portable devices, thus this limits the practical application of complex activity detection. In addition, since portable devices do not possess high-performance Graphic Processing Units (GPUs), there is hardly any improvement in Action Game (ACT) experience. Besides, in order to deal with multi-sensor collaboration, all previous human activity recognition models typically treated the representations from different sensor signal sources equally. However, distinct types of activities should adopt different fusion strategies. In this paper, a novel scheme is proposed. This scheme is used to train 2-bit Convolutional Neural Networks with weights and activations constrained to {-0.5,0,0.5}. It takes into account the correlation between different sensor signal sources and the activity types. This model, which we refer to as DFTerNet, aims at producing a more reliable inference and better trade-offs for practical applications. Our basic idea is to exploit quantization of weights and activations directly in pre-trained filter banks and adopt dynamic fusion strategies for different activity types. Experiments demonstrate that by using dynamic fusion strategy can exceed the baseline model performance by up to ~5% on activity recognition like OPPORTUNITY and PAMAP2 datasets. Using the quantization method proposed, we were able to achieve performances closer to that of full-precision counterpart. These results were also verified using the UniMiB-SHAR dataset. In addition, the proposed method can achieve ~9x acceleration on CPUs and ~11x memory saving.Comment: 19 pages, 5 figures, 6 tables, accepted by IEEE Acces

LQ-Nets: Learned Quantization for Highly Accurate and Compact Deep Neural Networks

Although weight and activation quantization is an effective approach for Deep Neural Network (DNN) compression and has a lot of potentials to increase inference speed leveraging bit-operations, there is still a noticeable gap in terms of prediction accuracy between the quantized model and the full-precision model. To address this gap, we propose to jointly train a quantized, bit-operation-compatible DNN and its associated quantizers, as opposed to using fixed, handcrafted quantization schemes such as uniform or logarithmic quantization. Our method for learning the quantizers applies to both network weights and activations with arbitrary-bit precision, and our quantizers are easy to train. The comprehensive experiments on CIFAR-10 and ImageNet datasets show that our method works consistently well for various network structures such as AlexNet, VGG-Net, GoogLeNet, ResNet, and DenseNet, surpassing previous quantization methods in terms of accuracy by an appreciable margin. Code available at https://github.com/Microsoft/LQ-NetsComment: ECCV'18 (European Conference on Computer Vision); Main paper + suppl. materia

Overcoming Challenges in Fixed Point Training of Deep Convolutional Networks

It is known that training deep neural networks, in particular, deep convolutional networks, with aggressively reduced numerical precision is challenging. The stochastic gradient descent algorithm becomes unstable in the presence of noisy gradient updates resulting from arithmetic with limited numeric precision. One of the well-accepted solutions facilitating the training of low precision fixed point networks is stochastic rounding. However, to the best of our knowledge, the source of the instability in training neural networks with noisy gradient updates has not been well investigated. This work is an attempt to draw a theoretical connection between low numerical precision and training algorithm stability. In doing so, we will also propose and verify through experiments methods that are able to improve the training performance of deep convolutional networks in fixed point.Comment: ICML2016 - Workshop on On-Device Intelligenc

NICE: Noise Injection and Clamping Estimation for Neural Network Quantization

Convolutional Neural Networks (CNN) are very popular in many fields including computer vision, speech recognition, natural language processing, to name a few. Though deep learning leads to groundbreaking performance in these domains, the networks used are very demanding computationally and are far from real-time even on a GPU, which is not power efficient and therefore does not suit low power systems such as mobile devices. To overcome this challenge, some solutions have been proposed for quantizing the weights and activations of these networks, which accelerate the runtime significantly. Yet, this acceleration comes at the cost of a larger error. The \uniqname method proposed in this work trains quantized neural networks by noise injection and a learned clamping, which improve the accuracy. This leads to state-of-the-art results on various regression and classification tasks, e.g., ImageNet classification with architectures such as ResNet-18/34/50 with low as 3-bit weights and activations. We implement the proposed solution on an FPGA to demonstrate its applicability for low power real-time applications. The implementation of the paper is available at https://github.com/Lancer555/NIC

Learned Step Size Quantization

Deep networks run with low precision operations at inference time offer power and space advantages over high precision alternatives, but need to overcome the challenge of maintaining high accuracy as precision decreases. Here, we present a method for training such networks, Learned Step Size Quantization, that achieves the highest accuracy to date on the ImageNet dataset when using models, from a variety of architectures, with weights and activations quantized to 2-, 3- or 4-bits of precision, and that can train 3-bit models that reach full precision baseline accuracy. Our approach builds upon existing methods for learning weights in quantized networks by improving how the quantizer itself is configured. Specifically, we introduce a novel means to estimate and scale the task loss gradient at each weight and activation layer's quantizer step size, such that it can be learned in conjunction with other network parameters. This approach works using different levels of precision as needed for a given system and requires only a simple modification of existing training code.Comment: International Conference on Learning Representations (2020

SWALP : Stochastic Weight Averaging in Low-Precision Training

Low precision operations can provide scalability, memory savings, portability, and energy efficiency. This paper proposes SWALP, an approach to low precision training that averages low-precision SGD iterates with a modified learning rate schedule. SWALP is easy to implement and can match the performance of full-precision SGD even with all numbers quantized down to 8 bits, including the gradient accumulators. Additionally, we show that SWALP converges arbitrarily close to the optimal solution for quadratic objectives, and to a noise ball asymptotically smaller than low precision SGD in strongly convex settings.Comment: Published at ICML 201