Reducing the precision of weights and activation functions in neural network training, with minimal impact on performance, is essential for the deployment of these models in resource-constrained environments. We apply mean-field techniques to networks with quantized activations in order to evaluate the degree to which quantization degrades signal propagation at initialization. We derive initialization schemes which maximize signal propagation in such networks and suggest why this is helpful for generalization. Building on these results, we obtain a closed form implicit equation for $L_{\max}$, the maximal trainable depth (and hence model capacity), given $N$, the number of quantization levels in the activation function. Solving this equation numerically, we obtain asymptotically: $L_{\max}\propto N^{1.82}$.
Layer-wise Quantization for Quantized Optimistic Dual Averaging
National University of Singapore (NUS)（新加坡国立大学）；EPFL（洛桑联邦理工学院）；Neural Magic；University of Oslo (UiO)（奥斯陆大学）；Integreat, Norwegian Centre for Knowledge-driven Machine Learning（挪威知识驱动机器学习中心）；Institute of Science and Technology Austria (ISTA)（奥地利科学技术研究所）
Marvell Technology Inc.（美满科技公司）；Nokia Solutions and Networks Oy（诺基亚解决方案与网络公司）；Nokia of America Corporation（诺基亚美国公司）；Nokia Solutions and Networks Sp. z o.o.（诺基亚解决方案与网络有限责任公司）；Nokia Paris Saclay（诺基亚巴黎萨克雷（此处保留英文原名，因“Paris Saclay”是地名相关，中文常不直译机构名，按原文处理））
This paper presents a methodology to separate the quantization process from the hardware-specific model compilation stage via a pre-quantized deep learning model description in standard ONNX format. Separating the quantization process from the model compilation stage enables independent development. The methodology is expressive to convey hardware-specific operations and to embed key quantization parameters into a ONNX model which enables hardware/software co-design. Detailed examples are given for both MLP and CNN based networks, which can be extended to other networks in a straightforward fa…
We present a novel technique, called Term Revealing (TR), for furthering quantization at run time for improved performance of Deep Neural Networks (DNNs) already quantized with conventional quantization methods. TR operates on power-of-two terms in binary expressions of values. In computing a dot-product computation, TR dynamically selects a fixed number of largest terms to use from the values of the two vectors in the dot product. By exploiting normal-like weight and data distributions typically present in DNNs, TR has a minimal impact on DNN model performance (i.e., accuracy or perplexity). …
Quantized deep neural networks (QDNNs) are necessary for low-power, high throughput, and embedded applications. Previous studies mostly focused on developing optimization methods for the quantization of given models. However, quantization sensitivity depends on the model architecture. Therefore, the model selection needs to be a part of the QDNN design process. Also, the characteristics of weight and activation quantization are quite different. This study proposes a holistic approach for the optimization of QDNNs, which contains QDNN training methods as well as quantization-friendly architectu…
Memory-augmented neural networks (MANNs) refer to a class of neural network models equipped with external memory (such as neural Turing machines and memory networks). These neural networks outperform conventional recurrent neural networks (RNNs) in terms of learning long-term dependency, allowing them to solve intriguing AI tasks that would otherwise be hard to address. This paper concerns the problem of quantizing MANNs. Quantization is known to be effective when we deploy deep models on embedded systems with limited resources. Furthermore, quantization can substantially reduce the energy con…
The number of parameters in deep neural networks (DNNs) is rapidly increasing to support complicated tasks and to improve model accuracy. Correspondingly, the amount of computations and required memory footprint increase as well. Quantization is an efficient method to address such concerns by compressing DNNs such that computations can be simplified while required storage footprint is significantly reduced. Unfortunately, commercial CPUs and GPUs do not fully support quantization because only fixed data transfers (such as 32 bits) are allowed. As a result, even if weights are quantized into a …
Stanford University（斯坦福大学）；Amazon AI（亚马逊人工智能）；UC Santa Barbara（加州大学圣巴巴拉分校）
To make deep neural networks feasible in resource-constrained environments (such as mobile devices), it is beneficial to quantize models by using low-precision weights. One common technique for quantizing neural networks is the straight-through gradient method, which enables back-propagation through the quantization mapping. Despite its empirical success, little is understood about why the straight-through gradient method works. Building upon a novel observation that the straight-through gradient method is in fact identical to the well-known Nesterov's dual-averaging algorithm on a quantizatio…
Deep quantization of neural networks (below eight bits) offers significant promise in reducing their compute and storage cost. Albeit alluring, without special techniques for training and optimization, deep quantization results in significant accuracy loss. To further mitigate this loss, we propose a novel sinusoidal regularization, called SinReQ1, for deep quantized training. SinReQ adds a periodic term to the original objective function of the underlying training algorithm. SinReQ exploits the periodicity, differentiability, and the desired convexity profile in sinusoidal functions to automa…
The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；JD Explore Academy（京东探索研究院）；Tencent AI Lab（腾讯人工智能实验室）；Tencent（腾讯）
In this paper, we present a distributed variant of adaptive stochastic gradient method for training deep neural networks in the parameter-server model. To reduce the communication cost among the workers and server, we incorporate two types of quantization schemes, i.e., gradient quantization and weight quantization, into the proposed distributed Adam. Besides, to reduce the bias introduced by quantization operations, we propose an error-feedback technique to compensate for the quantized gradient. Theoretically, in the stochastic nonconvex setting, we show that the distributed adaptive gradient…
INT8 quantization has become one of the standard techniques for deploying convolutional neural networks (CNNs) on edge devices to reduce the memory and computational resource usages. By analyzing quantized performances of existing mobile-target network architectures, we can raise an issue regarding the importance of network architecture for optimal INT8 quantization. In this paper, we present a new network architecture search (NAS) procedure to find a network that guarantees both full-precision (FLOAT32) and quantized (INT8) performances. We first propose critical but straightforward optimizat…
Due to its efficiency and ease to implement, stochastic gradient descent (SGD) has been widely used in machine learning. In particular, SGD is one of the most popular optimization methods for distributed learning. Recently, quantized SGD (QSGD), which adopts quantization to reduce the communication cost in SGD-based distributed learning, has attracted much attention. Although several QSGD methods have been proposed, some of them are heuristic without theoretical guarantee, and others have high quantization variance which makes the convergence become slow. In this paper, we propose a new method…
Artificial Intelligence Research Lab（人工智能研究实验室）；Fit-For-Purpose Technologies
Accelerating deep neural network (DNN) inference on resource-limited devices is one of the most important barriers to ensuring a wider and more inclusive adoption. To alleviate this, DNN binary quantization for faster convolution and memory savings is one of the most promising strategies despite its serious drop in accuracy. The present paper therefore proposes a novel binary quantization function based on quantized compressed sensing (QCS). Theoretical arguments conjecture that our proposal preserves the practical benefits of standard methods, while reducing the quantization error and the res…
A popular approach to learning encoders for lossy compression is to use additive uniform noise during training as a differentiable approximation to test-time quantization. We demonstrate that a uniform noise channel can also be implemented at test time using universal quantization (Ziv, 1985). This allows us to eliminate the mismatch between training and test phases while maintaining a completely differentiable loss function. Implementing the uniform noise channel is a special case of the more general problem of communicating a sample, which we prove is computationally hard if we do not make a…
We formulate the notion of minimax estimation under storage or communication constraints, and prove an extension to Pinsker's theorem for nonparametric estimation over Sobolev ellipsoids. Placing limits on the number of bits used to encode any estimator, we give tight lower and upper bounds on the excess risk due to quantization in terms of the number of bits, the signal size, and the noise level. This establishes the Pareto optimal tradeoff between storage and risk under quantization constraints for Sobolev spaces. Our results and proof techniques combine elements of rate distortion theory an…
