Quantization enables efficient acceleration of deep neural networks by reducing model memory footprint and exploiting low-cost integer math hardware units. Quantization maps floating-point weights and activations in a trained model to low-bitwidth integer values using scale factors. Excessive quantization, reducing precision too aggressively, results in accuracy degradation. When scale factors are shared at a coarse granularity across many dimensions of each tensor, effective precision of individual elements within the tensor are limited. To reduce quantization-related accuracy loss, we propose using a separate scale factor for each small vector of ($\approx$16-64) elements within a single dimension of a tensor. To achieve an efficient hardware implementation, the per-vector scale factors can be implemented with low-bitwidth integers when calibrated using a two-level quantization scheme. We find that per-vector scaling consistently achieves better inference accuracy at low precision compared to conventional scaling techniques for popular neural networks without requiring retraining. We also modify a deep learning accelerator hardware design to study the area and energy overheads of per-vector scaling support. Our evaluation demonstrates that per-vector scaled quantization with 4-bit weights and activations achieves 37% area saving and 24% energy saving while maintaining over 75% accuracy for ResNet50 on ImageNet. 4-bit weights and 8-bit activations achieve near-full-precision accuracy for both BERT-base and BERT-large on SQuAD while reducing area by 26% compared to an 8-bit baseline.
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…
Quantization of neural networks has become common practice, driven by the need for efficient implementations of deep neural networks on embedded devices. In this paper, we exploit an oft-overlooked degree of freedom in most networks - for a given layer, individual output channels can be scaled by any factor provided that the corresponding weights of the next layer are inversely scaled. Therefore, a given network has many factorizations which change the weights of the network without changing its function. We present a conceptually simple and easy to implement method that uses this property and…
Modern approaches for fast retrieval of similar vectors on billion-scaled datasets rely on compressed-domain approaches such as binary sketches or product quantization. These methods minimize a certain loss, typically the mean squared error or other objective functions tailored to the retrieval problem. In this paper, we re-interpret popular methods such as binary hashing or product quantizers as auto-encoders, and point out that they implicitly make suboptimal assumptions on the form of the decoder. We design backward-compatible decoders that improve the reconstruction of the vectors from the…
Quantization is emerging as an efficient approach to promote hardware-friendly deep learning and run deep neural networks on resource-limited hardware. However, it still causes a significant decrease to the network in accuracy. We summarize challenges of quantization into two categories: Quantization for Diverse Architectures and Quantization on Complex Scenes. Our studies focus mainly on applying quantization on various architectures and scenes and pushing the limit of quantization to extremely compress and accelerate networks. The comprehensive research on quantization will achieve more powe…
Center for Energy-Efficient Computing and Applications, Peking University（北京大学高能效计算与应用中心）；Houmo AI（后摩智能）
Network quantization is a powerful technique to compress convolutional neural networks. The quantization granularity determines how to share the scaling factors in weights, which affects the performance of network quantization. Most existing approaches share the scaling factors layerwisely or channelwisely for quantization of convolutional layers. Channelwise quantization and layerwise quantization have been widely used in various applications. However, other quantization granularities are rarely explored. In this paper, we will explore the sub-layerwise granularity that shares the scaling fac…
Vector quantization (VQ) techniques are widely used in similarity search for data compression, fast metric computation and etc. Originally designed for Euclidean distance, existing VQ techniques (e.g., PQ, AQ) explicitly or implicitly minimize the quantization error. In this paper, we present a new angle to analyze the quantization error, which decomposes the quantization error into norm error and direction error. We show that quantization errors in norm have much higher influence on inner products than quantization errors in direction, and small quantization error does not necessarily lead to…
Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院）；AITRICS
Network quantization, which aims to reduce the bit-lengths of the network weights and activations, has emerged for their deployments to resource-limited devices. Although recent studies have successfully discretized a full-precision network, they still incur large quantization errors after training, thus giving rise to a significant performance gap between a full-precision network and its quantized counterpart. In this work, we propose a novel quantization method for neural networks, Cluster-Promoting Quantization (CPQ) that finds the optimal quantization grids while naturally encouraging the …
Intel – Artificial Intelligence Products Group (AIPG)（英特尔——人工智能产品集团（AIPG））；Technion – Israel Institute of Technology（以色列理工学院）
Neural network quantization enables the deployment of large models on resource-constrained devices. Current post-training quantization methods fall short in terms of accuracy for INT4 (or lower) but provide reasonable accuracy for INT8 (or above). In this work, we study the effect of quantization on the structure of the loss landscape. Additionally, we show that the structure is flat and separable for mild quantization, enabling straightforward post-training quantization methods to achieve good results. We show that with more aggressive quantization, the loss landscape becomes highly non-separ…
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 …
Shanghai Jiao Tong University（上海交通大学）；Qualcomm AI Research（高通人工智能研究院）
Network quantization is an effective method for the deployment of neural networks on memory and energy constrained mobile devices. In this paper, we propose a Dynamic Network Quantization (DNQ) framework which is composed of two modules: a bit-width controller and a quantizer. Unlike most existing quantization methods that use a universal quantization bit-width for the whole network, we utilize policy gradient to train an agent to learn the bit-width of each layer by the bit-width controller. This controller can make a trade-off between accuracy and compression ratio. Given the quantization bi…
Shanghai Jiao Tong University（上海交通大学）；University of Chinese Academy of Sciences（中国科学院大学）
Network quantization is an effective solution to compress deep neural networks for practical usage. Existing network quantization methods cannot sufficiently exploit the depth information to generate low-bit compressed network. In this paper, we propose two novel network quantization approaches, single-level network quantization (SLQ) for high-bit quantization and multi-level network quantization (MLQ) for extremely low-bit quantization (ternary).We are the first to consider the network quantization from both width and depth level. In the width level, parameters are divided into two parts: one…
The University of Hong Kong（香港大学）；CentraleSupélec（中央理工-高等电力学院）；University of Paris-Saclay（巴黎萨克雷大学）
Edge machine learning involves the deployment of learning algorithms at the wireless network edge so as to leverage massive mobile data for enabling intelligent applications. The mainstream edge learning approach, federated learning, has been developed based on distributed gradient descent. Based on the approach, stochastic gradients are computed at edge devices and then transmitted to an edge server for updating a global AI model. Since each stochastic gradient is typically high-dimensional (with millions to billions of coefficients), communication overhead becomes a bottleneck for edge learn…
Habana Labs – An Intel company（哈巴纳实验室——英特尔旗下公司）；Department of Electrical Engineering - Technion（以色列理工学院电气工程系）
Neural network quantization methods often involve simulating the quantization process during training, making the trained model highly dependent on the target bit-width and precise way quantization is performed. Robust quantization offers an alternative approach with improved tolerance to different classes of data-types and quantization policies. It opens up new exciting applications where the quantization process is not static and can vary to meet different circumstances and implementations. To address this issue, we propose a method that provides intrinsic robustness to the model against a b…
Network quantization is one of network compression techniques to reduce the redundancy of deep neural networks. It reduces the number of distinct network parameter values by quantization in order to save the storage for them. In this paper, we design network quantization schemes that minimize the performance loss due to quantization given a compression ratio constraint. We analyze the quantitative relation of quantization errors to the neural network loss function and identify that the Hessian-weighted distortion measure is locally the right objective function for the optimization of network q…
MoQE: Improve Quantization Model performance via Mixture of Quantization Experts
Beijing University of Posts and Telecommunications（北京邮电大学）；Institute of Computing Technology, Chinese Academy of Sciences（中国科学院计算技术研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Peng Cheng Laboratory（鹏城实验室）；North University of China（北方大学）
Neural network models are resource hungry. It is difficult to deploy such deep networks on devices with limited resources, like smart wearables, cellphones, drones, and autonomous vehicles. Low bit quantization such as binary and ternary quantization is a common approach to alleviate this resource requirements. Ternary quantization provides a more flexible model and outperforms binary quantization in terms of accuracy, however doubles the memory footprint and increases the computational cost. Contrary to these approaches, mixed quantized models allow a trade-off between accuracy and memory foo…
Quantization techniques applied to the inference of deep neural networks have enabled fast and efficient execution on resource-constraint devices. The success of quantization during inference has motivated the academic community to explore fully quantized training, i.e. quantizing back-propagation as well. However, effective gradient quantization is still an open problem. Gradients are unbounded and their distribution changes significantly during training, which leads to the need for dynamic quantization. As we show, dynamic quantization can lead to significant memory overhead and additional d…
