Low-bit Quantization of Neural Networks for Efficient Inference

arXiv (Cornell University), 2022

Recent advancements in machine learning achieved by Deep Neural Networks (DNNs) have been significant. While demonstrating high accuracy, DNNs are associated with a huge number of parameters and computation, which leads to high memory usage and energy consumption. As a result, deploying of DNNs on devices with constrained hardware resources poses significant challenges. To overcome this, various compression techniques have been widely employed to optimize DNN accelerators. A promising approach is quantization, in which the full-precision values are stored in low bit-width precision. Quantization not only reduces memory requirements but also replaces high-cost operations with low-cost ones. DNN quantization offers flexibility and efficiency in hardware design, making it a widely adopted technique in various methods. Since quantization has been extensively utilized in previous works, there is a need for an integrated report that provides an understanding, analysis, and comparison of different quantization approaches. Consequently, we present a comprehensive survey of quantization concepts and methods, with a focus on image classification. We describe clustering-based quantization methods and explore the use of a scale factor parameter for approximating full-precision values. Moreover, we thoroughly review the training of quantized DNN, including the use of straight-through estimator and quantized regularization. We explain the replacement of floating-point operations with low-cost bitwise operations in a quantized DNN and the sensitivity of different layers in quantization. Furthermore, we highlight the evaluation metrics for quantized methods and important benchmarks in image classification task. We also present the accuracy of the state-of-the-art methods on CIFAR-10 and ImageNet. This paper attempts to make the readers familiar with the basic and advanced concepts of quantization, introduce important works in DNN quantization, and highlight challenges for future research in this field.

ArXiv, 2019

This paper addresses a challenging problem - how to reduce energy consumption without incurring performance drop when deploying deep neural networks (DNNs) at the inference stage. In order to alleviate the computation and storage burdens, we propose a novel dataflow-based joint quantization approach with the hypothesis that a fewer number of quantization operations would incur less information loss and thus improve the final performance. It first introduces a quantization scheme with efficient bit-shifting and rounding operations to represent network parameters and activations in low precision. Then it restructures the network architectures to form unified modules for optimization on the quantized model. Extensive experiments on ImageNet and KITTI validate the effectiveness of our model, demonstrating that state-of-the-art results for various tasks can be achieved by this quantized model. Besides, we designed and synthesized an RTL model to measure the hardware costs among various q...

2019

Convolutional neural networks require significant memory bandwidth and storage for intermediate computations, apart from substantial computing resources. Neural network quantization has significant benefits in reducing the amount of intermediate results, but it often requires the full datasets and time-consuming fine tuning to recover the accuracy lost after quantization. This paper introduces the first practical 4-bit post training quantization approach: it does not involve training the quantized model (fine-tuning), nor it requires the availability of the full dataset. We target the quantization of both activations and weights and suggest three complementary methods for minimizing quantization error at the tensor level, two of whom obtain a closed-form analytical solution. Combining these methods, our approach achieves accuracy that is just a few percents less the state-of-the-art baseline across a wide range of convolutional models. The source code to replicate all experiments is...

2021

Quantizing deep networks with adaptive bit-widths is a promising technique for efficient inference across many devices and resource constraints. In contrast to static methods that repeat the quantization process and train different models for different constraints, adaptive quantization enables us to flexibly adjust the bit-widths of a single deep network during inference for instant adaptation in different scenarios. While existing research shows encouraging results on common image classification benchmarks, this paper investigates how to train such adaptive networks more effectively. Specifically, we present two novel techniques for quantizing deep neural networks with adaptive bit-widths of weights and activations. First, we propose a collaborative strategy to choose a high-precision “teacher” for transferring knowledge to the low-precision “student” while jointly optimizing the model with all bit-widths. Second, to effectively transfer knowledge, we develop a dynamic block swapp...

2022 Design, Automation & Test in Europe Conference & Exhibition (DATE)

Large DNNs with mixed-precision quantization can achieve ultra-high compression while retaining high classification performance. However, because of the challenges in finding an accurate metric that can guide the optimization process, these methods either sacrifice significant performance compared to the 32-bit floating-point (FP-32) baseline or rely on a computeexpensive, iterative training policy that requires the availability of a pre-trained baseline. To address this issue, this paper presents BMPQ, a training method that uses bit gradients to analyze layer sensitivities and yield mixed-precision quantized models. BMPQ requires a single training iteration but does not need a pre-trained baseline. It uses an integer linear program (ILP) to dynamically adjust the precision of layers during training, subject to a fixed hardware budget. To evaluate the efficacy of BMPQ, we conduct extensive experiments with VGG16 and ResNet18 on CIFAR-10, CIFAR-100, and Tiny-ImageNet datasets. Compared to the baseline FP-32 models, BMPQ can yield models that have 15.4× fewer parameter bits with negligible drop in accuracy. Compared to the SOTA "during training", mixed-precision training scheme, our models are 2.1×, 2.2×, and 2.9× smaller, on CIFAR-10, CIFAR-100, and Tiny-ImageNet, respectively, with an improved accuracy of up to 14.54%. Index Terms-Mixed-precision quantization, model compression, energy-efficient DNN training, one-shot quantization † This work was supported in parts by NSF and DARPA with grant numbers 1763747 and HR00112190120, respectively. 1 All layer weights/activations have the same bit widths.

2020

In this paper, we propose a number of novel techniques and numerical representation formats that enable, for the very first time, the precision of training systems to be aggressively scaled from 8-bits to 4-bits. To enable this advance, we explore a novel adaptive Gradient Scaling technique (GradScale) that addresses the challenges of insufficient range and resolution in quantized gradients as well as explores the impact of quantization errors observed during model training. We theoretically analyze the role of bias in gradient quantization and propose solutions that mitigate the impact of this bias on model convergence. Finally, we examine our techniques on a spectrum of deep learning models in computer vision, speech and NLP. In combination with previously proposed solutions for 4-bit quantization of weight and activation tensors, 4-bit training shows non-significant loss in accuracy across application domains while enabling significant hardware acceleration (>7× over state of ...

ArXiv, 2017

This paper presents incremental network quantization (INQ), a novel method, targeting to efficiently convert any pre-trained full-precision convolutional neural network (CNN) model into a low-precision version whose weights are constrained to be either powers of two or zero. Unlike existing methods which are struggled in noticeable accuracy loss, our INQ has the potential to resolve this issue, as benefiting from two innovations. On one hand, we introduce three interdependent operations, namely weight partition, group-wise quantization and re-training. A well-proven measure is employed to divide the weights in each layer of a pre-trained CNN model into two disjoint groups. The weights in the first group are responsible to form a low-precision base, thus they are quantized by a variable-length encoding method. The weights in the other group are responsible to compensate for the accuracy loss from the quantization, thus they are the ones to be re-trained. On the other hand, these thre...

ArXiv, 2018

Unlike traditional approaches that focus on the quantization at the network level, in this work we propose to minimize the quantization effect at the tensor level. We analyze the trade-off between quantization noise and clipping distortion in low precision networks. We identify the statistics of various tensors, and derive exact expressions for the mean-square-error degradation due to clipping. By optimizing these expressions, we show marked improvements over standard quantization schemes that normally avoid clipping. For example, just by choosing the accurate clipping values, more than 40\% accuracy improvement is obtained for the quantization of VGG16-BN to 4-bits of precision. Our results have many applications for the quantization of neural networks at both training and inference time. One immediate application is for a rapid deployment of neural networks to low-precision accelerators without time-consuming fine tuning or the availability of the full datasets.

2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2018

Inference for state-of-the-art deep neural networks is computationally expensive, making them difficult to deploy on constrained hardware environments. An efficient way to reduce this complexity is to quantize the weight parameters and/or activations during training by approximating their distributions with a limited entry codebook. For very low-precisions, such as binary or ternary networks with 1-8-bit activations, the information loss from quantization leads to significant accuracy degradation due to large gradient mismatches between the forward and backward functions. In this paper, we introduce a quantization method to reduce this loss by learning a symmetric codebook for particular weight subgroups. These subgroups are determined based on their locality in the weight matrix, such that the hardware simplicity of the low-precision representations is preserved. Empirically, we show that symmetric quantization can substantially improve accuracy for networks with extremely low-precision weights and activations. We also demonstrate that this representation imposes minimal or no hardware implications to more coarse-grained approaches.

2021 IEEE International Symposium on High-Performance Computer Architecture (HPCA), 2021

Deep Neural Networks (DNNs) have achieved extraordinary performance in various application domains. To support diverse DNN models, efficient implementations of DNN inference on edge-computing platforms, e.g., ASICs, FPGAs, and embedded systems, are extensively investigated. Due to the huge model size and computation amount, model compression is a critical step to deploy DNN models on edge devices. This paper focuses on weight quantization, a hardware-friendly model compression approach that is complementary to weight pruning. Unlike existing methods that use the same quantization scheme for all weights, we propose the first solution that applies different quantization schemes for different rows of the weight matrix. It is motivated by (1) the distribution of the weights in the different rows are not the same; and (2) the potential of achieving better utilization of heterogeneous FPGA hardware resources. To achieve that, we first propose a hardware-friendly quantization scheme named sum-of-power-of-2 (SP2) suitable for Gaussianlike weight distribution, in which the multiplication arithmetic can be replaced with logic shifter and adder, thereby enabling highly efficient implementations with the FPGA LUT resources. In contrast, the existing fixed-point quantization is suitable for Uniform-like weight distribution and can be implemented efficiently by DSP. Then to fully explore the resources, we propose an FPGA-centric mixed scheme quantization (MSQ) with an ensemble of the proposed SP2 and the fixed-point schemes. Combining the two schemes can maintain, or even increase accuracy due to better matching with weight distributions. For the FPGA implementations, we develop a parameterized architecture with heterogeneous Generalized Matrix Multiplication (GEMM) cores-one using LUTs for computations with SP2 quantized weights and the other utilizing DSPs for fixedpoint quantized weights. Given the partition ratio among the two schemes based on resource characterization, MSQ quantization training algorithm derives an optimally quantized model for the FPGA implementation. We evaluate our FPGA-centric quantization framework across multiple application domains. With optimal SP2/fixed-point ratios on two FPGA devices, i.e., Zynq XC7Z020 and XC7Z045, we achieve performance improvement of 2.1 × −4.1× compared to solely exploiting DSPs for all multiplication operations. In addition, the CNN implementations with the proposed MSQ scheme can achieve higher accuracy and comparable hardware utilization efficiency compared to the state-of-the-art designs.

2018

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 tradit...

2024

Large-scale deep neural networks (DNNs) have achieved remarkable success in many application scenarios. However, high computational complexity and energy costs of modern DNNs make their deployment on edge devices challenging. Model quantization is a common approach to deal with deployment constraints, but searching for optimized bit-widths can be challenging. In this work, we present Adaptive Bit-Width Quantization Aware Training (AdaQAT), a learning-based method that automatically optimizes weight and activation signal bit-widths during training for more efficient DNN inference. We use relaxed real-valued bitwidths that are updated using a gradient descent rule, but are otherwise discretized for all quantization operations. The result is a simple and flexible QAT approach for mixed-precision uniform quantization problems. Compared to other methods that are generally designed to be run on a pretrained network, AdaQAT works well in both training from scratch and fine-tuning scenarios. Initial results on the CIFAR-10 and ImageNet datasets using ResNet20 and ResNet18 models, respectively, indicate that our method is competitive with other state-of-the-art mixed-precision quantization approaches.

Cornell University - arXiv, 2022

Deep Learning has been one of the most disruptive technological advancements in recent times. The high performance of deep learning models comes at the expense of high computational, storage and power requirements. Sensing the immediate need for accelerating and compressing these models to improve on-device performance, we introduce Deeplite Neutrino for production-ready optimization of the models and Deeplite Runtime for deployment of ultra-low bit quantized models on Arm-based platforms. We implement low-level quantization kernels for Armv7 and Armv8 architectures enabling deployment on the vast array of 32-bit and 64-bit Arm-based devices. With efficient implementations using vectorization, parallelization, and tiling, we realize speedups of up to 2x and 2.2x compared to TensorFlow Lite with XNNPACK backend on classification and detection models, respectively. We also achieve significant speedups of up to 5x and 3.2x compared to ONNX Runtime for classification and detection models, respectively.

arXiv (Cornell University), 2019

Effective employment of deep neural networks (DNNs) in mobile devices and embedded systems is hampered by requirements for memory and computational power. This paper presents a non-uniform quantization approach which allows for dynamic quantization of DNN parameters for different layers and within the same layer. A virtual bit shift (VBS) scheme is also proposed to improve the accuracy of the proposed scheme. Our method reduces the memory requirements, preserving the performance of the network. The performance of our method is validated in a speech enhancement application, where a fully connected DNN is used to predict the clean speech spectrum from the input noisy speech spectrum. A DNN is optimized and its memory footprint and performance are evaluated using the short-time objective intelligibility, STOI, metric. The application of the low-bit quantization allows a 50% reduction of the DNN memory footprint while the STOI performance drops only by 2.7%.

IEEE Micro

Deep Quantization (below eight bits) can significantly reduce DNN computation and storage by decreasing the bitwidth of network encodings. However, without arduous manual effort, this deep quantization can lead to significant accuracy loss, leaving it in a position of questionable utility. We propose a systematic approach to tackle this problem, by automating the process of discovering the bitwidths through an end-to-end deep reinforcement learning framework (RELEQ). This framework utilizes the sample efficiency of Proximal Policy Optimization (PPO) to explore the exponentially large space of possible assignment of the bitwidths to the layers. We show how RELEQ can balance speed and quality, and provide a heterogeneous bitwidth assignment for quantization of a large variety of deep networks with minimal accuracy loss (≤ 0.3% loss) while minimizing the computation and storage costs. With these DNNs, RELEQ enables conventional hardware and custom DNN accelerator to achieve 2.2× speedup over 8-bit execution.