ARFeb 3, 2023Code
PDPU: An Open-Source Posit Dot-Product Unit for Deep Learning ApplicationsQiong Li, Chao Fang, Zhongfeng Wang
Posit has been a promising alternative to the IEEE-754 floating point format for deep learning applications due to its better trade-off between dynamic range and accuracy. However, hardware implementation of posit arithmetic requires further exploration, especially for the dot-product operations dominated in deep neural networks (DNNs). It has been implemented by either the combination of multipliers and an adder tree or cascaded fused multiply-add units, leading to poor computational efficiency and excessive hardware overhead. To address this issue, we propose an open-source posit dot-product unit, namely PDPU, that facilitates resource-efficient and high-throughput dot-product hardware implementation. PDPU not only features the fused and mixed-precision architecture that eliminates redundant latency and hardware resources, but also has a fine-grained 6-stage pipeline, improving computational efficiency. A configurable PDPU generator is further developed to meet the diverse needs of various DNNs for computational accuracy. Experimental results evaluated under the 28nm CMOS process show that PDPU reduces area, latency, and power by up to 43%, 64%, and 70%, respectively, compared to the existing implementations. Hence, PDPU has great potential as the computing core of posit-based accelerators for deep learning applications.
AROct 24, 2022Code
NASA: Neural Architecture Search and Acceleration for Hardware Inspired Hybrid NetworksHuihong Shi, Haoran You, Yang Zhao et al.
Multiplication is arguably the most cost-dominant operation in modern deep neural networks (DNNs), limiting their achievable efficiency and thus more extensive deployment in resource-constrained applications. To tackle this limitation, pioneering works have developed handcrafted multiplication-free DNNs, which require expert knowledge and time-consuming manual iteration, calling for fast development tools. To this end, we propose a Neural Architecture Search and Acceleration framework dubbed NASA, which enables automated multiplication-reduced DNN development and integrates a dedicated multiplication-reduced accelerator for boosting DNNs' achievable efficiency. Specifically, NASA adopts neural architecture search (NAS) spaces that augment the state-of-the-art one with hardware-inspired multiplication-free operators, such as shift and adder, armed with a novel progressive pretrain strategy (PGP) together with customized training recipes to automatically search for optimal multiplication-reduced DNNs; On top of that, NASA further develops a dedicated accelerator, which advocates a chunk-based template and auto-mapper dedicated for NASA-NAS resulting DNNs to better leverage their algorithmic properties for boosting hardware efficiency. Experimental results and ablation studies consistently validate the advantages of NASA's algorithm-hardware co-design framework in terms of achievable accuracy and efficiency tradeoffs. Codes are available at https://github.com/GATECH-EIC/NASA.
CLOct 28, 2022
BEBERT: Efficient and Robust Binary Ensemble BERTJiayi Tian, Chao Fang, Haonan Wang et al.
Pre-trained BERT models have achieved impressive accuracy on natural language processing (NLP) tasks. However, their excessive amount of parameters hinders them from efficient deployment on edge devices. Binarization of the BERT models can significantly alleviate this issue but comes with a severe accuracy drop compared with their full-precision counterparts. In this paper, we propose an efficient and robust binary ensemble BERT (BEBERT) to bridge the accuracy gap. To the best of our knowledge, this is the first work employing ensemble techniques on binary BERTs, yielding BEBERT, which achieves superior accuracy while retaining computational efficiency. Furthermore, we remove the knowledge distillation procedures during ensemble to speed up the training process without compromising accuracy. Experimental results on the GLUE benchmark show that the proposed BEBERT significantly outperforms the existing binary BERT models in accuracy and robustness with a 2x speedup on training time. Moreover, our BEBERT has only a negligible accuracy loss of 0.3% compared to the full-precision baseline while saving 15x and 13x in FLOPs and model size, respectively. In addition, BEBERT also outperforms other compressed BERTs in accuracy by up to 6.7%.
CVNov 9, 2022
ViTALiTy: Unifying Low-rank and Sparse Approximation for Vision Transformer Acceleration with a Linear Taylor AttentionJyotikrishna Dass, Shang Wu, Huihong Shi et al.
Vision Transformer (ViT) has emerged as a competitive alternative to convolutional neural networks for various computer vision applications. Specifically, ViT multi-head attention layers make it possible to embed information globally across the overall image. Nevertheless, computing and storing such attention matrices incurs a quadratic cost dependency on the number of patches, limiting its achievable efficiency and scalability and prohibiting more extensive real-world ViT applications on resource-constrained devices. Sparse attention has been shown to be a promising direction for improving hardware acceleration efficiency for NLP models. However, a systematic counterpart approach is still missing for accelerating ViT models. To close the above gap, we propose a first-of-its-kind algorithm-hardware codesigned framework, dubbed ViTALiTy, for boosting the inference efficiency of ViTs. Unlike sparsity-based Transformer accelerators for NLP, ViTALiTy unifies both low-rank and sparse components of the attention in ViTs. At the algorithm level, we approximate the dot-product softmax operation via first-order Taylor attention with row-mean centering as the low-rank component to linearize the cost of attention blocks and further boost the accuracy by incorporating a sparsity-based regularization. At the hardware level, we develop a dedicated accelerator to better leverage the resulting workload and pipeline from ViTALiTy's linear Taylor attention which requires the execution of only the low-rank component, to further boost the hardware efficiency. Extensive experiments and ablation studies validate that ViTALiTy offers boosted end-to-end efficiency (e.g., $3\times$ faster and $3\times$ energy-efficient) under comparable accuracy, with respect to the state-of-the-art solution.
ARAug 12, 2022
An Algorithm-Hardware Co-Optimized Framework for Accelerating N:M Sparse TransformersChao Fang, Aojun Zhou, Zhongfeng Wang
The Transformer has been an indispensable staple in deep learning. However, for real-life applications, it is very challenging to deploy efficient Transformers due to immense parameters and operations of models. To relieve this burden, exploiting sparsity is an effective approach to accelerate Transformers. Newly emerging Ampere GPUs leverage a 2:4 sparsity pattern to achieve model acceleration, while it can hardly meet the diverse algorithm and hardware constraints when deploying models. By contrast, we propose an algorithm-hardware co-optimized framework to flexibly and efficiently accelerate Transformers by utilizing general N:M sparsity patterns. (1) From algorithm perspective, we propose a sparsity inheritance mechanism along with an inherited dynamic pruning (IDP) method to obtain a series of N:M sparse candidate Transformers rapidly. A model compression scheme is further proposed to significantly reduce the storage requirement for deployment. (2) From hardware perspective, we present a flexible and efficient hardware architecture, namely STA, to achieve significant speedup when deploying N:M sparse Transformers. STA features not only a computing engine unifying both sparse-dense and dense-dense matrix multiplications with high computational efficiency but also a scalable softmax module eliminating the latency from intermediate off-chip data communication. Experimental results show that compared to other methods, N:M sparse Transformers, generated using IDP, achieves an average of 6.7% improvement on accuracy with high training efficiency. Moreover, STA can achieve 14.47x and 11.33x speedup compared to Intel i9-9900X and NVIDIA RTX 2080 Ti, respectively, and perform 2.00-19.47x faster inference than the state-of-the-art FPGA-based accelerators for Transformers.
LGAug 1, 2022
GANDSE: Generative Adversarial Network based Design Space Exploration for Neural Network Accelerator DesignLang Feng, Wenjian Liu, Chuliang Guo et al.
With the popularity of deep learning, the hardware implementation platform of deep learning has received increasing interest. Unlike the general purpose devices, e.g., CPU, or GPU, where the deep learning algorithms are executed at the software level, neural network hardware accelerators directly execute the algorithms to achieve higher both energy efficiency and performance improvements. However, as the deep learning algorithms evolve frequently, the engineering effort and cost of designing the hardware accelerators are greatly increased. To improve the design quality while saving the cost, design automation for neural network accelerators was proposed, where design space exploration algorithms are used to automatically search the optimized accelerator design within a design space. Nevertheless, the increasing complexity of the neural network accelerators brings the increasing dimensions to the design space. As a result, the previous design space exploration algorithms are no longer effective enough to find an optimized design. In this work, we propose a neural network accelerator design automation framework named GANDSE, where we rethink the problem of design space exploration, and propose a novel approach based on the generative adversarial network (GAN) to support an optimized exploration for high dimension large design space. The experiments show that GANDSE is able to find the more optimized designs in negligible time compared with approaches including multilayer perceptron and deep reinforcement learning.
ARSep 15, 2023
A Precision-Scalable RISC-V DNN Processor with On-Device Learning Capability at the Extreme EdgeLongwei Huang, Chao Fang, Qiong Li et al.
Extreme edge platforms, such as in-vehicle smart devices, require efficient deployment of quantized deep neural networks (DNNs) to enable intelligent applications with limited amounts of energy, memory, and computing resources. However, many edge devices struggle to boost inference throughput of various quantized DNNs due to the varying quantization levels, and these devices lack floating-point (FP) support for on-device learning, which prevents them from improving model accuracy while ensuring data privacy. To tackle the challenges above, we propose a precision-scalable RISC-V DNN processor with on-device learning capability. It facilitates diverse precision levels of fixed-point DNN inference, spanning from 2-bit to 16-bit, and enhances on-device learning through improved support with FP16 operations. Moreover, we employ multiple methods such as FP16 multiplier reuse and multi-precision integer multiplier reuse, along with balanced mapping of FPGA resources, to significantly improve hardware resource utilization. Experimental results on the Xilinx ZCU102 FPGA show that our processor significantly improves inference throughput by 1.6$\sim$14.6$\times$ and energy efficiency by 1.1$\sim$14.6$\times$ across various DNNs, compared to the prior art, XpulpNN. Additionally, our processor achieves a 16.5$\times$ higher FP throughput for on-device learning.
LGSep 7, 2024Code
NASH: Neural Architecture and Accelerator Search for Multiplication-Reduced Hybrid ModelsYang Xu, Huihong Shi, Zhongfeng Wang
The significant computational cost of multiplications hinders the deployment of deep neural networks (DNNs) on edge devices. While multiplication-free models offer enhanced hardware efficiency, they typically sacrifice accuracy. As a solution, multiplication-reduced hybrid models have emerged to combine the benefits of both approaches. Particularly, prior works, i.e., NASA and NASA-F, leverage Neural Architecture Search (NAS) to construct such hybrid models, enhancing hardware efficiency while maintaining accuracy. However, they either entail costly retraining or encounter gradient conflicts, limiting both search efficiency and accuracy. Additionally, they overlook the acceleration opportunity introduced by accelerator search, yielding sub-optimal hardware performance. To overcome these limitations, we propose NASH, a Neural architecture and Accelerator Search framework for multiplication-reduced Hybrid models. Specifically, as for NAS, we propose a tailored zero-shot metric to pre-identify promising hybrid models before training, enhancing search efficiency while alleviating gradient conflicts. Regarding accelerator search, we innovatively introduce coarse-to-fine search to streamline the search process. Furthermore, we seamlessly integrate these two levels of searches to unveil NASH, obtaining the optimal model and accelerator pairing. Experiments validate our effectiveness, e.g., when compared with the state-of-the-art multiplication-based system, we can achieve $\uparrow$$2.14\times$ throughput and $\uparrow$$2.01\times$ FPS with $\uparrow$$0.25\%$ accuracy on CIFAR-100, and $\uparrow$$1.40\times$ throughput and $\uparrow$$1.19\times$ FPS with $\uparrow$$0.56\%$ accuracy on Tiny-ImageNet. Codes are available at \url{https://github.com/xuyang527/NASH.}
LGNov 4, 2022
An Efficient FPGA-based Accelerator for Deep ForestMingyu Zhu, Jiapeng Luo, Wendong Mao et al.
Deep Forest is a prominent machine learning algorithm known for its high accuracy in forecasting. Compared with deep neural networks, Deep Forest has almost no multiplication operations and has better performance on small datasets. However, due to the deep structure and large forest quantity, it suffers from large amounts of calculation and memory consumption. In this paper, an efficient hardware accelerator is proposed for deep forest models, which is also the first work to implement Deep Forest on FPGA. Firstly, a delicate node computing unit (NCU) is designed to improve inference speed. Secondly, based on NCU, an efficient architecture and an adaptive dataflow are proposed, in order to alleviate the problem of node computing imbalance in the classification process. Moreover, an optimized storage scheme in this design also improves hardware utilization and power efficiency. The proposed design is implemented on an FPGA board, Intel Stratix V, and it is evaluated by two typical datasets, ADULT and Face Mask Detection. The experimental results show that the proposed design can achieve around 40x speedup compared to that on a 40 cores high performance x86 CPU.
CLNov 16, 2022
Fast and Accurate FSA System Using ELBERT: An Efficient and Lightweight BERTSiyuan Lu, Chenchen Zhou, Keli Xie et al.
With the development of deep learning and Transformer-based pre-trained models like BERT, the accuracy of many NLP tasks has been dramatically improved. However, the large number of parameters and computations also pose challenges for their deployment. For instance, using BERT can improve the predictions in the financial sentiment analysis (FSA) task but slow it down, where speed and accuracy are equally important in terms of profits. To address these issues, we first propose an efficient and lightweight BERT (ELBERT) along with a novel confidence-window-based (CWB) early exit mechanism. Based on ELBERT, an innovative method to accelerate text processing on the GPU platform is developed, solving the difficult problem of making the early exit mechanism work more effectively with a large input batch size. Afterward, a fast and high-accuracy FSA system is built. Experimental results show that the proposed CWB early exit mechanism achieves significantly higher accuracy than existing early exit methods on BERT under the same computation cost. By using this acceleration method, our FSA system can boost the processing speed by nearly 40 times to over 1000 texts per second with sufficient accuracy, which is nearly twice as fast as FastBERT, thus providing a more powerful text processing capability for modern trading systems.
CVAug 16, 2023
S2R: Exploring a Double-Win Transformer-Based Framework for Ideal and Blind Super-ResolutionMinghao She, Wendong Mao, Huihong Shi et al.
Nowadays, deep learning based methods have demonstrated impressive performance on ideal super-resolution (SR) datasets, but most of these methods incur dramatically performance drops when directly applied in real-world SR reconstruction tasks with unpredictable blur kernels. To tackle this issue, blind SR methods are proposed to improve the visual results on random blur kernels, which causes unsatisfactory reconstruction effects on ideal low-resolution images similarly. In this paper, we propose a double-win framework for ideal and blind SR task, named S2R, including a light-weight transformer-based SR model (S2R transformer) and a novel coarse-to-fine training strategy, which can achieve excellent visual results on both ideal and random fuzzy conditions. On algorithm level, S2R transformer smartly combines some efficient and light-weight blocks to enhance the representation ability of extracted features with relatively low number of parameters. For training strategy, a coarse-level learning process is firstly performed to improve the generalization of the network with the help of a large-scale external dataset, and then, a fast fine-tune process is developed to transfer the pre-trained model to real-world SR tasks by mining the internal features of the image. Experimental results show that the proposed S2R outperforms other single-image SR models in ideal SR condition with only 578K parameters. Meanwhile, it can achieve better visual results than regular blind SR models in blind fuzzy conditions with only 10 gradient updates, which improve convergence speed by 300 times, significantly accelerating the transfer-learning process in real-world situations.
LGSep 22, 2023
Efficient N:M Sparse DNN Training Using Algorithm, Architecture, and Dataflow Co-DesignChao Fang, Wei Sun, Aojun Zhou et al.
Sparse training is one of the promising techniques to reduce the computational cost of DNNs while retaining high accuracy. In particular, N:M fine-grained structured sparsity, where only N out of consecutive M elements can be nonzero, has attracted attention due to its hardware-friendly pattern and capability of achieving a high sparse ratio. However, the potential to accelerate N:M sparse DNN training has not been fully exploited, and there is a lack of efficient hardware supporting N:M sparse training. To tackle these challenges, this paper presents a computation-efficient training scheme for N:M sparse DNNs using algorithm, architecture, and dataflow co-design. At the algorithm level, a bidirectional weight pruning method, dubbed BDWP, is proposed to leverage the N:M sparsity of weights during both forward and backward passes of DNN training, which can significantly reduce the computational cost while maintaining model accuracy. At the architecture level, a sparse accelerator for DNN training, namely SAT, is developed to neatly support both the regular dense operations and the computation-efficient N:M sparse operations. At the dataflow level, multiple optimization methods ranging from interleave mapping, pre-generation of N:M sparse weights, and offline scheduling, are proposed to boost the computational efficiency of SAT. Finally, the effectiveness of our training scheme is evaluated on a Xilinx VCU1525 FPGA card using various DNN models and datasets. Experimental results show the SAT accelerator with the BDWP sparse training method under 2:8 sparse ratio achieves an average speedup of 1.75x over that with the dense training, accompanied by a negligible accuracy loss of 0.56% on average. Furthermore, our proposed training scheme significantly improves the training throughput by 2.97~25.22x and the energy efficiency by 1.36~3.58x over prior FPGA-based accelerators.
LGSep 26, 2024
Efficient Arbitrary Precision Acceleration for Large Language Models on GPU Tensor CoresShaobo Ma, Chao Fang, Haikuo Shao et al.
Large language models (LLMs) have been widely applied but face challenges in efficient inference. While quantization methods reduce computational demands, ultra-low bit quantization with arbitrary precision is hindered by limited GPU Tensor Core support and inefficient memory management, leading to suboptimal acceleration. To address these challenges, we propose a comprehensive acceleration scheme for arbitrary precision LLMs. At its core, we introduce a novel bipolar-INT data format that facilitates parallel computing and supports symmetric quantization, effectively reducing data redundancy. Building on this, we implement an arbitrary precision matrix multiplication scheme that decomposes and recovers matrices at the bit level, enabling flexible precision while maximizing GPU Tensor Core utilization. Furthermore, we develop an efficient matrix preprocessing method that optimizes data layout for subsequent computations. Finally, we design a data recovery-oriented memory management system that strategically utilizes fast shared memory, significantly enhancing kernel execution speed and minimizing memory access latency. Experimental results demonstrate our approach's effectiveness, with up to 2.4\times speedup in matrix multiplication compared to NVIDIA's CUTLASS. When integrated into LLMs, we achieve up to 6.7\times inference acceleration. These improvements significantly enhance LLM inference efficiency, enabling broader and more responsive applications of LLMs.
LGJul 16, 2024
Co-Designing Binarized Transformer and Hardware Accelerator for Efficient End-to-End Edge DeploymentYuhao Ji, Chao Fang, Shaobo Ma et al.
Transformer models have revolutionized AI tasks, but their large size hinders real-world deployment on resource-constrained and latency-critical edge devices. While binarized Transformers offer a promising solution by significantly reducing model size, existing approaches suffer from algorithm-hardware mismatches with limited co-design exploration, leading to suboptimal performance on edge devices. Hence, we propose a co-design method for efficient end-to-end edge deployment of Transformers from three aspects: algorithm, hardware, and joint optimization. First, we propose BMT, a novel hardware-friendly binarized Transformer with optimized quantization methods and components, and we further enhance its model accuracy by leveraging the weighted ternary weight splitting training technique. Second, we develop a streaming processor mixed binarized Transformer accelerator, namely BAT, which is equipped with specialized units and scheduling pipelines for efficient inference of binarized Transformers. Finally, we co-optimize the algorithm and hardware through a design space exploration approach to achieve a global trade-off between accuracy, latency, and robustness for real-world deployments. Experimental results show our co-design achieves up to 2.14-49.37x throughput gains and 3.72-88.53x better energy efficiency over state-of-the-art Transformer accelerators, enabling efficient end-to-end edge deployment.
36.0ROMay 17
Beyond Geometry: Efficient Topologically-Grounded Navigation in Complex 3D EnvironmentsYifan Du, Chengwei Zhang, Siyu Liao et al.
Ground robot navigation in complex 3D environments is often hindered by geometric ambiguity, where non-traversable structures such as furniture share local geometric properties with navigable ground. Furthermore, the computational cost of searching massive voxel spaces remains a significant challenge. To address these issues, we present a surface extraction framework that constructs a reduced state space of physically reachable standing positions by enforcing ground support, overhead clearance, and seed-based connectivity constraints. Evaluation across five Matterport3D indoor scenes and three PCT benchmark scenes demonstrates over 80\% state space reduction and sub-millisecond A* search on the Matterport3D scenes, with 100\% planning success across all 300 tested queries.
ARSep 27, 2025
SnipSnap: A Joint Compression Format and Dataflow Co-Optimization Framework for Efficient Sparse LLM Accelerator DesignJunyi Wu, Chao Fang, Zhongfeng Wang
The growing scale of large language models (LLMs) has intensified demands on computation and memory, making efficient inference a key challenge. While sparsity can reduce these costs, existing design space exploration (DSE) frameworks often overlook compression formats, a key factor for leveraging sparsity on accelerators. This paper proposes SnipSnap, a joint compression format and dataflow co-optimization framework for efficient sparse LLM accelerator design. SnipSnap introduces: (1) a hierarchical compression format encoding to expand the design space; (2) an adaptive compression engine for selecting formats under diverse sparsity; and (3) a progressive co-search workflow that jointly optimizes dataflow and compression formats. SnipSnap achieves 18.24% average memory energy savings via format optimization, along with 2248.3$\times$ and 21.0$\times$ speedups over Sparseloop and DiMO-Sparse frameworks, respectively.
CVMay 6, 2024Code
Trio-ViT: Post-Training Quantization and Acceleration for Softmax-Free Efficient Vision TransformerHuihong Shi, Haikuo Shao, Wendong Mao et al.
Motivated by the huge success of Transformers in the field of natural language processing (NLP), Vision Transformers (ViTs) have been rapidly developed and achieved remarkable performance in various computer vision tasks. However, their huge model sizes and intensive computations hinder ViTs' deployment on embedded devices, calling for effective model compression methods, such as quantization. Unfortunately, due to the existence of hardware-unfriendly and quantization-sensitive non-linear operations, particularly {Softmax}, it is non-trivial to completely quantize all operations in ViTs, yielding either significant accuracy drops or non-negligible hardware costs. In response to challenges associated with \textit{standard ViTs}, we focus our attention towards the quantization and acceleration for \textit{efficient ViTs}, which not only eliminate the troublesome Softmax but also integrate linear attention with low computational complexity, and propose Trio-ViT accordingly. Specifically, at the algorithm level, we develop a {tailored post-training quantization engine} taking the unique activation distributions of Softmax-free efficient ViTs into full consideration, aiming to boost quantization accuracy. Furthermore, at the hardware level, we build an accelerator dedicated to the specific Convolution-Transformer hybrid architecture of efficient ViTs, thereby enhancing hardware efficiency. Extensive experimental results consistently prove the effectiveness of our Trio-ViT framework. {Particularly, we can gain up to $\uparrow$$\mathbf{3.6}\times$, $\uparrow$$\mathbf{5.0}\times$, and $\uparrow$$\mathbf{7.3}\times$ FPS under comparable accuracy over state-of-the-art ViT accelerators, as well as $\uparrow$$\mathbf{6.0}\times$, $\uparrow$$\mathbf{1.5}\times$, and $\uparrow$$\mathbf{2.1}\times$ DSP efficiency.} Codes are available at \url{https://github.com/shihuihong214/Trio-ViT}.
ARJan 22, 2024
BETA: Binarized Energy-Efficient Transformer Accelerator at the EdgeYuhao Ji, Chao Fang, Zhongfeng Wang
Existing binary Transformers are promising in edge deployment due to their compact model size, low computational complexity, and considerable inference accuracy. However, deploying binary Transformers faces challenges on prior processors due to inefficient execution of quantized matrix multiplication (QMM) and the energy consumption overhead caused by multi-precision activations. To tackle the challenges above, we first develop a computation flow abstraction method for binary Transformers to improve QMM execution efficiency by optimizing the computation order. Furthermore, a binarized energy-efficient Transformer accelerator, namely BETA, is proposed to boost the efficient deployment at the edge. Notably, BETA features a configurable QMM engine, accommodating diverse activation precisions of binary Transformers and offering high-parallelism and high-speed for QMMs with impressive energy efficiency. Experimental results evaluated on ZCU102 FPGA show BETA achieves an average energy efficiency of 174 GOPS/W, which is 1.76~21.92x higher than prior FPGA-based accelerators, showing BETA's good potential for edge Transformer acceleration.
ARNov 24, 2024
Anda: Unlocking Efficient LLM Inference with a Variable-Length Grouped Activation Data FormatChao Fang, Man Shi, Robin Geens et al.
The widely-used, weight-only quantized large language models (LLMs), which leverage low-bit integer (INT) weights and retain floating-point (FP) activations, reduce storage requirements while maintaining accuracy. However, this shifts the energy and latency bottlenecks towards the FP activations that are associated with costly memory accesses and computations. Existing LLM accelerators focus primarily on computation optimizations, overlooking the potential of jointly optimizing FP computations and data movement, particularly for the dominant FP-INT GeMM operations in LLM inference. To address these challenges, we investigate the sensitivity of activation precision across various LLM modules and its impact on overall model accuracy. Based on our findings, we first propose the Anda data type: an adaptive data format with group-shared exponent bits and dynamic mantissa bit allocation. Secondly, we develop an iterative post-training adaptive precision search algorithm that optimizes the bit-width for different LLM modules to balance model accuracy, energy efficiency, and inference speed. Lastly, a suite of hardware optimization techniques is proposed to maximally exploit the benefits of the Anda format. These include a bit-plane-based data organization scheme, Anda-enhanced processing units with bit-serial computation, and a runtime bit-plane Anda compressor to simultaneously optimize storage, computation, and memory footprints. Our evaluations on FPINT GeMM operations show that Anda achieves a 2.4x speedup, 4.0x area efficiency, and 3.1x energy efficiency improvement on average for popular LLMs including OPT, LLaMA, and LLaMA-2 series over the GPU-like FP-FP baseline. Anda demonstrates strong adaptability across various application scenarios, accuracy requirements, and system performance, enabling efficient LLM inference across a wide range of deployment scenarios.
ARMar 29, 2024
An FPGA-Based Reconfigurable Accelerator for Convolution-Transformer Hybrid EfficientViTHaikuo Shao, Huihong Shi, Wendong Mao et al.
Vision Transformers (ViTs) have achieved significant success in computer vision. However, their intensive computations and massive memory footprint challenge ViTs' deployment on embedded devices, calling for efficient ViTs. Among them, EfficientViT, the state-of-the-art one, features a Convolution-Transformer hybrid architecture, enhancing both accuracy and hardware efficiency. Unfortunately, existing accelerators cannot fully exploit the hardware benefits of EfficientViT due to its unique architecture. In this paper, we propose an FPGA-based accelerator for EfficientViT to advance the hardware efficiency frontier of ViTs. Specifically, we design a reconfigurable architecture to efficiently support various operation types, including lightweight convolutions and attention, boosting hardware utilization. Additionally, we present a time-multiplexed and pipelined dataflow to facilitate both intra- and inter-layer fusions, reducing off-chip data access costs. Experimental results show that our accelerator achieves up to 780.2 GOPS in throughput and 105.1 GOPS/W in energy efficiency at 200MHz on the Xilinx ZCU102 FPGA, which significantly outperforms prior works.
LGNov 3, 2025
Memory-Efficient Training with In-Place FFT ImplementationXinyu Ding, Bangtian Liu, Siyu Liao et al.
Fast Fourier Transforms (FFT) are widely used to reduce memory and computational costs in deep learning. However, existing implementations, including standard FFT and real FFT (rFFT), cannot achieve true in-place computation. In particular, rFFT maps an input of size n to a complex output of size n/2+1, causing dimensional mismatch and requiring additional memory allocation. We propose the first real-domain, fully in-place FFT framework (rdFFT) that preserves input-output memory space consistency. By leveraging butterfly operation symmetry and conjugate properties in the frequency domain, we design an implicit complex encoding scheme that eliminates intermediate cache usage entirely. Experiments on multiple natural language understanding tasks demonstrate the method effectiveness in reducing training memory cost, offering a promising direction for frequency-domain lightweight adaptation.
ARFeb 22, 2024
An FPGA-Based Accelerator Enabling Efficient Support for CNNs with Arbitrary Kernel SizesMiaoxin Wang, Xiao Wu, Jun Lin et al.
Convolutional neural networks (CNNs) with large kernels, drawing inspiration from the key operations of vision transformers (ViTs), have demonstrated impressive performance in various vision-based applications. To address the issue of computational efficiency degradation in existing designs for supporting large-kernel convolutions, an FPGA-based inference accelerator is proposed for the efficient deployment of CNNs with arbitrary kernel sizes. Firstly, a Z-flow method is presented to optimize the computing data flow by maximizing data reuse opportunity. Besides, the proposed design, incorporating the kernel-segmentation (Kseg) scheme, enables extended support for large-kernel convolutions, significantly reducing the storage requirements for overlapped data. Moreover, based on the analysis of typical block structures in emerging CNNs, vertical-fused (VF) and horizontal-fused (HF) methods are developed to optimize CNN deployments from both computation and transmission perspectives. The proposed hardware accelerator, evaluated on Intel Arria 10 FPGA, achieves up to 3.91 times better DSP efficiency than prior art on the same network. Particularly, it demonstrates efficient support for large-kernel CNNs, achieving throughputs of 169.68 GOPS and 244.55 GOPS for RepLKNet-31 and PyConvResNet-50, respectively, both of which are implemented on hardware for the first time.
ARMay 25, 2025
FastMamba: A High-Speed and Efficient Mamba Accelerator on FPGA with Accurate QuantizationAotao Wang, Haikuo Shao, Shaobo Ma et al.
State Space Models (SSMs), like recent Mamba2, have achieved remarkable performance and received extensive attention. However, deploying Mamba2 on resource-constrained edge devices encounters many problems: severe outliers within the linear layer challenging the quantization, diverse and irregular element-wise tensor operations, and hardware-unfriendly nonlinear functions in the SSM block. To address these issues, this paper presents FastMamba, a dedicated accelerator on FPGA with hardware-algorithm co-design to promote the deployment efficiency of Mamba2. Specifically, we successfully achieve 8-bit quantization for linear layers through Hadamard transformation to eliminate outliers. Moreover, a hardware-friendly and fine-grained power-of-two quantization framework is presented for the SSM block and convolution layer, and a first-order linear approximation is developed to optimize the nonlinear functions. Based on the accurate algorithm quantization, we propose an accelerator that integrates parallel vector processing units, pipelined execution dataflow, and an efficient SSM Nonlinear Approximation Unit, which enhances computational efficiency and reduces hardware complexity. Finally, we evaluate FastMamba on Xilinx VC709 FPGA. For the input prefill task on Mamba2-130M, FastMamba achieves 68.80\times and 8.90\times speedup over Intel Xeon 4210R CPU and NVIDIA RTX 3090 GPU, respectively. In the output decode experiment with Mamba2-2.7B, FastMamba attains 6\times higher energy efficiency than RTX 3090 GPU.
LGMay 23, 2025
FlashForge: Ultra-Efficient Prefix-Aware Attention for LLM DecodingZhibin Wang, Rui Ning, Chao Fang et al.
Prefix-sharing among multiple prompts presents opportunities to combine the operations of the shared prefix, while attention computation in the decode stage, which becomes a critical bottleneck with increasing context lengths, is a memory-intensive process requiring heavy memory access on the key-value (KV) cache of the prefixes. Therefore, in this paper, we explore the potential of prefix-sharing in the attention computation of the decode stage. However, the tree structure of the prefix-sharing mechanism presents significant challenges for attention computation in efficiently processing shared KV cache access patterns while managing complex dependencies and balancing irregular workloads. To address the above challenges, we propose a dedicated attention kernel to combine the memory access of shared prefixes in the decoding stage, namely FlashForge. FlashForge delivers two key innovations: a novel shared-prefix attention kernel that optimizes memory hierarchy and exploits both intra-block and inter-block parallelism, and a comprehensive workload balancing mechanism that efficiently estimates cost, divides tasks, and schedules execution. Experimental results show that FlashForge achieves an average 1.9x speedup and 120.9x memory access reduction compared to the state-of-the-art FlashDecoding kernel regarding attention computation in the decode stage and 3.8x end-to-end time per output token compared to the vLLM.
CLMay 1, 2025
Block Circulant Adapter for Large Language ModelsXinyu Ding, Meiqi Wang, Siyu Liao et al.
Fine-tuning large language models (LLMs) is difficult due to their huge model size. Recent Fourier domain-based methods show potential for reducing fine-tuning costs. We propose a block circulant matrix-based fine-tuning method with a stable training heuristic to leverage the properties of circulant matrices and one-dimensional Fourier transforms to reduce storage and computation costs. Experiments show that our method uses $14\times$ less number of parameters than VeRA, $16\times$ smaller than LoRA and $32\times$ less FLOPs than FourierFT, while maintaining close or better task performance. Our approach presents a promising way in frequency domain to fine-tune large models on downstream tasks.
LGMay 1, 2025
Parameter-Efficient Fine-Tuning with Circulant and Diagonal VectorsXinyu Ding, Lexuan Chen, Siyu Liao et al.
Foundation models have achieved tremendous success in different domains. However, their huge computation and storage complexity make these models difficult to fine-tune and also less applicable in practice. Recent study shows training in Fourier domain can be an effective fine-tuning method in terms of both model performance and number of training parameters. In this work, we propose to further reduce the complexity by the factorization through the product of interleaved circulant and diagonal matrices. In addition, we address the case of non-square fine-tuning weights by partitioning the circulant matrix into blocks. Our method avoids the construction of weight change matrix and utilizes 1D fast Fourier transform (FFT) instead of 2D FFT. Experimental results show that our method achieves similar or better performance across various tasks with much less floating-point operations (FLOPs) and the number of trainable parameters.
ARApr 7, 2025
AccLLM: Accelerating Long-Context LLM Inference Via Algorithm-Hardware Co-DesignYanbiao Liang, Huihong Shi, Haikuo Shao et al.
Recently, large language models (LLMs) have achieved huge success in the natural language processing (NLP) field, driving a growing demand to extend their deployment from the cloud to edge devices. However, deploying LLMs on resource-constrained edge devices poses significant challenges, including (1) intensive computations and huge model sizes, (2) great memory and bandwidth demands introduced by the autoregressive generation process, and (3) limited scalability for handling long sequences. To address these challenges, we propose AccLLM, a comprehensive acceleration framework that enables efficient and fast long-context LLM inference through algorithm and hardware co-design. At the algorithmic level, we integrate (1) pruning, (2) Λ-shaped attention, and (3) an innovative W2A8KV4 (2-bit weights, 8-bit activations, and 4-bit KV cache) quantization scheme, thus effectively reducing memory and bandwidth requirements while facilitating LLMs' long-sequence generation. At the hardware level, we design a dedicated FPGA-based accelerator with a reconfigurable computing engine to effectively and flexibly accommodate diverse operations arising from our compression algorithm, thereby fully translating the algorithmic innovations into tangible hardware efficiency. We validate AccLLM on the Xilinx Alveo U280 FPGA, demonstrating a 4.07x energy efficiency and a 2.98x throughput compared to the state-of-the-art work FlightLLM.
CVSep 7, 2025
StripDet: Strip Attention-Based Lightweight 3D Object Detection from Point CloudWeichao Wang, Wendong Mao, Zhongfeng Wang
The deployment of high-accuracy 3D object detection models from point cloud remains a significant challenge due to their substantial computational and memory requirements. To address this, we introduce StripDet, a novel lightweight framework designed for on-device efficiency. First, we propose the novel Strip Attention Block (SAB), a highly efficient module designed to capture long-range spatial dependencies. By decomposing standard 2D convolutions into asymmetric strip convolutions, SAB efficiently extracts directional features while reducing computational complexity from quadratic to linear. Second, we design a hardware-friendly hierarchical backbone that integrates SAB with depthwise separable convolutions and a simple multiscale fusion strategy, achieving end-to-end efficiency. Extensive experiments on the KITTI dataset validate StripDet's superiority. With only 0.65M parameters, our model achieves a 79.97% mAP for car detection, surpassing the baseline PointPillars with a 7x parameter reduction. Furthermore, StripDet outperforms recent lightweight and knowledge distillation-based methods, achieving a superior accuracy-efficiency trade-off while establishing itself as a practical solution for real-world 3D detection on edge devices.
LGAug 26, 2025
APT-LLM: Exploiting Arbitrary-Precision Tensor Core Computing for LLM AccelerationShaobo Ma, Chao Fang, Haikuo Shao et al.
Large language models (LLMs) have revolutionized AI applications, yet their enormous computational demands severely limit deployment and real-time performance. Quantization methods can help reduce computational costs, however, attaining the extreme efficiency associated with ultra-low-bit quantized LLMs at arbitrary precision presents challenges on GPUs. This is primarily due to the limited support for GPU Tensor Cores, inefficient memory management, and inflexible kernel optimizations. To tackle these challenges, we propose a comprehensive acceleration scheme for arbitrary precision LLMs, namely APT-LLM. Firstly, we introduce a novel data format, bipolar-INT, which allows for efficient and lossless conversion with signed INT, while also being more conducive to parallel computation. We also develop a matrix multiplication (MatMul) method allowing for arbitrary precision by dismantling and reassembling matrices at the bit level. This method provides flexible precision and optimizes the utilization of GPU Tensor Cores. In addition, we propose a memory management system focused on data recovery, which strategically employs fast shared memory to substantially increase kernel execution speed and reduce memory access latency. Finally, we develop a kernel mapping method that dynamically selects the optimal configurable hyperparameters of kernels for varying matrix sizes, enabling optimal performance across different LLM architectures and precision settings. In LLM inference, APT-LLM achieves up to a 3.99$\times$ speedup compared to FP16 baselines and a 2.16$\times$ speedup over NVIDIA CUTLASS INT4 acceleration on RTX 3090. On RTX 4090 and H800, APT-LLM achieves up to 2.44$\times$ speedup over FP16 and 1.65$\times$ speedup over CUTLASS integer baselines.
CVJul 13, 2025
A Memory-Efficient Framework for Deformable Transformer with Neural Architecture SearchWendong Mao, Mingfan Zhao, Jianfeng Guan et al.
Deformable Attention Transformers (DAT) have shown remarkable performance in computer vision tasks by adaptively focusing on informative image regions. However, their data-dependent sampling mechanism introduces irregular memory access patterns, posing significant challenges for efficient hardware deployment. Existing acceleration methods either incur high hardware overhead or compromise model accuracy. To address these issues, this paper proposes a hardware-friendly optimization framework for DAT. First, a neural architecture search (NAS)-based method with a new slicing strategy is proposed to automatically divide the input feature into uniform patches during the inference process, avoiding memory conflicts without modifying model architecture. The method explores the optimal slice configuration by jointly optimizing hardware cost and inference accuracy. Secondly, an FPGA-based verification system is designed to test the performance of this framework on edge-side hardware. Algorithm experiments on the ImageNet-1K dataset demonstrate that our hardware-friendly framework can maintain have only 0.2% accuracy drop compared to the baseline DAT. Hardware experiments on Xilinx FPGA show the proposed method reduces DRAM access times to 18% compared with existing DAT acceleration methods.
ARMay 25, 2025
Enable Lightweight and Precision-Scalable Posit/IEEE-754 Arithmetic in RISC-V Cores for Transprecision ComputingQiong Li, Chao Fang, Longwei Huang et al.
While posit format offers superior dynamic range and accuracy for transprecision computing, its adoption in RISC-V processors is hindered by the lack of a unified solution for lightweight, precision-scalable, and IEEE-754 arithmetic compatible hardware implementation. To address these challenges, we enhance RISC-V processors by 1) integrating dedicated posit codecs into the original FPU for lightweight implementation, 2) incorporating multi/mixed-precision support with dynamic exponent size for precision-scalability, and 3) reusing and customizing ISA extensions for IEEE-754 compatible posit operations. Our comprehensive evaluation spans the modified FPU, RISC-V core, and SoC levels. It demonstrates that our implementation achieves 47.9% LUTs and 57.4% FFs reduction compared to state-of-the-art posit-enabled RISC-V processors, while achieving up to 2.54$\times$ throughput improvement in various GEMM kernels.
GRApr 8, 2025
CDM-QTA: Quantized Training Acceleration for Efficient LoRA Fine-Tuning of Diffusion ModelJinming Lu, Minghao She, Wendong Mao et al.
Fine-tuning large diffusion models for custom applications demands substantial power and time, which poses significant challenges for efficient implementation on mobile devices. In this paper, we develop a novel training accelerator specifically for Low-Rank Adaptation (LoRA) of diffusion models, aiming to streamline the process and reduce computational complexity. By leveraging a fully quantized training scheme for LoRA fine-tuning, we achieve substantial reductions in memory usage and power consumption while maintaining high model fidelity. The proposed accelerator features flexible dataflow, enabling high utilization for irregular and variable tensor shapes during the LoRA process. Experimental results show up to 1.81x training speedup and 5.50x energy efficiency improvements compared to the baseline, with minimal impact on image generation quality.
CVDec 27, 2021
Learning Robust and Lightweight Model through Separable Structured TransformationsXian Wei, Yanhui Huang, Yangyu Xu et al.
With the proliferation of mobile devices and the Internet of Things, deep learning models are increasingly deployed on devices with limited computing resources and memory, and are exposed to the threat of adversarial noise. Learning deep models with both lightweight and robustness is necessary for these equipments. However, current deep learning solutions are difficult to learn a model that possesses these two properties without degrading one or the other. As is well known, the fully-connected layers contribute most of the parameters of convolutional neural networks. We perform a separable structural transformation of the fully-connected layer to reduce the parameters, where the large-scale weight matrix of the fully-connected layer is decoupled by the tensor product of several separable small-sized matrices. Note that data, such as images, no longer need to be flattened before being fed to the fully-connected layer, retaining the valuable spatial geometric information of the data. Moreover, in order to further enhance both lightweight and robustness, we propose a joint constraint of sparsity and differentiable condition number, which is imposed on these separable matrices. We evaluate the proposed approach on MLP, VGG-16 and Vision Transformer. The experimental results on datasets such as ImageNet, SVHN, CIFAR-100 and CIFAR10 show that we successfully reduce the amount of network parameters by 90%, while the robust accuracy loss is less than 1.5%, which is better than the SOTA methods based on the original fully-connected layer. Interestingly, it can achieve an overwhelming advantage even at a high compression rate, e.g., 200 times.
AROct 12, 2021
Memory-Efficient CNN Accelerator Based on Interlayer Feature Map CompressionZhuang Shao, Xiaoliang Chen, Li Du et al.
Existing deep convolutional neural networks (CNNs) generate massive interlayer feature data during network inference. To maintain real-time processing in embedded systems, large on-chip memory is required to buffer the interlayer feature maps. In this paper, we propose an efficient hardware accelerator with an interlayer feature compression technique to significantly reduce the required on-chip memory size and off-chip memory access bandwidth. The accelerator compresses interlayer feature maps through transforming the stored data into frequency domain using hardware-implemented 8x8 discrete cosine transform (DCT). The high-frequency components are removed after the DCT through quantization. Sparse matrix compression is utilized to further compress the interlayer feature maps. The on-chip memory allocation scheme is designed to support dynamic configuration of the feature map buffer size and scratch pad size according to different network-layer requirements. The hardware accelerator combines compression, decompression, and CNN acceleration into one computing stream, achieving minimal compressing and processing delay. A prototype accelerator is implemented on an FPGA platform and also synthesized in TSMC 28-nm COMS technology. It achieves 403GOPS peak throughput and 1.4x~3.3x interlayer feature map reduction by adding light hardware area overhead, making it a promising hardware accelerator for intelligent IoT devices.
CLJul 1, 2021
Elbert: Fast Albert with Confidence-Window Based Early ExitKeli Xie, Siyuan Lu, Meiqi Wang et al.
Despite the great success in Natural Language Processing (NLP) area, large pre-trained language models like BERT are not well-suited for resource-constrained or real-time applications owing to the large number of parameters and slow inference speed. Recently, compressing and accelerating BERT have become important topics. By incorporating a parameter-sharing strategy, ALBERT greatly reduces the number of parameters while achieving competitive performance. Nevertheless, ALBERT still suffers from a long inference time. In this work, we propose the ELBERT, which significantly improves the average inference speed compared to ALBERT due to the proposed confidence-window based early exit mechanism, without introducing additional parameters or extra training overhead. Experimental results show that ELBERT achieves an adaptive inference speedup varying from 2$\times$ to 10$\times$ with negligible accuracy degradation compared to ALBERT on various datasets. Besides, ELBERT achieves higher accuracy than existing early exit methods used for accelerating BERT under the same computation cost. Furthermore, to understand the principle of the early exit mechanism, we also visualize the decision-making process of it in ELBERT.
LGSep 6, 2019
Training Deep Neural Networks Using Posit Number SystemJinming Lu, Siyuan Lu, Zhisheng Wang et al.
With the increasing size of Deep Neural Network (DNN) models, the high memory space requirements and computational complexity have become an obstacle for efficient DNN implementations. To ease this problem, using reduced-precision representations for DNN training and inference has attracted many interests from researchers. This paper first proposes a methodology for training DNNs with the posit arithmetic, a type- 3 universal number (Unum) format that is similar to the floating point(FP) but has reduced precision. A warm-up training strategy and layer-wise scaling factors are adopted to stabilize training and fit the dynamic range of DNN parameters. With the proposed training methodology, we demonstrate the first successful training of DNN models on ImageNet image classification task in 16 bits posit with no accuracy loss. Then, an efficient hardware architecture for the posit multiply-and-accumulate operation is also proposed, which can achieve significant improvement in energy efficiency than traditional floating-point implementations. The proposed design is helpful for future low-power DNN training accelerators.
CVMay 31, 2019
Design Light-weight 3D Convolutional Networks for Video Recognition Temporal Residual, Fully Separable Block, and Fast AlgorithmHaonan Wang, Jun Lin, Zhongfeng Wang
Deep 3-dimensional (3D) Convolutional Network (ConvNet) has shown promising performance on video recognition tasks because of its powerful spatio-temporal information fusion ability. However, the extremely intensive requirements on memory access and computing power prohibit it from being used in resource-constrained scenarios, such as portable and edge devices. So in this paper, we first propose a two-stage Fully Separable Block (FSB) to significantly compress the model sizes of 3D ConvNets. Then a feature enhancement approach named Temporal Residual Gradient (TRG) is developed to improve the performance of compressed model on video tasks, which provides higher accuracy, faster convergency and better robustness. Moreover, in order to further decrease the computing workload, we propose a hybrid Fast Algorithm (hFA) to drastically reduce the computation complexity of convolutions. These methods are effectively combined to design a light-weight and efficient ConvNet for video recognition tasks. Experiments on the popular dataset report 2.3x compression rate, 3.6x workload reduction, and 6.3% top-1 accuracy gain, over the state-of-the-art SlowFast model, which is already a highly compact model. The proposed methods also show good adaptability on traditional 3D ConvNet, demonstrating 7.4x more compact model, 11.0x less workload, and 3.0% higher accuracy
SPMay 8, 2019
A Hardware-Oriented and Memory-Efficient Method for CTC DecodingSiyuan Lu, Jinming Lu, Jun Lin et al.
The Connectionist Temporal Classification (CTC) has achieved great success in sequence to sequence analysis tasks such as automatic speech recognition (ASR) and scene text recognition (STR). These applications can use the CTC objective function to train the recurrent neural networks (RNNs), and decode the outputs of RNNs during inference. While hardware architectures for RNNs have been studied, hardware-based CTCdecoders are desired for high-speed CTC-based inference systems. This paper, for the first time, provides a low-complexity and memory-efficient approach to build a CTC-decoder based on the beam search decoding. Firstly, we improve the beam search decoding algorithm to save the storage space. Secondly, we compress a dictionary (reduced from 26.02MB to 1.12MB) and use it as the language model. Meanwhile searching this dictionary is trivial. Finally, a fixed-point CTC-decoder for an English ASR and an STR task using the proposed method is implemented with C++ language. It is shown that the proposed method has little precision loss compared with its floating-point counterpart. Our experiments demonstrate the compression ratio of the storage required by the proposed beam search decoding algorithm are 29.49 (ASR) and 17.95 (STR).
LGJul 4, 2018
SGAD: Soft-Guided Adaptively-Dropped Neural NetworkZhisheng Wang, Fangxuan Sun, Jun Lin et al.
Deep neural networks (DNNs) have been proven to have many redundancies. Hence, many efforts have been made to compress DNNs. However, the existing model compression methods treat all the input samples equally while ignoring the fact that the difficulties of various input samples being correctly classified are different. To address this problem, DNNs with adaptive dropping mechanism are well explored in this work. To inform the DNNs how difficult the input samples can be classified, a guideline that contains the information of input samples is introduced to improve the performance. Based on the developed guideline and adaptive dropping mechanism, an innovative soft-guided adaptively-dropped (SGAD) neural network is proposed in this paper. Compared with the 32 layers residual neural networks, the presented SGAD can reduce the FLOPs by 77% with less than 1% drop in accuracy on CIFAR-10.
CVJul 10, 2016
Intra-layer Nonuniform Quantization for Deep Convolutional Neural NetworkFangxuan Sun, Jun Lin, Zhongfeng Wang
Deep convolutional neural network (DCNN) has achieved remarkable performance on object detection and speech recognition in recent years. However, the excellent performance of a DCNN incurs high computational complexity and large memory requirement. In this paper, an equal distance nonuniform quantization (ENQ) scheme and a K-means clustering nonuniform quantization (KNQ) scheme are proposed to reduce the required memory storage when low complexity hardware or software implementations are considered. For the VGG-16 and the AlexNet, the proposed nonuniform quantization schemes reduce the number of required memory storage by approximately 50\% while achieving almost the same or even better classification accuracy compared to the state-of-the-art quantization method. Compared to the ENQ scheme, the proposed KNQ scheme provides a better tradeoff when higher accuracy is required.