Low-precision training is considered an effective strategy for reducing both training and downstream inference costs. Previous scaling laws for precision mainly focus on integer quantization, which pay less attention to the constituents in floating-point (FP) quantization, and thus cannot well fit the LLM losses in this scenario. In contrast, while FP quantization training is more commonly implemented in production, it's research has been relatively superficial. In this paper, we thoroughly explore the effects of FP quantization targets, exponent bits, mantissa bits, and the calculation granularity of the scaling factor in FP quantization training performance of LLM models. In addition to an accurate FP quantization unified scaling law, we also provide valuable suggestions for the community: (1) Exponent bits contribute slightly more to the model performance than mantissa bits. We provide the optimal exponent-mantissa bit ratio for different bit numbers, which is available for future reference by hardware manufacturers; (2) We discover the formation of the critical data size in low-precision LLM training. Too much training data exceeding the critical data size will inversely bring in degradation of LLM performance; (3) The optimal FP quantization precision is directly proportional to the computational power, but within a wide computational power range. We estimate that the best cost-performance precision should lie between 4-8 bits.
AFPQ: Asymmetric Floating Point Quantization for LLMs
Shanghai Jiao Tong University（上海交通大学）；Microsoft Research Asia（微软亚洲研究院）；The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））；University of Science and Technology of China（中国科学技术大学）
We present an overview of techniques for quantizing convolutional neural networks for inference with integer weights and activations. Per-channel quantization of weights and per-layer quantization of activations to 8-bits of precision post-training produces classification accuracies within 2% of floating point networks for a wide variety of CNN architectures. Model sizes can be reduced by a factor of 4 by quantizing weights to 8-bits, even when 8-bit arithmetic is not supported. This can be achieved with simple, post training quantization of weights.We benchmark latencies of quantized networks…
Analog mixed-signal (AMS) devices promise faster, more energy-efficient deep neural network (DNN) inference than their digital counterparts. However, recent studies show that DNNs on AMS devices with fixed-point numbers can incur an accuracy penalty because of precision loss. To mitigate this penalty, we present a novel AMS-compatible adaptive block floating-point (ABFP) number representation. We also introduce amplification (or gain) as a method for increasing the accuracy of the number representation without increasing the bit precision of the output. We evaluate the effectiveness of ABFP on…
Department of Computer Science and Technology, University of Cambridge（计算机科学与技术系，剑桥大学）；Department of Electrical & Electronic Engineering, Imperial College London（电气与电子工程系，伦敦帝国学院）；Department of Computer Science, University of Hong Kong（计算机科学系，香港大学）；School of Informatics, University of Edinburgh（信息学院，爱丁堡大学）
Stanford University（斯坦福大学）；Intel AI Lab（英特尔人工智能实验室）
Training with larger number of parameters while keeping fast iterations is an increasingly adopted strategy and trend for developing better performing Deep Neural Network (DNN) models. This necessitates increased memory footprint and computational requirements for training. Here we introduce a novel methodology for training deep neural networks using 8-bit floating point (FP8) numbers. Reduced bit precision allows for a larger effective memory and increased computational speed. We name this method Shifted and Squeezed FP8 (S2FP8). We show that, unlike previous 8-bit precision training methods,…
We propose a Quantization Guided Training (QGT) method to guide DNN training towards optimized low-bit-precision targets and reach extreme compression levels below 8-bit precision. Unlike standard quantization-aware training (QAT) approaches, QGT uses customized regularization to encourage weight values towards a distribution that maximizes accuracy while reducing quantization errors. One of the main benefits of this approach is the ability to identify compression bottlenecks. We validate QGT using state-of-the-art model architectures on vision datasets. We also demonstrate the effectiveness o…
Task-Stratified Knowledge Scaling Laws for Post-Training Quantized Large Language Models
School of Advanced Interdisciplinary Sciences, University of Chinese Academy of Sciences（中国科学院大学先进交叉学科学院）；The Key Laboratory of Cognition and Decision Intelligence for Complex Systems, Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所认知与决策智能复杂系统重点实验室）；School of Artificial Intelligence, University of Chinese Academy of Sciences（中国科学院大学人工智能学院）；College of Computer Science, Inner Mongolia University（内蒙古大学计算机学院）
Qualcomm AI Research（高通人工智能研究院）；University of California, Irvine（加利福尼亚大学尔湾分校）
We present a differentiable joint pruning and quantization (DJPQ) scheme. We frame neural network compression as a joint gradient-based optimization problem, trading off between model pruning and quantization automatically for hardware efficiency. DJPQ incorporates variational information bottleneck based structured pruning and mixed-bit precision quantization into a single differentiable loss function. In contrast to previous works which consider pruning and quantization separately, our method enables users to find the optimal trade-off between both in a single training procedure. To utilize …
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…
While neural networks have advanced the frontiers in many machine learning applications, they often come at a high computational cost. Reducing the power and latency of neural network inference is vital to integrating modern networks into edge devices with strict power and compute requirements. Neural network quantization is one of the most effective ways of achieving these savings, but the additional noise it induces can lead to accuracy degradation. In this white paper, we present an overview of neural network quantization using AI Model Efficiency Toolkit (AIMET). AIMET is a library of stat…
Northeastern University（东北大学）；Simon Fraser University（西蒙弗雷泽大学）；University of California, Irvine（加州大学欧文分校）；ETH Zurich（苏黎世联邦理工学院）；The University of Texas at Austin（德克萨斯大学奥斯汀分校）
Vision transformers (ViTs) are emerging with significantly improved accuracy in computer vision tasks. However, their complex architecture and enormous computation/storage demand impose urgent needs for new hardware accelerator design methodology. This work proposes an FPGA-aware automatic ViT acceleration framework based on the proposed mixed-scheme quantization. To the best of our knowledge, this is the first FPGA-based ViT acceleration framework exploring model quantization. Compared with state-of-the-art ViT quantization work (algorithmic approach only without hardware acceleration), our q…
While neural networks have advanced the frontiers in many applications, they often come at a high computational cost. Reducing the power and latency of neural network inference is key if we want to integrate modern networks into edge devices with strict power and compute requirements. Neural network quantization is one of the most effective ways of achieving these savings but the additional noise it induces can lead to accuracy degradation. In this white paper, we introduce state-of-the-art algorithms for mitigating the impact of quantization noise on the network's performance while maintainin…
VQKV: High-Fidelity and High-Ratio Cache Compression via Vector-Quantization
LUMIA Lab（LUMIA实验室）；School of Artificial Intelligence（人工智能学院）；Shanghai Jiao Tong University（上海交通大学）；Shanghai Innovation Institute（上海创新研究院）；Shanghai Artificial Intelligence Laboratory（上海人工智能实验室）；University of Cambridge（剑桥大学）；National University of Singapore（新加坡国立大学）
Meta Reality Lab Research（Meta现实实验室研究部门）；AGH UST（AGH科技大学）
Deploying Deep Neural Networks in low-power embedded devices for real time-constrained applications requires optimization of memory and computational complexity of the networks, usually by quantizing the weights. Most of the existing works employ linear quantization which causes considerable degradation in accuracy for weight bit widths lower than 8. Since the distribution of weights is usually non-uniform (with most weights concentrated around zero), other methods, such as logarithmic quantization, are more suitable as they are able to preserve the shape of the weight distribution more precis…
Oregon State University（俄勒冈州立大学）；University of Maryland, College Park（马里兰大学学院市分校）
Quantization is a popular technique that $transforms$ the parameter representation of a neural network from floating-point numbers into lower-precision ones ($e.g.$, 8-bit integers). It reduces the memory footprint and the computational cost at inference, facilitating the deployment of resource-hungry models. However, the parameter perturbations caused by this transformation result in $behavioral$ $disparities$ between the model before and after quantization. For example, a quantized model can misclassify some test-time samples that are otherwise classified correctly. It is not known whether s…
We propose a novel 2-stage sub 8-bit quantization aware training algorithm for all components of a 250K parameter feedforward, streaming, state-free keyword spotting model. For the 1st-stage, we adapt a recently proposed quantization technique using a non-linear transformation with tanh(.) on dense layer weights. In the 2nd-stage, we use linear quantization methods on the rest of the network, including other parameters (bias, gain, batchnorm), inputs, and activations. We conduct large scale experiments, training on 26,000 hours of de-identified production, far-field and near-field audio data (…
Ecole Polytechnique Montreal（蒙特利尔高等理工学院）；Mila-University of Montreal（蒙特利尔大学Mila）；Polytechnique Montreal（蒙特利尔高等理工学院）
Model quantization is leveraged to reduce the memory consumption and the computation time of deep neural networks. This is achieved by representing weights and activations with a lower bit resolution when compared to their high precision floating point counterparts. The suitable level of quantization is directly related to the model performance. Lowering the quantization precision (e.g. 2 bits), reduces the amount of memory required to store model parameters and the amount of logic required to implement computational blocks, which contributes to reducing the power consumption of the entire sys…
Research Center for Information Technology Innovation, Academia Sinica（中央研究院资讯科技创新研究中心）；National Taiwan University（台湾大学）
Numerous studies have investigated the effectiveness of neural network quantization on pattern classification tasks. The present study, for the first time, investigated the performance of speech enhancement (a regression task in speech processing) using a novel exponent-only floating-point quantized neural network (EOFP-QNN). The proposed EOFP-QNN consists of two stages: mantissa-quantization and exponent-quantization. In the mantissa-quantization stage, EOFP-QNN learns how to quantize the mantissa bits of the model parameters while preserving the regression accuracy using the least mantissa p…
Shedding the Bits: Pushing the Boundaries of Quantization with Minifloats on FPGAs
School of Computing, National University of Singapore（新加坡国立大学计算机学院）；AMD Research and Advanced Development（AMD研究与高级开发部）；Tampere University（坦佩雷大学）；AMD（AMD公司）
Harvard University（哈佛大学）；Franklin and Marshall College（富兰克林与马歇尔学院）
Block Floating Point (BFP) can efficiently support quantization for Deep Neural Network (DNN) training by providing a wide dynamic range via a shared exponent across a group of values. In this paper, we propose a Fast First, Accurate Second Training (FAST) system for DNNs, where the weights, activations, and gradients are represented in BFP. FAST supports matrix multiplication with variable precision BFP input operands, enabling incremental increases in DNN precision throughout training. By increasing the BFP precision across both training iterations and DNN layers, FAST can greatly shorten th…
Deep learning as a means to inferencing has proliferated thanks to its versatility and ability to approach or exceed human-level accuracy. These computational models have seemingly insatiable appetites for computational resources not only while training, but also when deployed at scales ranging from data centers all the way down to embedded devices. As such, increasing consideration is being made to maximize the computational efficiency given limited hardware and energy resources and, as a result, inferencing with reduced precision has emerged as a viable alternative to the IEEE 754 Standard f…
Center for Data Science（数据科学中心）；Peking University（北京大学）；Megvii（旷视科技）；School of Mathematical Sciences（数学科学学院）
Quantized Neural Networks (QNNs) use low bit-width fixed-point numbers for representing weight parameters and activations, and are often used in real-world applications due to their saving of computation resources and reproducibility of results. Batch Normalization (BN) poses a challenge for QNNs for requiring floating points in reciprocal operations, and previous QNNs either require computing BN at high precision or revise BN to some variants in heuristic ways. In this work, we propose a novel method to quantize BN by converting an affine transformation of two floating points to a fixed-point…
University of Stuttgart（斯图加特大学）；Huawei Technologies Co., Ltd（华为技术有限公司）；Huawei Technologies Duesseldorf GmbH（华为技术杜塞尔多夫有限公司）
Finding optimal message quantization is a key requirement for low complexity belief propagation (BP) decoding. To this end, we propose a floating-point surrogate model that imitates quantization effects as additions of uniform noise, whose amplitudes are trainable variables. We verify that the surrogate model closely matches the behavior of a fixed-point implementation and propose a hand-crafted loss function to realize a trade-off between complexity and error-rate performance. A deep learning-based method is then applied to optimize the message bitwidths. Moreover, we show that parameter shar…
