Memory footprint is one of the main limiting factors for large neural network training. In backpropagation, one needs to store the input to each operation in the computational graph. Every modern neural network model has quite a few pointwise nonlinearities in its architecture, and such operation induces additional memory costs which -- as we show -- can be significantly reduced by quantization of the gradients. We propose a systematic approach to compute optimal quantization of the retained gradients of the pointwise nonlinear functions with only a few bits per each element. We show that such approximation can be achieved by computing optimal piecewise-constant approximation of the derivative of the activation function, which can be done by dynamic programming. The drop-in replacements are implemented for all popular nonlinearities and can be used in any existing pipeline. We confirm the memory reduction and the same convergence on several open benchmarks.
University of Toronto（多伦多大学）；Shanghai Jiao Tong University（上海交通大学）；Vector Institute（向量研究所）
Training deep learning models can be computationally expensive. Prior works have shown that increasing the batch size can potentially lead to better overall throughput. However, the batch size is frequently limited by the accelerator memory capacity due to the activations/feature maps stored for the training backward pass, as larger batch sizes require larger feature maps to be stored. Transformer-based models, which have recently seen a surge in popularity due to their good performance and applicability to a variety of tasks, have a similar problem. To remedy this issue, we propose Tempo, a n…
University of Bologna（博洛尼亚大学）；University of Modena and Reggio Emilia（摩德纳-雷焦艾米利亚大学）；ETH Zurich（苏黎世联邦理工学院）；Politecnico di Torino（都灵理工大学）
Hearth Rate (HR) monitoring is increasingly performed in wrist-worn devices using low-cost photoplethysmography (PPG) sensors. However, Motion Artifacts (MAs) caused by movements of the subject's arm affect the performance of PPG-based HR tracking. This is typically addressed coupling the PPG signal with acceleration measurements from an inertial sensor. Unfortunately, most standard approaches of this kind rely on hand-tuned parameters, which impair their generalization capabilities and their applicability to real data in the field. In contrast, methods based on deep learning, despite their be…
Deep Neural Networks (DNNs) have achieved tremendous success for cognitive applications. The core operation in a DNN is the dot product between quantized inputs and weights. Prior works exploit the weight/input repetition that arises due to quantization to avoid redundant computations in Convolutional Neural Networks (CNNs). However, in this paper we show that their effectiveness is severely limited when applied to Fully-Connected (FC) layers, which are commonly used in state-of-the-art DNNs, as it is the case of modern Recurrent Neural Networks (RNNs) and Transformer models. To improve energy…
Parameter quantization in convolutional neural networks (CNNs) can help generate efficient models with lower memory footprint and computational complexity. But, homogeneous quantization can result in significant degradation of CNN model accuracy. In contrast, heterogeneous quantization represents a promising approach to realize compact, quantized models with higher inference accuracies. In this paper, we propose HQNNA, a CNN accelerator based on non-coherent silicon photonics that can accelerate both homogeneously quantized and heterogeneously quantized CNN models. Our analyses show that HQNNA…
Australian National University（澳大利亚国立大学）；Amazon Science（亚马逊科学）；DATA61, CSIRO（联邦科学与工业研究组织数据61）
Neural network quantization has become increasingly popular due to efficient memory consumption and faster computation resulting from bitwise operations on the quantized networks. Even though they exhibit excellent generalization capabilities, their robustness properties are not well-understood. In this work, we systematically study the robustness of quantized networks against gradient based adversarial attacks and demonstrate that these quantized models suffer from gradient vanishing issues and show a fake sense of robustness. By attributing gradient vanishing to poor forward-backward signal …
The increasing size of neural network models has been critical for improvements in their accuracy, but device memory is not growing at the same rate. This creates fundamental challenges for training neural networks within limited memory environments. In this work, we propose ActNN, a memory-efficient training framework that stores randomly quantized activations for back propagation. We prove the convergence of ActNN for general network architectures, and we characterize the impact of quantization on the convergence via an exact expression for the gradient variance. Using our theory, we propose…
UC San Diego（加州大学圣地亚哥分校）；Microsoft Research Redmond（微软雷德蒙德研究院）；Megvii Inc.（旷视科技）
The problem of quantizing the activations of a deep neural network is considered. An examination of the popular binary quantization approach shows that this consists of approximating a classical non-linearity, the hyperbolic tangent, by two functions: a piecewise constant sign function, which is used in feedforward network computations, and a piecewise linear hard tanh function, used in the backpropagation step during network learning. The problem of approximating the ReLU non-linearity, widely used in the recent deep learning literature, is then considered. An half-wave Gaussian quantizer (HW…
The deep layers of modern neural networks extract a rather rich set of features as an input propagates through the network. This paper sets out to harvest these rich intermediate representations for quantization with minimal accuracy loss while significantly reducing the memory footprint and compute intensity of the DNN. This paper utilizes knowledge distillation through teacher-student paradigm (Hinton et al., 2015) in a novel setting that exploits the feature extraction capability of DNNs for higher-accuracy quantization. As such, our algorithm logically divides a pretrained full-precision D…
Université de Montréal（蒙特利尔大学）；MILA；IMT Atlantique（IMT大西洋高等矿业学院）；Lab-STICC（STICC实验室）；ISCAS 2019（ISCAS 2019（会议名称，不提取））
Convolutional Neural Networks (CNNs) are state-of-the-art in numerous computer vision tasks such as object classification and detection. However, the large amount of parameters they contain leads to a high computational complexity and strongly limits their usability in budget-constrained devices such as embedded devices. In this paper, we propose a combination of a new pruning technique and a quantization scheme that effectively reduce the complexity and memory usage of convolutional layers of CNNs, and replace the complex convolutional operation by a low-cost multiplexer. We perform experimen…
University of Southern California（南加州大学）；Emory University（埃默里大学）；Xidian University（西安电子科技大学）
Adversarial data examples have drawn significant attention from the machine learning and security communities. A line of work on tackling adversarial examples is certified robustness via randomized smoothing that can provide a theoretical robustness guarantee. However, such a mechanism usually uses floating-point arithmetic for calculations in inference and requires large memory footprints and daunting computational costs. These defensive models cannot run efficiently on edge devices nor be deployed on integer-only logical units such as Turing Tensor Cores or integer-only ARM processors. To ov…
We describe a large vocabulary speech recognition system that is accurate, has low latency, and yet has a small enough memory and computational footprint to run faster than real-time on a Nexus 5 Android smartphone. We employ a quantized Long Short-Term Memory (LSTM) acoustic model trained with connectionist temporal classification (CTC) to directly predict phoneme targets, and further reduce its memory footprint using an SVD-based compression scheme. Additionally, we minimize our memory footprint by using a single language model for both dictation and voice command domains, constructed using …
AMD（超威半导体公司）；Fermi National Accelerator Laboratory（费米国家加速器实验室）；Massachusetts Institute of Technology（麻省理工学院）；European Organization for Nuclear Research (CERN)（欧洲核子研究组织（CERN））；Heidelberg University（海德堡大学）；Harvard University（哈佛大学）；University of Washington（华盛顿大学）
We present extensions to the Open Neural Network Exchange (ONNX) intermediate representation format to represent arbitrary-precision quantized neural networks. We first introduce support for low precision quantization in existing ONNX-based quantization formats by leveraging integer clipping, resulting in two new backward-compatible variants: the quantized operator format with clipping and quantize-clip-dequantize (QCDQ) format. We then introduce a novel higher-level ONNX format called quantized ONNX (QONNX) that introduces three new operators -- Quant, BipolarQuant, and Trunc -- in order to r…
Training on the Edge enables neural networks to learn continuously from new data after deployment on memory-constrained edge devices. Previous work is mostly concerned with reducing the number of model parameters which is only beneficial for inference. However, memory footprint from activations is the main bottleneck for training on the edge. Existing incremental training methods fine-tune the last few layers sacrificing accuracy gains from re-training the whole model. In this work, we investigate the memory footprint of training deep learning models, and use our observations to propose BitTra…
In low-latency or mobile applications, lower computation complexity, lower memory footprint and better energy efficiency are desired. Many prior works address this need by removing redundant parameters. Parameter quantization replaces floating-point arithmetic with lower precision fixed-point arithmetic, further reducing complexity. Typical training of quantized weight neural networks starts from fully quantized weights. Quantization creates random noise. As a way to compensate for this noise, during training, we propose to quantize some weights while keeping others in floating-point precision…
Quantizing neural networks to low-bitwidth is important for model deployment on resource-limited edge hardware. Although a quantized network has a smaller model size and memory footprint, it is fragile to adversarial attacks. However, few methods study the robustness and training efficiency of quantized networks. To this end, we propose a new method by recasting robust quantization as an online domain generalization problem, termed ODG-Q, which generates diverse adversarial data at a low cost during training. ODG-Q consistently outperforms existing works against various adversarial attacks. Fo…
University of Bologna（博洛尼亚大学）；University of Modena and Reggio Emilia（摩德纳-雷焦艾米利亚大学）；ETH Zürich（苏黎世联邦理工学院）
In the last few years, research and development on Deep Learning models and techniques for ultra-low-power devices in a word, TinyML has mainly focused on a train-then-deploy assumption, with static models that cannot be adapted to newly collected data without cloud-based data collection and fine-tuning. Latent Replay-based Continual Learning (CL) techniques[1] enable online, serverless adaptation in principle, but so farthey have still been too computation and memory-hungry for ultra-low-power TinyML devices, which are typically based on microcontrollers. In this work, we introduce a HW/SW pl…
We consider learning deep neural networks (DNNs) that consist of low-precision weights and activations for efficient inference of fixed-point operations. In training low-precision networks, gradient descent in the backward pass is performed with high-precision weights while quantized low-precision weights and activations are used in the forward pass to calculate the loss function for training. Thus, the gradient descent becomes suboptimal, and accuracy loss follows. In order to reduce the mismatch in the forward and backward passes, we utilize mean squared quantization error (MSQE) regularizat…
Model compression has gained a lot of attention due to its ability to reduce hardware resource requirements significantly while maintaining accuracy of DNNs. Model compression is especially useful for memory-intensive recurrent neural networks because smaller memory footprint is crucial not only for reducing storage requirement but also for fast inference operations. Quantization is known to be an effective model compression method and researchers are interested in minimizing the number of bits to represent parameters. In this work, we introduce an iterative technique to apply quantization, pr…
The biggest challenge for the deployment of Deep Neural Networks (DNNs) close to the generated data on edge devices is their size, i.e., memory footprint and computational complexity. Both are significantly reduced with quantization. With the resulting lower word-length, the energy efficiency of DNNs increases proportionally. However, lower word-length typically causes accuracy degradation. To counteract this effect, the quantized DNN is retrained. Unfortunately, training costs up to 5000x more energy than the inference of the quantized DNN. To address this issue, we propose a post-training qu…
Fraunhofer Heinrich Hertz Institute（弗劳恩霍夫海因里希·赫兹研究所）
Deep Neural Networks are successful but highly computationally expensive learning systems. One of the main sources of time and energy drains is the well known backpropagation (backprop) algorithm, which roughly accounts for 2/3 of the computational complexity of training. In this work we propose a method for reducing the computational cost of backprop, which we named dithered backprop. It consists in applying a stochastic quantization scheme to intermediate results of the method. The particular quantisation scheme, called non-subtractive dither (NSD), induces sparsity which can be exploited by…
ETH Zürich（苏黎世联邦理工学院）；University of Bologna（博洛尼亚大学）；Huawei Technologies（华为技术有限公司）
Motor-Imagery Brain--Machine Interfaces (MI-BMIs)promise direct and accessible communication between human brains and machines by analyzing brain activities recorded with Electroencephalography (EEG). Latency, reliability, and privacy constraints make it unsuitable to offload the computation to the cloud. Practical use cases demand a wearable, battery-operated device with low average power consumption for long-term use. Recently, sophisticated algorithms, in particular deep learning models, have emerged for classifying EEG signals. While reaching outstanding accuracy, these models often exceed…
Technion – Israel Institute of Technology（以色列理工学院）
Deep neural networks (DNNs) are used by different applications that are executed on a range of computer architectures, from IoT devices to supercomputers. The footprint of these networks is huge as well as their computational and communication needs. In order to ease the pressure on resources, research indicates that in many cases a low precision representation (1-2 bit per parameter) of weights and other parameters can achieve similar accuracy while requiring less resources. Using quantized values enables the use of FPGAs to run NNs, since FPGAs are well fitted to these primitives; e.g., FPGA…
Neural network training is computationally and memory intensive. Sparse training can reduce the burden on emerging hardware platforms designed to accelerate sparse computations, but it can affect network convergence. In this work, we propose a novel CNN training algorithm Sparse Weight Activation Training (SWAT). SWAT is more computation and memory-efficient than conventional training. SWAT modifies back-propagation based on the empirical insight that convergence during training tends to be robust to the elimination of (i) small magnitude weights during the forward pass and (ii) both small mag…
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）；University of California, Irvine（加利福尼亚大学尔湾分校）；Qualcomm AI Research（高通人工智能研究院）
Training activation quantized neural networks involves minimizing a piecewise constant function whose gradient vanishes almost everywhere, which is undesirable for the standard back-propagation or chain rule. An empirical way around this issue is to use a straight-through estimator (STE) (Bengio et al., 2013) in the backward pass only, so that the "gradient" through the modified chain rule becomes non-trivial. Since this unusual "gradient" is certainly not the gradient of loss function, the following question arises: why searching in its negative direction minimizes the training loss? In this …
Quantization based on the binary codes is gaining attention because each quantized bit can be directly utilized for computations without dequantization using look-up tables. Previous attempts, however, only allow for integer numbers of quantization bits, which ends up restricting the search space for compression ratio and accuracy. In this paper, we propose an encryption algorithm/architecture to compress quantized weights so as to achieve fractional numbers of bits per weight. Decryption during inference is implemented by digital XOR-gate networks added into the neural network model while XOR…
Residual neural networks can be viewed as the forward Euler discretization of an Ordinary Differential Equation (ODE) with a unit time step. This has recently motivated researchers to explore other discretization approaches and train ODE based networks. However, an important challenge of neural ODEs is their prohibitive memory cost during gradient backpropogation. Recently a method proposed in [8], claimed that this memory overhead can be reduced from O(LN_t), where N_t is the number of time steps, down to O(L) by solving forward ODE backwards in time, where L is the depth of the network. Howe…
BEP: A Binary Error Propagation Algorithm for Binary Neural Networks Training
Department of Electronics, Information and Bioengineering, Politecnico di Milano（电子、信息与生物工程系，米兰理工学院）；Faculty of Informatics and IDSIA, Università della Svizzera italiana（信息学院和IDSIA，瑞士大学）；Department of Computing Sciences and BIDSA, Bocconi University（计算科学系和BIDSA，博科尼大学）
Binary Quantized Neural Network Training Is W[1]-Hard Parameterized by Input and Output Dimensions
Key Laboratory of System Software (Chinese Academy of Sciences)（系统软件重点实验室（中国科学院））；State Key Laboratory of Computer Science（计算机科学国家重点实验室）；Institute of Software, Chinese Academy of Sciences（中国科学院软件研究所）；School of Computer Science and Technology, University of Chinese Academy of Sciences（中国科学院大学计算机科学与技术学院）
We propose DoReFa-Net, a method to train convolutional neural networks that have low bitwidth weights and activations using low bitwidth parameter gradients. In particular, during backward pass, parameter gradients are stochastically quantized to low bitwidth numbers before being propagated to convolutional layers. As convolutions during forward/backward passes can now operate on low bitwidth weights and activations/gradients respectively, DoReFa-Net can use bit convolution kernels to accelerate both training and inference. Moreover, as bit convolutions can be efficiently implemented on CPU, F…
Processing-in-memory (PIM), an increasingly studied neuromorphic hardware, promises orders of energy and throughput improvements for deep learning inference. Leveraging the massively parallel and efficient analog computing inside memories, PIM circumvents the bottlenecks of data movements in conventional digital hardware. However, an extra quantization step (i.e. PIM quantization), typically with limited resolution due to hardware constraints, is required to convert the analog computing results into digital domain. Meanwhile, non-ideal effects extensively exist in PIM quantization because of t…
Sharif University of Technology（谢里夫理工大学）；Technical University of Munich（慕尼黑工业大学）
Although prior art has demonstrated negligible accuracy drop in sub-byte quantization -- where weights and/or activations are represented by less than 8 bits -- popular SIMD instructions of CPUs do not natively support these datatypes. While recent methods, such as ULPPACK, are already using sub-byte quantization on general-purpose CPUs with vector units, they leave out several empty bits between the sub-byte values in memory and in vector registers to avoid overflow to the neighbours during the operations. This results in memory footprint and bandwidth-usage inefficiencies and suboptimal perf…
Intel – Artificial Intelligence Products Group (AIPG)（英特尔 - 人工智能产品组（AIPG））；Technion – Israel Institute of Technology（以色列理工学院）
Convolutional neural networks (CNNs) achieve state-of-the-art accuracy in a variety of tasks in computer vision and beyond. One of the major obstacles hindering the ubiquitous use of CNNs for inference on low-power edge devices is their high computational complexity and memory bandwidth requirements. The latter often dominates the energy footprint on modern hardware. In this paper, we introduce a lossy transform coding approach, inspired by image and video compression, designed to reduce the memory bandwidth due to the storage of intermediate activation calculation results. Our method does not…
Many neural network quantization techniques have been developed to decrease the computational and memory footprint of deep learning. However, these methods are evaluated subject to confounding tradeoffs that may affect inference acceleration or resource complexity in exchange for higher accuracy. In this work, we articulate a variety of tradeoffs whose impact is often overlooked and empirically analyze their impact on uniform and mixed-precision post-training quantization, finding that these confounding tradeoffs may have a larger impact on quantized network accuracy than the actual quantizati…
