We consider the one-bit quantizer that minimizes the mean squared error for a source living in a real Hilbert space. The optimal quantizer is a projection followed by a thresholding operation, and we provide methods for identifying the optimal direction along which to project. As an application of our methods, we characterize the optimal one-bit quantizer for a continuous-time random process that exhibits low-dimensional structure. We numerically show that this optimal quantizer is found by a neural-network-based compressor trained via stochastic gradient descent.
In this paper, we will show that the quantization in layer's input is more important than parameters' quantization for loss function. And the algorithm which is based on the layer's input quantization error is better than hessian-based mixed precision layout algorithm.
To adopt convolutional neural networks (CNN) for a range of resource-constrained targets, it is necessary to compress the CNN models by performing quantization, whereby precision representation is converted to a lower bit representation. To overcome problems such as sensitivity of the training dataset, high computational requirements, and large time consumption, post-training quantization methods that do not require retraining have been proposed. In addition, to compensate for the accuracy drop without retraining, previous studies on post-training quantization have proposed several complementary methods: calibration, schemes, clipping, granularity, and mixed-precision. To generate a quantized model with minimal error, it is necessary to study all possible combinations of the methods because each of them is complementary and the CNN models have different characteristics. However, an exhaustive or a heuristic search is either too time-consuming or suboptimal. To overcome this challenge, we propose an auto-tuner known as Quantune, which builds a gradient tree boosting model to accelerate the search for the configurations of quantization and reduce the quantization error. We evaluate and compare Quantune with the random, grid, and genetic algorithms. The experimental results show that Quantune reduces the search time for quantization by approximately 36.5x with an accuracy loss of 0.07 ~ 0.65% across six CNN models, including the fragile ones (MobileNet, SqueezeNet, and ShuffleNet). To support multiple targets and adopt continuously evolving quantization works, Quantune is implemented on a full-fledged compiler for deep learning as an open-sourced project.
Neural network quantization is a promising compression technique to reduce memory footprint and save energy consumption, potentially leading to real-time inference. However, there is a performance gap between quantized and full-precision models. To reduce it, existing quantization approaches require high-precision INT32 or full-precision multiplication during inference for scaling or dequantization. This introduces a noticeable cost in terms of memory, speed, and required energy. To tackle these issues, we present F8Net, a novel quantization framework consisting of only fixed-point 8-bit multiplication. To derive our method, we first discuss the advantages of fixed-point multiplication with different formats of fixed-point numbers and study the statistical behavior of the associated fixed-point numbers. Second, based on the statistical and algorithmic analysis, we apply different fixed-point formats for weights and activations of different layers. We introduce a novel algorithm to automatically determine the right format for each layer during training. Third, we analyze a previous quantization algorithm -- parameterized clipping activation (PACT) -- and reformulate it using fixed-point arithmetic. Finally, we unify the recently proposed method for quantization fine-tuning and our fixed-point approach to show the potential of our method. We verify F8Net on ImageNet for MobileNet V1/V2 and ResNet18/50. Our approach achieves comparable and better performance, when compared not only to existing quantization techniques with INT32 multiplication or floating-point arithmetic, but also to the full-precision counterparts, achieving state-of-the-art performance.
We apply object detection techniques based on deep convolutional blocks to end-to-end jet identification and reconstruction tasks encountered at the CERN Large Hadron Collider (LHC). Collision events produced at the LHC and represented as an image composed of calorimeter and tracker cells are given as an input to a Single Shot Detection network. The algorithm, named PFJet-SSD performs simultaneous localization, classification and regression tasks to cluster jets and reconstruct their features. This all-in-one single feed-forward pass gives advantages in terms of execution time and an improved accuracy w.r.t. traditional rule-based methods. A further gain is obtained from network slimming, homogeneous quantization, and optimized runtime for meeting memory and latency constraints of a typical real-time processing environment. We experiment with 8-bit and ternary quantization, benchmarking their accuracy and inference latency against a single-precision floating-point. We show that the ternary network closely matches the performance of its full-precision equivalent and outperforms the state-of-the-art rule-based algorithm. Finally, we report the inference latency on different hardware platforms and discuss future applications.
With the emergence of Artificial Intelligence (AI), new attention has been given to implement AI algorithms on resource constrained tiny devices to expand the application domain of IoT. Multimodal Learning has recently become very popular with the classification task due to its impressive performance for both image and audio event classification. This paper presents TinyM$^2$Net -- a flexible system algorithm co-designed multimodal learning framework for resource constrained tiny devices. The framework was designed to be evaluated on two different case-studies: COVID-19 detection from multimodal audio recordings and battle field object detection from multimodal images and audios. In order to compress the model to implement on tiny devices, substantial network architecture optimization and mixed precision quantization were performed (mixed 8-bit and 4-bit). TinyM$^2$Net shows that even a tiny multimodal learning model can improve the classification performance than that of any unimodal frameworks. The most compressed TinyM$^2$Net achieves 88.4% COVID-19 detection accuracy (14.5% improvement from unimodal base model) and 96.8% battle field object detection accuracy (3.9% improvement from unimodal base model). Finally, we test our TinyM$^2$Net models on a Raspberry Pi 4 to see how they perform when deployed to a resource constrained tiny device.
For binary neural networks (BNNs) to become the mainstream on-device computer vision algorithm, they must achieve a superior speed-vs-accuracy tradeoff than 8-bit quantization and establish a similar degree of general applicability in vision tasks. To this end, we propose a BNN framework comprising 1) a minimalistic inference scheme for hardware-friendliness, 2) an over-parameterized training scheme for high accuracy, and 3) a simple procedure to adapt to different vision tasks. The resultant framework overtakes 8-bit quantization in the speed-vs-accuracy tradeoff for classification, detection, segmentation, super-resolution and matching: our BNNs not only retain the accuracy levels of their 8-bit baselines but also showcase 1.3-2.4$\times$ faster FPS on mobile CPUs. Similar conclusions can be drawn for prototypical systolic-array-based AI accelerators, where our BNNs promise 2.8-7$\times$ fewer execution cycles than 8-bit and 2.1-2.7$\times$ fewer cycles than alternative BNN designs. These results suggest that the time for large-scale BNN adoption could be upon us.
This paper presents a learning-based method to improve bi-prediction in video coding. In conventional video coding solutions, the motion compensation of blocks from already decoded reference pictures stands out as the principal tool used to predict the current frame. Especially, the bi-prediction, in which a block is obtained by averaging two different motion-compensated prediction blocks, significantly improves the final temporal prediction accuracy. In this context, we introduce a simple neural network that further improves the blending operation. A complexity balance, both in terms of network size and encoder mode selection, is carried out. Extensive tests on top of the recently standardized VVC codec are performed and show a BD-rate improvement of -1.4% in random access configuration for a network size of fewer than 10k parameters. We also propose a simple CPU-based implementation and direct network quantization to assess the complexity/gains tradeoff in a conventional codec framework.
Keyword Spotting nowadays is an integral part of speech-oriented user interaction targeted for smart devices. To this extent, neural networks are extensively used for their flexibility and high accuracy. However, coming up with a suitable configuration for both accuracy requirements and hardware deployment is a challenge. We propose a regression-based network exploration technique that considers the scaling of the network filters ($s$) and quantization ($q$) of the network layers, leading to a friendly and energy-efficient configuration for FPGA hardware implementation. We experiment with different combinations of $\mathcal{NN}\scriptstyle\langle q,\,s\rangle \displaystyle$ on the FPGA to profile the energy consumption of the deployed network so that the user can choose the most energy-efficient network configuration promptly. Our accelerator design is deployed on the Xilinx AC 701 platform and has at least 2.1$\times$ and 4$\times$ improvements on energy and energy efficiency results, respectively, compared to recent hardware implementations for keyword spotting.
Quantization of the weights and activations is one of the main methods to reduce the computational footprint of Deep Neural Networks (DNNs) training. Current methods enable 4-bit quantization of the forward phase. However, this constitutes only a third of the training process. Reducing the computational footprint of the entire training process requires the quantization of the neural gradients, i.e., the loss gradients with respect to the outputs of intermediate neural layers. Previous works separately showed that accurate 4-bit quantization of the neural gradients needs to (1) be unbiased and (2) have a log scale. However, no previous work aimed to combine both ideas, as we do in this work. Specifically, we examine the importance of having unbiased quantization in quantized neural network training, where to maintain it, and how to combine it with logarithmic quantization. Based on this, we suggest a $\textit{logarithmic unbiased quantization}$ (LUQ) method to quantize both the forward and backward phases to 4-bit, achieving state-of-the-art results in 4-bit training without the overhead. For example, in ResNet50 on ImageNet, we achieved a degradation of 1.1%. We further improve this to a degradation of only 0.32% after three epochs of high precision fine-tuning, combined with a variance reduction method -- where both these methods add overhead comparable to previously suggested methods.
Although the semantic communications have exhibited satisfactory performance in a large number of tasks, the impact of semantic noise and the robustness of the systems have not been well investigated. Semantic noise is a particular kind of noise in semantic communication systems, which refers to the misleading between the intended semantic symbols and received ones. In this paper, we first propose a framework for the robust end-to-end semantic communication systems to combat the semantic noise. Particularly, we analyze the causes of semantic noise and propose a practical method to generate it. To remove the effect of semantic noise, adversarial training is proposed to incorporate the samples with semantic noise in the training dataset. Then, the masked autoencoder (MAE) is designed as the architecture of a robust semantic communication system, where a portion of the input is masked. To further improve the robustness of semantic communication systems, we firstly employ the vector quantization-variational autoencoder (VQ-VAE) to design a discrete codebook shared by the transmitter and the receiver for encoded feature representation. Thus, the transmitter simply needs to transmit the indices of these features in the codebook. Simulation results show that our proposed method significantly improves the robustness of semantic communication systems against semantic noise with significant reduction on the transmission overhead.
Power consumption is a major obstacle in the deployment of deep neural networks (DNNs) on end devices. Existing approaches for reducing power consumption rely on quite general principles, including avoidance of multiplication operations and aggressive quantization of weights and activations. However, these methods do not take into account the precise power consumed by each module in the network, and are therefore not optimal. In this paper we develop accurate power consumption models for all arithmetic operations in the DNN, under various working conditions. We reveal several important factors that have been overlooked to date. Based on our analysis, we present PANN (power-aware neural network), a simple approach for approximating any full-precision network by a low-power fixed-precision variant. Our method can be applied to a pre-trained network, and can also be used during training to achieve improved performance. In contrast to previous methods, PANN incurs only a minor degradation in accuracy w.r.t. the full-precision version of the network, even when working at the power-budget of a 2-bit quantized variant. In addition, our scheme enables to seamlessly traverse the power-accuracy trade-off at deployment time, which is a major advantage over existing quantization methods that are constrained to specific bit widths.
With the recent boom of video-based social platforms (e.g., YouTube and TikTok), video retrieval using sentence queries has become an important demand and attracts increasing research attention. Despite the decent performance, existing text-video retrieval models in vision and language communities are impractical for large-scale Web search because they adopt brute-force search based on high-dimensional embeddings. To improve efficiency, Web search engines widely apply vector compression libraries (e.g., FAISS) to post-process the learned embeddings. Unfortunately, separate compression from feature encoding degrades the robustness of representations and incurs performance decay. To pursue a better balance between performance and efficiency, we propose the first quantized representation learning method for cross-view video retrieval, namely Hybrid Contrastive Quantization (HCQ). Specifically, HCQ learns both coarse-grained and fine-grained quantizations with transformers, which provide complementary understandings for texts and videos and preserve comprehensive semantic information. By performing Asymmetric-Quantized Contrastive Learning (AQ-CL) across views, HCQ aligns texts and videos at coarse-grained and multiple fine-grained levels. This hybrid-grained learning strategy serves as strong supervision on the cross-view video quantization model, where contrastive learning at different levels can be mutually promoted. Extensive experiments on three Web video benchmark datasets demonstrate that HCQ achieves competitive performance with state-of-the-art non-compressed retrieval methods while showing high efficiency in storage and computation. Code and configurations are available at https://github.com/gimpong/WWW22-HCQ.
Over the past decade, deep learning (DL) has led to significant advancements in various fields of artificial intelligence, including machine translation (MT). These advancements would not be possible without the ever-growing volumes of data and the hardware that allows large DL models to be trained efficiently. Due to the large amount of computing cores as well as dedicated memory, graphics processing units (GPUs) are a more effective hardware solution for training and inference with DL models than central processing units (CPUs). However, the former is very power demanding. The electrical power consumption has economical as well as ecological implications. This chapter focuses on the ecological footprint of neural MT systems. It starts from the power drain during the training of and the inference with neural MT models and moves towards the environment impact, in terms of carbon dioxide emissions. Different architectures (RNN and Transformer) and different GPUs (consumer-grate NVidia 1080Ti and workstation-grade NVidia P100) are compared. Then, the overall CO2 offload is calculated for Ireland and the Netherlands. The NMT models and their ecological impact are compared to common household appliances to draw a more clear picture. The last part of this chapter analyses quantization, a technique for reducing the size and complexity of models, as a way to reduce power consumption. As quantized models can run on CPUs, they present a power-efficient inference solution without depending on a GPU.
Image generative models can learn the distributions of the training data and consequently generate examples by sampling from these distributions. However, when the training dataset is corrupted with outliers, generative models will likely produce examples that are also similar to the outliers. In fact, a small portion of outliers may induce state-of-the-art generative models, such as Vector Quantized-Variational AutoEncoder (VQ-VAE), to learn a significant mode from the outliers. To mitigate this problem, we propose a robust generative model based on VQ-VAE, which we name Robust VQ-VAE (RVQ-VAE). In order to achieve robustness, RVQ-VAE uses two separate codebooks for the inliers and outliers. To ensure the codebooks embed the correct components, we iteratively update the sets of inliers and outliers during each training epoch. To ensure that the encoded data points are matched to the correct codebooks, we quantize using a weighted Euclidean distance, whose weights are determined by directional variances of the codebooks. Both codebooks, together with the encoder and decoder, are trained jointly according to the reconstruction loss and the quantization loss. We experimentally demonstrate that RVQ-VAE is able to generate examples from inliers even if a large portion of the training data points are corrupted.
In this work, PRUNIX, a framework for training and pruning convolutional neural networks is proposed for deployment on memristor crossbar based accelerators. PRUNIX takes into account the numerous non-ideal effects of memristor crossbars including weight quantization, state-drift, aging and stuck-at-faults. PRUNIX utilises a novel Group Sawtooth Regularization intended to improve non-ideality tolerance as well as sparsity, and a novel Adaptive Pruning Algorithm (APA) intended to minimise accuracy loss by considering the sensitivity of different layers of a CNN to pruning. We compare our regularization and pruning methods with other standards on multiple CNN architectures, and observe an improvement of 13% test accuracy when quantization and other non-ideal effects are accounted for with an overall sparsity of 85%, which is similar to other methods
Vector Quantization (VQ) is a method for discretizing latent representations and has become a major part of the deep learning toolkit. It has been theoretically and empirically shown that discretization of representations leads to improved generalization, including in reinforcement learning where discretization can be used to bottleneck multi-agent communication to promote agent specialization and robustness. The discretization tightness of most VQ-based methods is defined by the number of discrete codes in the representation vector and the codebook size, which are fixed as hyperparameters. In this work, we propose learning to dynamically select discretization tightness conditioned on inputs, based on the hypothesis that data naturally contains variations in complexity that call for different levels of representational coarseness. We show that dynamically varying tightness in communication bottlenecks can improve model performance on visual reasoning and reinforcement learning tasks.
Everyone "knows" that compressing a video will degrade the accuracy of object tracking. Yet, a literature search on this topic reveals that there is very little documented evidence for this presumed fact. Part of the reason is that, until recently, there were no object tracking datasets for uncompressed video, which made studying the effects of compression on tracking accuracy difficult. In this paper, using a recently published dataset that contains tracking annotations for uncompressed videos, we examined the degradation of tracking accuracy due to video compression using rigorous statistical methods. Specifically, we examined the impact of quantization parameter (QP) and motion search range (MSR) on Multiple Object Tracking Accuracy (MOTA). The results show that QP impacts MOTA at the 95% confidence level, while there is insufficient evidence to claim that MSR impacts MOTA. Moreover, regression analysis allows us to derive a quantitative relationship between MOTA and QP for the specific tracker used in the experiments.
Video compression is a central feature of the modern internet powering technologies from social media to video conferencing. While video compression continues to mature, for many compression settings, quality loss is still noticeable. These settings nevertheless have important applications to the efficient transmission of videos over bandwidth constrained or otherwise unstable connections. In this work, we develop a deep learning architecture capable of restoring detail to compressed videos which leverages the underlying structure and motion information embedded in the video bitstream. We show that this improves restoration accuracy compared to prior compression correction methods and is competitive when compared with recent deep-learning-based video compression methods on rate-distortion while achieving higher throughput. Furthermore, we condition our model on quantization data which is readily available in the bitstream. This allows our single model to handle a variety of different compression quality settings which required an ensemble of models in prior work.
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.