For distributed learning among collaborative users, this paper develops and analyzes a communication-efficient scheme for federated learning (FL) over the air, which incorporates 1-bit compressive sensing (CS) into analog aggregation transmissions. To facilitate design parameter optimization, we theoretically analyze the efficacy of the proposed scheme by deriving a closed-form expression for the expected convergence rate of the FL over the air. Our theoretical results reveal the tradeoff between convergence performance and communication efficiency as a result of the aggregation errors caused by sparsification, dimension reduction, quantization, signal reconstruction and noise. Then, we formulate 1-bit CS based FL over the air as a joint optimization problem to mitigate the impact of these aggregation errors through joint optimal design of worker scheduling and power scaling policy. An enumeration-based method is proposed to solve this non-convex problem, which is optimal but becomes computationally infeasible as the number of devices increases. For scalable computing, we resort to the alternating direction method of multipliers (ADMM) technique to develop an efficient implementation that is suitable for large-scale networks. Simulation results show that our proposed 1-bit CS based FL over the air achieves comparable performance to the ideal case where conventional FL without compression and quantification is applied over error-free aggregation, at much reduced communication overhead and transmission latency.
Quantization algorithms have been successfully adopted to option pricing in finance thanks to the high convergence rate of the numerical approximation. In particular, very recently, recursive marginal quantization has been proven to be a flexible and versatile tool when applied to stochastic volatility processes. In this paper we apply for the first time quantization techniques to the family of polynomial processes, by exploiting their peculiar nature. We focus our analysis on the stochastic volatility Jacobi process, by presenting two alternative quantization procedures: the first is a new discretization technique, whose foundation lies on the polynomial structure of the underlying process and which is suitable for vanilla option pricing, the second is based on recursive marginal quantization and it allows for pricing of (vanilla and) exotic derivatives. We prove theoretical results to assess the induced approximation errors, and we describe in numerical examples practical tools for fast vanilla and exotic option pricing.
This paper proposes two numerical solution based on Product Optimal Quantization for the pricing of Foreign Echange (FX) linked long term Bermudan options e.g. Bermudan Power Reverse Dual Currency options, where we take into account stochastic domestic and foreign interest rates on top of stochastic FX rate, hence we consider a 3-factor model. For these two numerical methods, we give an estimation of the $L^2$-error induced by such approximations and we illustrate them with market-based examples that highlight the speed of such methods.
Symmetry in biological and physical systems is a product of self organization driven by evolutionary processes, or mechanical systems under constraints. Symmetry based feature extrac-tion or representation by neural networks may unravel the most informative contents in large image databases. Despite significant achievements of artificial intelligence in recognition and classification of regular patterns, the problem of uncertainty remains a major challenge in ambiguous data. In this study, we present an artificial neural network that detects symmetry uncertainty states in human observers. To this end, we exploit a neural network metric in the output of a biologically inspired Self Organizing Map, the Quantization Error (SOM QE). Shape pairs with perfect geometric mirror symmetry but a non-homogenous appearance, caused by local variations in hue, saturation, or lightness within or across the shapes in a given pair produce, as shown here, longer choice RT for yes responses relative to symmetry. These data are consistently mirrored by the variations in the SOM QE from unsupervised neural network analysis of the same stimulus images. The neural network metric is thus capable of detecting and scaling human symmetry uncertainty in response to patterns. Such capacity is tightly linked to the metrics proven selectivity to local contrast and color variations in large and highly complex image data.
Intelligent reflecting surface (IRS) has emerged as a promising solution to enhance wireless information transmissions by adaptively controlling prorogation environment. Recently, the brand-new concept of utilizing IRS to implement a passive transmitter attracts researchers' attention since it potentially realizes low-complexity and hardware-efficient transmitters of multiple-input single/multiple-output (MISO/MIMO) systems. In this paper we investigate the problem of precoder design for a low-resolution IRS-based transmitter to implement multi-user MISO/MIMO wireless communications. Particularly, the IRS modulates information symbols by varying the phases of its reflecting elements and transmits them to $K$ single-antenna or multi-antenna users. We first aim to design the symbol-level precoder for IRS to realize the modulation and minimize the maximum symbol-error-rate (SER) of single-antenna receivers. In order to tackle this NP-hard problem, we first relax the low-resolution phase-shift constraint and solve this problem by Riemannian conjugate gradient (RCG) algorithm. Then, the low-resolution symbol-level precoding vector is obtained by direct quantization. Considering the large quantization error for 1-bit resolution case, the branch-and-bound method is utilized to solve the 1-bit resolution symbol-level precoding vector. For multi-antenna receivers, we propose to iteratively design the symbol-level precoder and combiner by decomposing the original large-scale optimization problem into several sub-problems. Simulation results validate the effectiveness of our proposed algorithms.
In HTTP Adaptive Streaming, video content is conventionally encoded by adapting its spatial resolution and quantization level to best match the prevailing network state and display characteristics. It is well known that the traditional solution, of using a fixed bitrate ladder, does not result in the highest quality of experience for the user. Hence, in this paper, we consider a content-driven approach for estimating the bitrate ladder, based on spatio-temporal features extracted from the uncompressed content. The method implements a content-driven interpolation. It uses the extracted features to train a machine learning model to infer the curvature points of the Rate-VMAF curves in order to guide a set of initial encodings. We employ the VMAF quality metric as a means of perceptually conditioning the estimation. When compared to exhaustive encoding that produces the reference ladder, the estimated ladder is composed by 74.3% of identical Rate-VMAF points with the reference ladder. The proposed method offers a significant reduction of the number of encodes required, 77.4%, at a small average Bj{\o}ntegaard Delta Rate cost, 1.12%.
We consider a multi-agent consensus problem in the presence of adversarial agents. The adversaries are able to listen to the inter-agent communications and try to estimate the state of the agents. The agents have a limited bit-rate for communication and are required to quantize the transmitted signal in order to meet the bit-rate constraint of the communication channel. We propose a consensus protocol that is protected against the adversaries, i.e., the expected mean-square error of the adversary state estimate is lower bounded. In order to deal with the bit-rate constraint, we propose a dynamic quantization scheme that guarantees protected consensus.
In this paper, we explore the small-cell uplink access point (AP) placement problem in the context of throughput-optimality and provide solutions while taking into consideration inter-cell interference. First, we briefly review the vector quantization (VQ) approach and related single user throughput-optimal formulations for AP placement. Then, we investigate the small-cell case with multiple users and expose the limitations of mean squared error based VQ for solving this problem. While the Lloyd algorithm from the VQ approach is found not to strictly solve the small-cell case, based on the tractability and quality of resulting AP placement, we deem it suitable as a simple and appropriate framework to solve more complicated problems. Accordingly, to minimize ICI and consequently enhance achievable throughput, we design two Lloyd-type algorithms, namely, the Interference Lloyd algorithm and the Inter-AP Lloyd algorithm, both of which incorporate ICI in their distortion functions. Simulation results show that both of the proposed algorithms provide superior 95\%-likely rate over the traditional Lloyd algorithm and the Inter-AP Lloyd algorithm yields a significant increase of up to 36.34\% in achievable rate over the Lloyd algorithm.
We present a scalable and efficient neural waveform coding system for speech compression. We formulate the speech coding problem as an autoencoding task, where a convolutional neural network (CNN) performs encoding and decoding as a neural waveform codec (NWC) during its feedforward routine. The proposed NWC also defines quantization and entropy coding as a trainable module, so the coding artifacts and bitrate control are handled during the optimization process. We achieve efficiency by introducing compact model components to NWC, such as gated residual networks and depthwise separable convolution. Furthermore, the proposed models are with a scalable architecture, cross-module residual learning (CMRL), to cover a wide range of bitrates. To this end, we employ the residual coding concept to concatenate multiple NWC autoencoding modules, where each NWC module performs residual coding to restore any reconstruction loss that its preceding modules have created. CMRL can scale down to cover lower bitrates as well, for which it employs linear predictive coding (LPC) module as its first autoencoder. The hybrid design integrates LPC and NWC by redefining LPC's quantization as a differentiable process, making the system training an end-to-end manner. The decoder of proposed system is with either one NWC (0.12 million parameters) in low to medium bitrate ranges (12 to 20 kbps) or two NWCs in the high bitrate (32 kbps). Although the decoding complexity is not yet as low as that of conventional speech codecs, it is significantly reduced from that of other neural speech coders, such as a WaveNet-based vocoder. For wide-band speech coding quality, our system yields comparable or superior performance to AMR-WB and Opus on TIMIT test utterances at low and medium bitrates. The proposed system can scale up to higher bitrates to achieve near transparent performance.
Quantization is a key technique to reduce the resource requirement and improve the performance of neural network deployment. However, different hardware backends such as x86 CPU, NVIDIA GPU, ARM CPU, and accelerators may demand different implementations for quantized networks. This diversity calls for specialized post-training quantization pipelines to built for each hardware target, an engineering effort that is often too large for developers to keep up with. We tackle this problem with an automated post-training quantization framework called HAGO. HAGO provides a set of general quantization graph transformations based on a user-defined hardware specification and implements a search mechanism to find the optimal quantization strategy while satisfying hardware constraints for any model. We observe that HAGO achieves speedups of 2.09x, 1.97x, and 2.48x on Intel Xeon Cascade Lake CPUs, NVIDIA Tesla T4 GPUs, ARM Cortex-A CPUs on Raspberry Pi4 relative to full precision respectively, while maintaining the highest reported post-training quantization accuracy in each case.
Model quantization is a promising approach to compress deep neural networks and accelerate inference, making it possible to be deployed on mobile and edge devices. To retain the high performance of full-precision models, most existing quantization methods focus on fine-tuning quantized model by assuming training datasets are accessible. However, this assumption sometimes is not satisfied in real situations due to data privacy and security issues, thereby making these quantization methods not applicable. To achieve zero-short model quantization without accessing training data, a tiny number of quantization methods adopt either post-training quantization or batch normalization statistics-guided data generation for fine-tuning. However, both of them inevitably suffer from low performance, since the former is a little too empirical and lacks training support for ultra-low precision quantization, while the latter could not fully restore the peculiarities of original data and is often low efficient for diverse data generation. To address the above issues, we propose a zero-shot adversarial quantization (ZAQ) framework, facilitating effective discrepancy estimation and knowledge transfer from a full-precision model to its quantized model. This is achieved by a novel two-level discrepancy modeling to drive a generator to synthesize informative and diverse data examples to optimize the quantized model in an adversarial learning fashion. We conduct extensive experiments on three fundamental vision tasks, demonstrating the superiority of ZAQ over the strong zero-shot baselines and validating the effectiveness of its main components. Code is available at <https://git.io/Jqc0y>.
Radio frequency interference (RFI) mitigation is critical to the proper operation of ultra-wideband (UWB) radar systems since RFI can severely degrade the radar imaging capability and target detection performance. In this paper, we address the RFI mitigation problem for one-bit UWB radar systems. A one-bit UWB system obtains its signed measurements via a low-cost and high rate sampling scheme, referred to as the Continuous Time Binary Value (CTBV) technology. This sampling strategy compares the signal to a known threshold varying with slow-time and therefore can be used to achieve a rather high sampling rate and quantization resolution with rather simple and affordable hardware. This paper establishes a proper data model for the RFI sources and proposes a novel RFI mitigation method for the one-bit UWB radar system that uses the CTBV sampling technique. Specifically, we first model the RFI sources as a sum of sinusoids with frequencies fixed during the coherent processing interval (CPI) and we exploit the sparsity of the RFI spectrum. We extend a majorization-minimization based 1bRELAX algorithm, referred to as 1bMMRELAX, to estimate the RFI source parameters from the signed measurements obtained by using the CTBV sampling strategy. We also devise a new fast frequency initialization method based on the Alternating Direction Method of Multipliers (ADMM) methodology for the extended 1bMMRELAX algorithm to significantly improve its computational efficiency. Moreover, an ADMM-based sparse method is introduced to recover the desired radar echoes using the estimated RFI parameters. Both simulated and experimental results are presented to demonstrate that our proposed algorithm outperforms the existing digital integration method, especially for severe RFI cases.
Federated learning (FL) is a powerful distributed machine learning framework where a server aggregates models trained by different clients without accessing their private data. Hierarchical FL, with a client-edge-cloud aggregation hierarchy, can effectively leverage both the cloud server's access to many clients' data and the edge servers' closeness to the clients to achieve a high communication efficiency. Neural network quantization can further reduce the communication overhead during model uploading. To fully exploit the advantages of hierarchical FL, an accurate convergence analysis with respect to the key system parameters is needed. Unfortunately, existing analysis is loose and does not consider model quantization. In this paper, we derive a tighter convergence bound for hierarchical FL with quantization. The convergence result leads to practical guidelines for important design problems such as the client-edge aggregation and edge-client association strategies. Based on the obtained analytical results, we optimize the two aggregation intervals and show that the client-edge aggregation interval should slowly decay while the edge-cloud aggregation interval needs to adapt to the ratio of the client-edge and edge-cloud propagation delay. Simulation results shall verify the design guidelines and demonstrate the effectiveness of the proposed aggregation strategy.
As soon as abstract mathematical computations were adapted to computation on digital computers, the problem of efficient representation, manipulation, and communication of the numerical values in those computations arose. Strongly related to the problem of numerical representation is the problem of quantization: in what manner should a set of continuous real-valued numbers be distributed over a fixed discrete set of numbers to minimize the number of bits required and also to maximize the accuracy of the attendant computations? This perennial problem of quantization is particularly relevant whenever memory and/or computational resources are severely restricted, and it has come to the forefront in recent years due to the remarkable performance of Neural Network models in computer vision, natural language processing, and related areas. Moving from floating-point representations to low-precision fixed integer values represented in four bits or less holds the potential to reduce the memory footprint and latency by a factor of 16x; and, in fact, reductions of 4x to 8x are often realized in practice in these applications. Thus, it is not surprising that quantization has emerged recently as an important and very active sub-area of research in the efficient implementation of computations associated with Neural Networks. In this article, we survey approaches to the problem of quantizing the numerical values in deep Neural Network computations, covering the advantages/disadvantages of current methods. With this survey and its organization, we hope to have presented a useful snapshot of the current research in quantization for Neural Networks and to have given an intelligent organization to ease the evaluation of future research in this area.
Low-bit quantization of network weights and activations can drastically reduce the memory footprint, complexity, energy consumption and latency of Deep Neural Networks (DNNs). However, low-bit quantization can also cause a considerable drop in accuracy, in particular when we apply it to complex learning tasks or lightweight DNN architectures. In this paper, we propose a training procedure that relaxes the low-bit quantization. We call this procedure \textit{DNN Quantization with Attention} (DQA). The relaxation is achieved by using a learnable linear combination of high, medium and low-bit quantizations. Our learning procedure converges step by step to a low-bit quantization using an attention mechanism with temperature scheduling. In experiments, our approach outperforms other low-bit quantization techniques on various object recognition benchmarks such as CIFAR10, CIFAR100 and ImageNet ILSVRC 2012, achieves almost the same accuracy as a full precision DNN, and considerably reduces the accuracy drop when quantizing lightweight DNN architectures.
Point clouds can be represented in many forms (views), typically, point-based sets, voxel-based cells or range-based images(i.e., panoramic view). The point-based view is geometrically accurate, but it is disordered, which makes it difficult to find local neighbors efficiently. The voxel-based view is regular, but sparse, and computation grows cubically when voxel resolution increases. The range-based view is regular and generally dense, however spherical projection makes physical dimensions distorted. Both voxel- and range-based views suffer from quantization loss, especially for voxels when facing large-scale scenes. In order to utilize different view's advantages and alleviate their own shortcomings in fine-grained segmentation task, we propose a novel range-point-voxel fusion network, namely RPVNet. In this network, we devise a deep fusion framework with multiple and mutual information interactions among these three views and propose a gated fusion module (termed as GFM), which can adaptively merge the three features based on concurrent inputs. Moreover, the proposed RPV interaction mechanism is highly efficient, and we summarize it into a more general formulation. By leveraging this efficient interaction and relatively lower voxel resolution, our method is also proved to be more efficient. Finally, we evaluated the proposed model on two large-scale datasets, i.e., SemanticKITTI and nuScenes, and it shows state-of-the-art performance on both of them. Note that, our method currently ranks 1st on SemanticKITTI leaderboard without any extra tricks.
In medical imaging, the characteristics purely derived from a disease should reflect the extent to which abnormal findings deviate from the normal features. Indeed, physicians often need corresponding images without abnormal findings of interest or, conversely, images that contain similar abnormal findings regardless of normal anatomical context. This is called comparative diagnostic reading of medical images, which is essential for a correct diagnosis. To support comparative diagnostic reading, content-based image retrieval (CBIR), which can selectively utilize normal and abnormal features in medical images as two separable semantic components, will be useful. Therefore, we propose a neural network architecture to decompose the semantic components of medical images into two latent codes: normal anatomy code and abnormal anatomy code. The normal anatomy code represents normal anatomies that should have existed if the sample is healthy, whereas the abnormal anatomy code attributes to abnormal changes that reflect deviation from the normal baseline. These latent codes are discretized through vector quantization to enable binary hashing, which can reduce the computational burden at the time of similarity search. By calculating the similarity based on either normal or abnormal anatomy codes or the combination of the two codes, our algorithm can retrieve images according to the selected semantic component from a dataset consisting of brain magnetic resonance images of gliomas. Our CBIR system qualitatively and quantitatively achieves remarkable results.
Binary neural networks (BNNs) have received increasing attention due to their superior reductions of computation and memory. Most existing works focus on either lessening the quantization error by minimizing the gap between the full-precision weights and their binarization or designing a gradient approximation to mitigate the gradient mismatch, while leaving the "dead weights" untouched. This leads to slow convergence when training BNNs. In this paper, for the first time, we explore the influence of "dead weights" which refer to a group of weights that are barely updated during the training of BNNs, and then introduce rectified clamp unit (ReCU) to revive the "dead weights" for updating. We prove that reviving the "dead weights" by ReCU can result in a smaller quantization error. Besides, we also take into account the information entropy of the weights, and then mathematically analyze why the weight standardization can benefit BNNs. We demonstrate the inherent contradiction between minimizing the quantization error and maximizing the information entropy, and then propose an adaptive exponential scheduler to identify the range of the "dead weights". By considering the "dead weights", our method offers not only faster BNN training, but also state-of-the-art performance on CIFAR-10 and ImageNet, compared with recent methods. Code can be available at https://github.com/z-hXu/ReCU.
Cloud-radio access network (C-RAN) can enable cell-less operation by connecting distributed remote radio heads (RRHs) via fronthaul links to a powerful central unit. In conventional C-RAN, baseband signals are forwarded after quantization/ compression to the central unit for centralized processing to keep the complexity of the RRHs low. However, the limited capacity of the fronthaul is thought to be a significant bottleneck in the ability of C-RAN to support large systems (e.g. massive machine-type communications (mMTC)). Therefore, in contrast to the conventional C-RAN, we propose a learning-based system in which the detection is performed locally at each RRH and only the likelihood information is conveyed to the CU. To this end, we develop a general set-theoretic learningmethod to estimate likelihood functions. The method can be used to extend existing detection methods to the C-RAN setting.
Powers-of-two (PoT) quantization reduces the number of bit operations of deep neural networks on resource-constrained hardware. However, PoT quantization triggers a severe accuracy drop because of its limited representation ability. Since DNN models have been applied for relatively complex tasks (e.g., classification for large datasets and object detection), improvement in accuracy for the PoT quantization method is required. Although some previous works attempt to improve the accuracy of PoT quantization, there is no work that balances accuracy and computation costs in a memory-efficient way. To address this problem, we propose an efficient PoT quantization scheme. Bit-level sparsity is introduced; weights (or activations) are rounded to values that can be calculated by n shift operations in multiplication. We also allow not only addition but also subtraction as each operation. Moreover, we use a two-stage fine-tuning algorithm to recover the accuracy drop that is triggered by introducing the bit-level sparsity. The experimental results on an object detection model (CenterNet, MobileNet-v2 backbone) on the COCO dataset show that our proposed method suppresses the accuracy drop by 0.3% at most while reducing the number of operations by about 75% and model size by 11.5% compared to the uniform method.