One-bit quantization, which relies on comparing the signals of interest with given threshold levels, has attracted considerable attention in signal processing for communications and sensing. A useful tool for covariance recovery in such settings is the arcsine law, that estimates the normalized covariance matrix of zero-mean stationary input signals. This relation, however, only considers a zero sampling threshold, which can cause a remarkable information loss. In this paper, the idea of the arcsine law is extended to the case where one-bit analog-to-digital converters (ADCs) apply time-varying thresholds. Specifically, three distinct approaches are proposed, investigated, and compared, to recover the autocorrelation sequence of the stationary signals of interest. Additionally, we will study a modification of the Bussgang law, a famous relation facilitating the recovery of the cross-correlation between the one-bit sampled data and the zero-mean stationary input signal. Similar to the case of the arcsine law, the Bussgang law only considers a zero sampling threshold. This relation is also extended to accommodate the more general case of time-varying thresholds for the stationary input signals.
In this paper, we introduce a novel algorithm, $\mathsf{CO}_3$, for communication-efficiency distributed Deep Neural Network (DNN) training. $\mathsf{CO}_3$ is a joint training/communication protocol, which encompasses three processing steps for the network gradients: (i) quantization through floating-point conversion, (ii) lossless compression, and (iii) error correction. These three components are crucial in the implementation of distributed DNN training over rate-constrained links. The interplay of these three steps in processing the DNN gradients is carefully balanced to yield a robust and high-performance scheme. The performance of the proposed scheme is investigated through numerical evaluations over CIFAR-10.
How to efficiently utilize the temporal features is crucial, yet challenging, for video restoration. The temporal features usually contain various noisy and uncorrelated information, and they may interfere with the restoration of the current frame. This paper proposes learning noise-robust feature representations to help video restoration. We are inspired by that the neural codec is a natural denoiser. In neural codec, the noisy and uncorrelated contents which are hard to predict but cost lots of bits are more inclined to be discarded for bitrate saving. Therefore, we design a neural compression module to filter the noise and keep the most useful information in features for video restoration. To achieve robustness to noise, our compression module adopts a spatial channel-wise quantization mechanism to adaptively determine the quantization step size for each position in the latent. Experiments show that our method can significantly boost the performance on video denoising, where we obtain 0.13 dB improvement over BasicVSR++ with only 0.23x FLOPs. Meanwhile, our method also obtains SOTA results on video deraining and dehazing.
The exponentially large discrete search space in mixed-precision quantization (MPQ) makes it hard to determine the optimal bit-width for each layer. Previous works usually resort to iterative search methods on the training set, which consume hundreds or even thousands of GPU-hours. In this study, we reveal that some unique learnable parameters in quantization, namely the scale factors in the quantizer, can serve as importance indicators of a layer, reflecting the contribution of that layer to the final accuracy at certain bit-widths. These importance indicators naturally perceive the numerical transformation during quantization-aware training, which can precisely provide quantization sensitivity metrics of layers. However, a deep network always contains hundreds of such indicators, and training them one by one would lead to an excessive time cost. To overcome this issue, we propose a joint training scheme that can obtain all indicators at once. It considerably speeds up the indicators training process by parallelizing the original sequential training processes. With these learned importance indicators, we formulate the MPQ search problem as a one-time integer linear programming (ILP) problem. That avoids the iterative search and significantly reduces search time without limiting the bit-width search space. For example, MPQ search on ResNet18 with our indicators takes only 0.06 s, which improves time efficiency exponentially compared to iterative search methods. Also, extensive experiments show our approach can achieve SOTA accuracy on ImageNet for far-ranging models with various constraints (e.g., BitOps, compress rate). Code is available on https://github.com/1hunters/LIMPQ.
Downsampling is one of the most basic image processing operations. Improper spatio-temporal downsampling applied on videos can cause aliasing issues such as moir\'e patterns in space and the wagon-wheel effect in time. Consequently, the inverse task of upscaling a low-resolution, low frame-rate video in space and time becomes a challenging ill-posed problem due to information loss and aliasing artifacts. In this paper, we aim to solve the space-time aliasing problem by learning a spatio-temporal downsampler. Towards this goal, we propose a neural network framework that jointly learns spatio-temporal downsampling and upsampling. It enables the downsampler to retain the key patterns of the original video and maximizes the reconstruction performance of the upsampler. To make the downsamping results compatible with popular image and video storage formats, the downsampling results are encoded to uint8 with a differentiable quantization layer. To fully utilize the space-time correspondences, we propose two novel modules for explicit temporal propagation and space-time feature rearrangement. Experimental results show that our proposed method significantly boosts the space-time reconstruction quality by preserving spatial textures and motion patterns in both downsampling and upscaling. Moreover, our framework enables a variety of applications, including arbitrary video resampling, blurry frame reconstruction, and efficient video storage.
Quantization has been applied to multiple domains in Deep Neural Networks (DNNs). We propose Depthwise Quantization (DQ) where $\textit{quantization}$ is applied to a decomposed sub-tensor along the $\textit{feature axis}$ of weak statistical dependence. The feature decomposition leads to an exponential increase in $\textit{representation capacity}$ with a linear increase in memory and parameter cost. In addition, DQ can be directly applied to existing encoder-decoder frameworks without modification of the DNN architecture. We use DQ in the context of Hierarchical Auto-Encoder and train end-to-end on an image feature representation. We provide an analysis on cross-correlation between spatial and channel features and we propose a decomposition of the image feature representation along the channel axis. The improved performance of the depthwise operator is due to the increased representation capacity from implicit feature decoupling. We evaluate DQ on the likelihood estimation task, where it outperforms the previous state-of-the-art on CIFAR-10, ImageNet-32 and ImageNet-64. We progressively train with increasing image size a single hierarchical model that uses 69% less parameters and has a faster convergence than the previous works.
Transformer-based language models have become a key building block for natural language processing. While these models are extremely accurate, they can be too large and computationally intensive to run on standard deployments. A variety of compression methods, including distillation, quantization, structured and unstructured pruning are known to decrease model size and increase inference speed, with low accuracy loss. In this context, this paper's contributions are two-fold. We perform an in-depth study of the accuracy-compression trade-off for unstructured weight pruning of BERT models. We introduce Optimal BERT Surgeon (oBERT), an efficient and accurate weight pruning method based on approximate second-order information, which we show to yield state-of-the-art results in both stages of language tasks: pre-training and fine-tuning. Specifically, oBERT extends existing work on unstructured second-order pruning by allowing for pruning blocks of weights, and by being applicable at the BERT scale. Second, we investigate the impact of this pruning method when compounding compression approaches to obtain highly compressed but accurate models for deployment on edge devices. These models significantly push boundaries of the current state-of-the-art sparse BERT models with respect to all metrics: model size, inference speed and task accuracy. For example, relative to the dense BERT-base, we obtain 10x model size compression (in MB) with < 1% accuracy drop, 10x CPU-inference speedup with < 2% accuracy drop, and 29x CPU-inference speedup with < 7.5% accuracy drop. Our code, fully integrated with Transformers and SparseML, is available at https://github.com/neuralmagic/sparseml/tree/main/research/optimal_BERT_surgeon_oBERT.
Mapping between discrete and continuous distributions is a difficult task and many have had to resort to heuristical approaches. We propose a tessellation-based approach that directly learns quantization boundaries in a continuous space, complete with exact likelihood evaluations. This is done through constructing normalizing flows on convex polytopes parameterized using a simple homeomorphism with an efficient log determinant Jacobian. We explore this approach in two application settings, mapping from discrete to continuous and vice versa. Firstly, a Voronoi dequantization allows automatically learning quantization boundaries in a multidimensional space. The location of boundaries and distances between regions can encode useful structural relations between the quantized discrete values. Secondly, a Voronoi mixture model has near-constant computation cost for likelihood evaluation regardless of the number of mixture components. Empirically, we show improvements over existing methods across a range of structured data modalities.
Recovering a high dynamic range (HDR) image from a single low dynamic range (LDR) image, namely inverse tone mapping (ITM), is challenging due to the lack of information in over- and under-exposed regions. Current methods focus exclusively on training high-performing but computationally inefficient ITM models, which in turn hinder deployment of the ITM models in resource-constrained environments with limited computing power such as edge and mobile device applications. To this end, we propose combining efficient operations of deep neural networks with a novel mixed quantization scheme to construct a well-performing but computationally efficient mixed quantization network (MQN) which can perform single image ITM on mobile platforms. In the ablation studies, we explore the effect of using different attention mechanisms, quantization schemes, and loss functions on the performance of MQN in ITM tasks. In the comparative analyses, ITM models trained using MQN perform on par with the state-of-the-art methods on benchmark datasets. MQN models provide up to 10 times improvement on latency and 25 times improvement on memory consumption.
Recently, federated learning (FL) has sparked widespread attention as a promising decentralized machine learning approach which provides privacy and low delay. However, communication bottleneck still constitutes an issue, that needs to be resolved for an efficient deployment of FL over wireless networks. In this paper, we aim to minimize the total convergence time of FL, by quantizing the local model parameters prior to uplink transmission. More specifically, the convergence analysis of the FL algorithm with stochastic quantization is firstly presented, which reveals the impact of the quantization error on the convergence rate. Following that, we jointly optimize the computing, communication resources and number of quantization bits, in order to guarantee minimized convergence time across all global rounds, subject to energy and quantization error requirements, which stem from the convergence analysis. The impact of the quantization error on the convergence time is evaluated and the trade-off among model accuracy and timely execution is revealed. Moreover, the proposed method is shown to result in faster convergence in comparison with baseline schemes. Finally, useful insights for the selection of the quantization error tolerance are provided.
Common state-of-the-art video codecs are optimized to deliver a low bitrate by providing a certain quality for the final human observer, which is achieved by rate-distortion optimization (RDO). But, with the steady improvement of neural networks solving computer vision tasks, more and more multimedia data is not observed by humans anymore, but directly analyzed by neural networks. In this paper, we propose a standard-compliant feature-based RDO (FRDO) that is designed to increase the coding performance, when the decoded frame is analyzed by a neural network in a video coding for machine scenario. To that extent, we replace the pixel-based distortion metrics in conventional RDO of VTM-8.0 with distortion metrics calculated in the feature space created by the first layers of a neural network. Throughout several tests with the segmentation network Mask R-CNN and single images from the Cityscapes dataset, we compare the proposed FRDO and its hybrid version HFRDO with different distortion measures in the feature space against the conventional RDO. With HFRDO, up to 5.49 % bitrate can be saved compared to the VTM-8.0 implementation in terms of Bj{\o}ntegaard Delta Rate and using the weighted average precision as quality metric. Additionally, allowing the encoder to vary the quantization parameter results in coding gains for the proposed HFRDO of up 9.95 % compared to conventional VTM.
Recently, post-training quantization (PTQ) has driven much attention to produce efficient neural networks without long-time retraining. Despite its low cost, current PTQ works tend to fail under the extremely low-bit setting. In this study, we pioneeringly confirm that properly incorporating activation quantization into the PTQ reconstruction benefits the final accuracy. To deeply understand the inherent reason, a theoretical framework is established, indicating that the flatness of the optimized low-bit model on calibration and test data is crucial. Based on the conclusion, a simple yet effective approach dubbed as QDROP is proposed, which randomly drops the quantization of activations during PTQ. Extensive experiments on various tasks including computer vision (image classification, object detection) and natural language processing (text classification and question answering) prove its superiority. With QDROP, the limit of PTQ is pushed to the 2-bit activation for the first time and the accuracy boost can be up to 51.49%. Without bells and whistles, QDROP establishes a new state of the art for PTQ. Our code is available at https://github.com/wimh966/QDrop and has been integrated into MQBench (https://github.com/ModelTC/MQBench)
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 precise. Moreover, using base-2 logarithmic representation allows optimizing the multiplication by replacing it with bit shifting. In this paper, we explore non-linear quantization techniques for exploiting lower bit precision and identify favorable hardware implementation options. We developed the Quantization Aware Training (QAT) algorithm that allowed training of low bit width Power-of-Two (PoT) networks and achieved accuracies on par with state-of-the-art floating point models for different tasks. We explored PoT weight encoding techniques and investigated hardware designs of MAC units for three different quantization schemes - uniform, PoT and Additive-PoT (APoT) - to show the increased efficiency when using the proposed approach. Eventually, the experiments showed that for low bit width precision, non-uniform quantization performs better than uniform, and at the same time, PoT quantization vastly reduces the computational complexity of the neural network.
Tiny machine learning (tinyML) has emerged during the past few years aiming to deploy machine learning models to embedded AI processors with highly constrained memory and computation capacity. Low precision quantization is an important model compression technique that can greatly reduce both memory consumption and computation cost of model inference. In this study, we focus on post-training quantization (PTQ) algorithms that quantize a model to low-bit (less than 8-bit) precision with only a small set of calibration data and benchmark them on different tinyML use cases. To achieve a fair comparison, we build a simulated quantization framework to investigate recent PTQ algorithms. Furthermore, we break down those algorithms into essential components and re-assembled a generic PTQ pipeline. With ablation study on different alternatives of components in the pipeline, we reveal key design choices when performing low precision quantization. We hope this work could provide useful data points and shed lights on the future research of low precision quantization.
Devices participating in federated learning (FL) typically have heterogeneous communication, computation, and memory resources. However, in synchronous FL, all devices need to finish training by the same deadline dictated by the server. Our results show that training a smaller subset of the neural network (NN) at constrained devices, i.e., dropping neurons/filters as proposed by state of the art, is inefficient, preventing these devices to make an effective contribution to the model. This causes unfairness w.r.t the achievable accuracies of constrained devices, especially in cases with a skewed distribution of class labels across devices. We present a novel FL technique, CoCoFL, which maintains the full NN structure on all devices. To adapt to the devices' heterogeneous resources, CoCoFL freezes and quantizes selected layers, reducing communication, computation, and memory requirements, whereas other layers are still trained in full precision, enabling to reach a high accuracy. Thereby, CoCoFL efficiently utilizes the available resources on devices and allows constrained devices to make a significant contribution to the FL system, increasing fairness among participants (accuracy parity) and significantly improving the final accuracy of the model.
Product quantization (PQ) coupled with a space rotation, is widely used in modern approximate nearest neighbor (ANN) search systems to significantly compress the disk storage for embeddings and speed up the inner product computation. Existing rotation learning methods, however, minimize quantization distortion for fixed embeddings, which are not applicable to an end-to-end training scenario where embeddings are updated constantly. In this paper, based on geometric intuitions from Lie group theory, in particular the special orthogonal group $SO(n)$, we propose a family of block Givens coordinate descent algorithms to learn rotation matrix that are provably convergent on any convex objectives. Compared to the state-of-the-art SVD method, the Givens algorithms are much more parallelizable, reducing runtime by orders of magnitude on modern GPUs, and converge more stably according to experimental studies. They further improve upon vanilla product quantization significantly in an end-to-end training scenario.
Deep learning training involves a large number of operations, which are dominated by high dimensionality Matrix-Vector Multiplies (MVMs). This has motivated hardware accelerators to enhance compute efficiency, but where data movement and accessing are proving to be key bottlenecks. In-Memory Computing (IMC) is an approach with the potential to overcome this, whereby computations are performed in-place within dense 2-D memory. However, IMC fundamentally trades efficiency and throughput gains for dynamic-range limitations, raising distinct challenges for training, where compute precision requirements are seen to be substantially higher than for inferencing. This paper explores training on IMC hardware by leveraging two recent developments: (1) a training algorithm enabling aggressive quantization through a radix-4 number representation; (2) IMC leveraging compute based on precision capacitors, whereby analog noise effects can be made well below quantization effects. Energy modeling calibrated to a measured silicon prototype implemented in 16nm CMOS shows that energy savings of over 400x can be achieved with full quantizer adaptability, where all training MVMs can be mapped to IMC, and 3x can be achieved for two-level quantizer adaptability, where two of the three training MVMs can be mapped to IMC.
This paper presents a new neural speech compression method that is practical in the sense that it operates at low bitrate, introduces a low latency, is compatible in computational complexity with current mobile devices, and provides a subjective quality that is comparable to that of standard mobile-telephony codecs. Other recently proposed neural vocoders also have the ability to operate at low bitrate. However, they do not produce the same level of subjective quality as standard codecs. On the other hand, standard codecs rely on objective and short-term metrics such as the segmental signal-to-noise ratio that correlate only weakly with perception. Furthermore, standard codecs are less efficient than unsupervised neural networks at capturing speech attributes, especially long-term ones. The proposed method combines a cognitive-coding encoder that extracts an interpretable unsupervised hierarchical representation with a multi stage decoder that has a GAN-based architecture. We observe that this method is very robust to the quantization of representation features. An AB test was conducted on a subset of the Harvard sentences that are commonly used to evaluate standard mobile-telephony codecs. The results show that the proposed method outperforms the standard AMR-WB codec in terms of delay, bitrate and subjective quality.
We study the problem of distributed mean estimation and optimization under communication constraints. We propose a correlated quantization protocol whose leading term in the error guarantee depends on the mean deviation of data points rather than only their absolute range. The design doesn't need any prior knowledge on the concentration property of the dataset, which is required to get such dependence in previous works. We show that applying the proposed protocol as sub-routine in distributed optimization algorithms leads to better convergence rates. We also prove the optimality of our protocol under mild assumptions. Experimental results show that our proposed algorithm outperforms existing mean estimation protocols on a diverse set of tasks.
With the advancement of Deep Neural Networks (DNN) and large amounts of sensor data from Internet of Things (IoT) systems, the research community has worked to reduce the computational and resource demands of DNN to compute on low-resourced microcontrollers (MCUs). However, most of the current work in embedded deep learning focuses on solving a single task efficiently, while the multi-tasking nature and applications of IoT devices demand systems that can handle a diverse range of tasks (activity, voice, and context recognition) with input from a variety of sensors, simultaneously. In this paper, we propose YONO, a product quantization (PQ) based approach that compresses multiple heterogeneous models and enables in-memory model execution and switching for dissimilar multi-task learning on MCUs. We first adopt PQ to learn codebooks that store weights of different models. Also, we propose a novel network optimization and heuristics to maximize the compression rate and minimize the accuracy loss. Then, we develop an online component of YONO for efficient model execution and switching between multiple tasks on an MCU at run time without relying on an external storage device. YONO shows remarkable performance as it can compress multiple heterogeneous models with negligible or no loss of accuracy up to 12.37$\times$. Besides, YONO's online component enables an efficient execution (latency of 16-159 ms per operation) and reduces model loading/switching latency and energy consumption by 93.3-94.5% and 93.9-95.0%, respectively, compared to external storage access. Interestingly, YONO can compress various architectures trained with datasets that were not shown during YONO's offline codebook learning phase showing the generalizability of our method. To summarize, YONO shows great potential and opens further doors to enable multi-task learning systems on extremely resource-constrained devices.