Since model quantization helps to reduce the model size and computation latency, it has been successfully applied in many applications of mobile phones, embedded devices and smart chips. The mixed-precision quantization model can match different quantization bit-precisions according to the sensitivity of different layers to achieve great performance. However, it is a difficult problem to quickly determine the quantization bit-precision of each layer in deep neural networks according to some constraints (e.g., hardware resources, energy consumption, model size and computation latency). To address this issue, we propose a novel sequential single path search (SSPS) method for mixed-precision quantization,in which the given constraints are introduced into its loss function to guide searching process. A single path search cell is used to combine a fully differentiable supernet, which can be optimized by gradient-based algorithms. Moreover, we sequentially determine the candidate precisions according to the selection certainties to exponentially reduce the search space and speed up the convergence of searching process. Experiments show that our method can efficiently search the mixed-precision models for different architectures (e.g., ResNet-20, 18, 34, 50 and MobileNet-V2) and datasets (e.g., CIFAR-10, ImageNet and COCO) under given constraints, and our experimental results verify that SSPS significantly outperforms their uniform counterparts.
In this work, we study the binary neural networks (BNNs) of which both the weights and activations are binary (i.e., 1-bit representation). Feature representation is critical for deep neural networks, while in BNNs, the features only differ in signs. Prior work introduces scaling factors into binary weights and activations to reduce the quantization error and effectively improves the classification accuracy of BNNs. However, the scaling factors not only increase the computational complexity of networks, but also make no sense to the signs of binary features. To this end, Self-Distribution Binary Neural Network (SD-BNN) is proposed. Firstly, we utilize Activation Self Distribution (ASD) to adaptively adjust the sign distribution of activations, thereby improve the sign differences of the outputs of the convolution. Secondly, we adjust the sign distribution of weights through Weight Self Distribution (WSD) and then fine-tune the sign distribution of the outputs of the convolution. Extensive experiments on CIFAR-10 and ImageNet datasets with various network structures show that the proposed SD-BNN consistently outperforms the state-of-the-art (SOTA) BNNs (e.g., achieves 92.5% on CIFAR-10 and 66.5% on ImageNet with ResNet-18) with less computation cost. Code is available at https://github.com/ pingxue-hfut/SD-BNN.
Quantization is spearheading the increase in performance and efficiency of neural network computing systems making headway into commodity hardware. We present SWIS - Shared Weight bIt Sparsity, a quantization framework for efficient neural network inference acceleration delivering improved performance and storage compression through an offline weight decomposition and scheduling algorithm. SWIS can achieve up to 54.3% (19.8%) point accuracy improvement compared to weight truncation when quantizing MobileNet-v2 to 4 (2) bits post-training (with retraining) showing the strength of leveraging shared bit-sparsity in weights. SWIS accelerator gives up to 6x speedup and 1.9x energy improvement overstate of the art bit-serial architectures.
Resistive Random-Access-Memory (ReRAM) crossbar is a promising technique for deep neural network (DNN) accelerators, thanks to its in-memory and in-situ analog computing abilities for Vector-Matrix Multiplication-and-Accumulations (VMMs). However, it is challenging for crossbar architecture to exploit the sparsity in the DNN. It inevitably causes complex and costly control to exploit fine-grained sparsity due to the limitation of tightly-coupled crossbar structure. As the countermeasure, we developed a novel ReRAM-based DNN accelerator, named Sparse-Multiplication-Engine (SME), based on a hardware and software co-design framework. First, we orchestrate the bit-sparse pattern to increase the density of bit-sparsity based on existing quantization methods. Second, we propose a novel weigh mapping mechanism to slice the bits of a weight across the crossbars and splice the activation results in peripheral circuits. This mechanism can decouple the tightly-coupled crossbar structure and cumulate the sparsity in the crossbar. Finally, a superior squeeze-out scheme empties the crossbars mapped with highly-sparse non-zeros from the previous two steps. We design the SME architecture and discuss its use for other quantization methods and different ReRAM cell technologies. Compared with prior state-of-the-art designs, the SME shrinks the use of crossbars up to 8.7x and 2.1x using Resent-50 and MobileNet-v2, respectively, with less than 0.3% accuracy drop on ImageNet.
Quantizing deep networks with adaptive bit-widths is a promising technique for efficient inference across many devices and resource constraints. In contrast to static methods that repeat the quantization process and train different models for different constraints, adaptive quantization enables us to flexibly adjust the bit-widths of a single deep network during inference for instant adaptation in different scenarios. While existing research shows encouraging results on common image classification benchmarks, this paper investigates how to train such adaptive networks more effectively. Specifically, we present two novel techniques for quantizing deep neural networks with adaptive bit-widths of weights and activations. First, we propose a collaborative strategy to choose a high-precision teacher for transferring knowledge to the low-precision student while jointly optimizing the model with all bit-widths. Second, to effectively transfer knowledge, we develop a dynamic block swapping method by randomly replacing the blocks in the lower-precision student network with the corresponding blocks in the higher-precision teacher network. Extensive experiments on multiple image classification datasets including video classification benchmarks for the first time, well demonstrate the efficacy of our approach over state-of-the-art methods.
We propose a convolutional neural network (CNN) architecture for image classification based on subband decomposition of the image using wavelets. The proposed architecture decomposes the input image spectra into multiple critically sampled subbands, extracts features using a single CNN per subband, and finally, performs classification by combining the extracted features using a fully connected layer. Processing each of the subbands by an individual CNN, thereby limiting the learning scope of each CNN to a single subband, imposes a form of structural regularization. This provides better generalization capability as seen by the presented results. The proposed architecture achieves best-in-class performance in terms of total multiply-add-accumulator operations and nearly best-in-class performance in terms of total parameters required, yet it maintains competitive classification performance. We also show the proposed architecture is more robust than the regular full-band CNN to noise caused by weight-and-bias quantization and input quantization.
Quantization has emerged as one of the most prevalent approaches to compress and accelerate neural networks. Recently, data-free quantization has been widely studied as a practical and promising solution. It synthesizes data for calibrating the quantized model according to the batch normalization (BN) statistics of FP32 ones and significantly relieves the heavy dependency on real training data in traditional quantization methods. Unfortunately, we find that in practice, the synthetic data identically constrained by BN statistics suffers serious homogenization at both distribution level and sample level and further causes a significant performance drop of the quantized model. We propose Diverse Sample Generation (DSG) scheme to mitigate the adverse effects caused by homogenization. Specifically, we slack the alignment of feature statistics in the BN layer to relax the constraint at the distribution level and design a layerwise enhancement to reinforce specific layers for different data samples. Our DSG scheme is versatile and even able to be applied to the state-of-the-art post-training quantization method like AdaRound. We evaluate the DSG scheme on the large-scale image classification task and consistently obtain significant improvements over various network architectures and quantization methods, especially when quantized to lower bits (e.g., up to 22% improvement on W4A4). Moreover, benefiting from the enhanced diversity, models calibrated by synthetic data perform close to those calibrated by real data and even outperform them on W4A4.
The method of random projection (RP) is the standard technique in machine learning and many other areas, for dimensionality reduction, approximate near neighbor search, compressed sensing, etc. Basically, RP provides a simple and effective scheme for approximating pairwise inner products and Euclidean distances in massive data. Closely related to RP, the method of random Fourier features (RFF) has also become popular, for approximating the Gaussian kernel. RFF applies a specific nonlinear transformation on the projected data from random projections. In practice, using the (nonlinear) Gaussian kernel often leads to better performance than the linear kernel (inner product), partly due to the tuning parameter $(\gamma)$ introduced in the Gaussian kernel. Recently, there has been a surge of interest in studying properties of RFF. After random projections, quantization is an important step for efficient data storage, computation, and transmission. Quantization for RP has also been extensive studied in the literature. In this paper, we focus on developing quantization algorithms for RFF. The task is in a sense challenging due to the tuning parameter $\gamma$ in the Gaussian kernel. For example, the quantizer and the quantized data might be tied to each specific tuning parameter $\gamma$. Our contribution begins with an interesting discovery, that the marginal distribution of RFF is actually free of the Gaussian kernel parameter $\gamma$. This small finding significantly simplifies the design of the Lloyd-Max (LM) quantization scheme for RFF in that there would be only one LM quantizer for RFF (regardless of $\gamma$). We also develop a variant named LM$^2$-RFF quantizer, which in certain cases is more accurate. Experiments confirm that the proposed quantization schemes perform well.
This letter studies a cloud radio access network (C-RAN) with multiple intelligent reflecting surfaces (IRS) deployed between users and remote radio heads (RRH). Specifically, we consider the uplink transmission where each RRH quantizes the received signals from the users by either point-to-point compression or Wyner-Ziv compression and then transmits the quantization bits to the BBU pool through capacity limited fronthhual links. To maximize the uplink sum rate, we jointly optimize the passive beamformers of IRSs and the quantization noise covariance matrices of fronthoul compression. An joint fronthaul compression and passive beamforming design is proposed by exploiting the Arimoto-Blahut algorithm and semidefinte relaxation (SDR). Numerical results show the performance gain achieved by the proposed algorithm.
Optimal transport (OT) is a popular tool in machine learning to compare probability measures geometrically, but it comes with substantial computational burden. Linear programming algorithms for computing OT distances scale cubically in the size of the input, making OT impractical in the large-sample regime. We introduce a practical algorithm, which relies on a quantization step, to estimate OT distances between measures given cheap sample access. We also provide a variant of our algorithm to improve the performance of approximate solvers, focusing on those for entropy-regularized transport. We give theoretical guarantees on the benefits of this quantization step and display experiments showing that it behaves well in practice, providing a practical approximation algorithm that can be used as a drop-in replacement for existing OT estimators.
In this paper, we present a deep reinforcement learning platform named FIXAR which employs fixed-point data types and arithmetic units for the first time using a SW/HW co-design approach. Starting from 32-bit fixed-point data, Quantization-Aware Training (QAT) reduces its data precision based on the range of activations and performs retraining to minimize the reward degradation. FIXAR proposes the adaptive array processing core composed of configurable processing elements to support both intra-layer parallelism and intra-batch parallelism for high-throughput inference and training. Finally, FIXAR was implemented on Xilinx U50 and achieves 25293.3 inferences per second (IPS) training throughput and 2638.0 IPS/W accelerator efficiency, which is 2.7 times faster and 15.4 times more energy efficient than those of the CPU-GPU platform without any accuracy degradation.
Traditionally, federated learning (FL) aims to train a single global model while collaboratively using multiple clients and a server. Two natural challenges that FL algorithms face are heterogeneity in data across clients and collaboration of clients with {\em diverse resources}. In this work, we introduce a \textit{quantized} and \textit{personalized} FL algorithm QuPeL that facilitates collective training with heterogeneous clients while respecting resource diversity. For personalization, we allow clients to learn \textit{compressed personalized models} with different quantization parameters depending on their resources. Towards this, first we propose an algorithm for learning quantized models through a relaxed optimization problem, where quantization values are also optimized over. When each client participating in the (federated) learning process has different requirements of the quantized model (both in value and precision), we formulate a quantized personalization framework by introducing a penalty term for local client objectives against a globally trained model to encourage collaboration. We develop an alternating proximal gradient update for solving this quantized personalization problem, and we analyze its convergence properties. Numerically, we show that optimizing over the quantization levels increases the performance and we validate that QuPeL outperforms both FedAvg and local training of clients in a heterogeneous setting.
Efficient machine learning implementations optimized for inference in hardware have wide-ranging benefits, depending on the application, from lower inference latency to higher data throughput and reduced energy consumption. Two popular techniques for reducing computation in neural networks are pruning, removing insignificant synapses, and quantization, reducing the precision of the calculations. In this work, we explore the interplay between pruning and quantization during the training of neural networks for ultra low latency applications targeting high energy physics use cases. Techniques developed for this study have potential applications across many other domains. We study various configurations of pruning during quantization-aware training, which we term quantization-aware pruning, and the effect of techniques like regularization, batch normalization, and different pruning schemes on performance, computational complexity, and information content metrics. We find that quantization-aware pruning yields more computationally efficient models than either pruning or quantization alone for our task. Further, quantization-aware pruning typically performs similar to or better in terms of computational efficiency compared to other neural architecture search techniques like Bayesian optimization. Surprisingly, while networks with different training configurations can have similar performance for the benchmark application, the information content in the network can vary significantly, affecting its generalizability.
With Motor-Imagery (MI) Brain--Machine Interfaces (BMIs) we may control machines by merely thinking of performing a motor action. Practical use cases require a wearable solution where the classification of the brain signals is done locally near the sensor using machine learning models embedded on energy-efficient microcontroller units (MCUs), for assured privacy, user comfort, and long-term usage. In this work, we provide practical insights on the accuracy-cost tradeoff for embedded BMI solutions. Our proposed Multispectral Riemannian Classifier reaches 75.1% accuracy on 4-class MI task. We further scale down the model by quantizing it to mixed-precision representations with a minimal accuracy loss of 1%, which is still 3.2% more accurate than the state-of-the-art embedded convolutional neural network. We implement the model on a low-power MCU with parallel processing units taking only 33.39ms and consuming 1.304mJ per classification.
Mixed-precision quantization can potentially achieve the optimal tradeoff between performance and compression rate of deep neural networks, and thus, have been widely investigated. However, it lacks a systematic method to determine the exact quantization scheme. Previous methods either examine only a small manually-designed search space or utilize a cumbersome neural architecture search to explore the vast search space. These approaches cannot lead to an optimal quantization scheme efficiently. This work proposes bit-level sparsity quantization (BSQ) to tackle the mixed-precision quantization from a new angle of inducing bit-level sparsity. We consider each bit of quantized weights as an independent trainable variable and introduce a differentiable bit-sparsity regularizer. BSQ can induce all-zero bits across a group of weight elements and realize the dynamic precision reduction, leading to a mixed-precision quantization scheme of the original model. Our method enables the exploration of the full mixed-precision space with a single gradient-based optimization process, with only one hyperparameter to tradeoff the performance and compression. BSQ achieves both higher accuracy and higher bit reduction on various model architectures on the CIFAR-10 and ImageNet datasets comparing to previous methods.
Although distributed machine learning has opened up many new and exciting research frontiers, fragmentation of models and data across different machines, nodes, and sites still results in considerable communication overhead, impeding reliable training in real-world contexts. The focus on gradients as the primary shared statistic during training has spawned a number of intuitive algorithms for distributed deep learning; however, gradient-centric training of large deep neural networks (DNNs) tends to be communication-heavy, often requiring additional adaptations such as sparsity constraints, compression, quantization, and more, to curtail bandwidth. We introduce an innovative, communication-friendly approach for training distributed DNNs, which capitalizes on the outer-product structure of the gradient as revealed by the mechanics of auto-differentiation. The exposed structure of the gradient evokes a new class of distributed learning algorithm, which is naturally more communication-efficient than full gradient sharing. Our approach, called distributed auto-differentiation (dAD), builds off a marriage of rank-based compression and the innate structure of the gradient as an outer-product. We demonstrate that dAD trains more efficiently than other state of the art distributed methods on modern architectures, such as transformers, when applied to large-scale text and imaging datasets. The future of distributed learning, we determine, need not be dominated by gradient-centric algorithms.
In this paper, we explore the possibility of deriving a quantum wavefunction for continuous-time recurrent neural network (CTRNN). We did this by first starting with a two-dimensional dynamical system that describes the classical dynamics of a continuous-time recurrent neural network, and then deriving a Hamiltonian. After this, we quantized this Hamiltonian on a Hilbert space $\mathbb{H} = L^2(\mathbb{R})$ using Weyl quantization. We then solved the Schrodinger equation which gave us the wavefunction in terms of Kummer's confluent hypergeometric function corresponding to the neural network structure. Upon applying spatial boundary conditions at infinity, we were able to derive conditions/restrictions on the weights and hyperparameters of the neural network, which could potentially give insights on the the nature of finding optimal weights of said neural networks.
Quantized neural networks (QNNs) are among the main approaches for deploying deep neural networks on low resource edge devices. Training QNNs using different levels of precision throughout the network (dynamic quantization) typically achieves superior trade-offs between performance and computational load. However, optimizing the different precision levels of QNNs can be complicated, as the values of the bit allocations are discrete and difficult to differentiate for. Also, adequately accounting for the dependencies between the bit allocation of different layers is not straight-forward. To meet these challenges, in this work we propose GradFreeBits: a novel joint optimization scheme for training dynamic QNNs, which alternates between gradient-based optimization for the weights, and gradient-free optimization for the bit allocation. Our method achieves better or on par performance with current state of the art low precision neural networks on CIFAR10/100 and ImageNet classification. Furthermore, our approach can be extended to a variety of other applications involving neural networks used in conjunction with parameters which are difficult to optimize for.
The application of machine learning(ML) and genetic programming(GP) to the image compression domain has produced promising results in many cases. The need for compression arises due to the exorbitant size of data shared on the internet. Compression is required for text, videos, or images, which are used almost everywhere on web be it news articles, social media posts, blogs, educational platforms, medical domain, government services, and many other websites, need packets for transmission and hence compression is necessary to avoid overwhelming the network. This paper discusses some of the implementations of image compression algorithms that use techniques such as Artificial Neural Networks, Residual Learning, Fuzzy Neural Networks, Convolutional Neural Nets, Deep Learning, Genetic Algorithms. The paper also describes an implementation of Vector Quantization using GA to generate codebook which is used for Lossy image compression. All these approaches prove to be very contrasting to the standard approaches to processing images due to the highly parallel and computationally extensive nature of machine learning algorithms. Such non-linear abilities of ML and GP make it widely popular for use in multiple domains. Traditional approaches are also combined with artificially intelligent systems, leading to hybrid systems, to achieve better results.
The Group Quantization formalism is a scheme for constructing a functional space that is an irreducible infinite dimensional representation of the Lie algebra belonging to a dynamical symmetry group. We apply this formalism to the construction of functional space and operators for quadratic potentials -- gaussian pricing kernels in finance. We describe the Black-Scholes theory, the Ho-Lee interest rate model and the Euclidean repulsive and attractive oscillators. The symmetry group used in this work has the structure of a principal bundle with base (dynamical) group a semi-direct extension of the Heisenberg-Weyl group by SL(2,R), and structure group (fiber) the positive real line.