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Graph Neural Networks (GNNs) are becoming a promising technique in various domains due to their excellent capabilities in modeling non-Euclidean data. Although a spectrum of accelerators has been proposed to accelerate the inference of GNNs, our analysis demonstrates that the latency and energy consumption induced by DRAM access still significantly impedes the improvement of performance and energy efficiency. To address this issue, we propose a Memory-Efficient GNN Accelerator (MEGA) through algorithm and hardware co-design in this work. Specifically, at the algorithm level, through an in-depth analysis of the node property, we observe that the data-independent quantization in previous works is not optimal in terms of accuracy and memory efficiency. This motivates us to propose the Degree-Aware mixed-precision quantization method, in which a proper bitwidth is learned and allocated to a node according to its in-degree to compress GNNs as much as possible while maintaining accuracy. At the hardware level, we employ a heterogeneous architecture design in which the aggregation and combination phases are implemented separately with different dataflows. In order to boost the performance and energy efficiency, we also present an Adaptive-Package format to alleviate the storage overhead caused by the fine-grained bitwidth and diverse sparsity, and a Condense-Edge scheduling method to enhance the data locality and further alleviate the access irregularity induced by the extremely sparse adjacency matrix in the graph. We implement our MEGA accelerator in a 28nm technology node. Extensive experiments demonstrate that MEGA can achieve an average speedup of 38.3x, 7.1x, 4.0x, 3.6x and 47.6x, 7.2x, 5.4x, 4.5x energy savings over four state-of-the-art GNN accelerators, HyGCN, GCNAX, GROW, and SGCN, respectively, while retaining task accuracy., Comment: 15pages, 22 figures. Accepted at HPCA 2024

As graph data size increases, the vast latency and memory consumption during inference pose a significant challenge to the real-world deployment of Graph Neural Networks (GNNs). While quantization is a powerful approach to reducing GNNs complexity, most previous works on GNNs quantization fail to exploit the unique characteristics of GNNs, suffering from severe accuracy degradation. Through an in-depth analysis of the topology of GNNs, we observe that the topology of the graph leads to significant differences between nodes, and most of the nodes in a graph appear to have a small aggregation value. Motivated by this, in this paper, we propose the Aggregation-Aware mixed-precision Quantization ($\rm A^2Q$) for GNNs, where an appropriate bitwidth is automatically learned and assigned to each node in the graph. To mitigate the vanishing gradient problem caused by sparse connections between nodes, we propose a Local Gradient method to serve the quantization error of the node features as the supervision during training. We also develop a Nearest Neighbor Strategy to deal with the generalization on unseen graphs. Extensive experiments on eight public node-level and graph-level datasets demonstrate the generality and robustness of our proposed method. Compared to the FP32 models, our method can achieve up to a 18.6x (i.e., 1.70bit) compression ratio with negligible accuracy degradation. Morever, compared to the state-of-the-art quantization method, our method can achieve up to 11.4\% and 9.5\% accuracy improvements on the node-level and graph-level tasks, respectively, and up to 2x speedup on a dedicated hardware accelerator., Comment: Accepted by ICLR2023

Derivatives are a key nonparametric functional in wide-ranging applications where the rate of change of an unknown function is of interest. In the Bayesian paradigm, Gaussian processes (GPs) are routinely used as a flexible prior for unknown functions, and are arguably one of the most popular tools in many areas. However, little is known about the optimal modelling strategy and theoretical properties when using GPs for derivatives. In this article, we study a plug-in strategy by differentiating the posterior distribution with GP priors for derivatives of any order. This practically appealing plug-in GP method has been previously perceived as suboptimal and degraded, but this is not necessarily the case. We provide posterior contraction rates for plug-in GPs and establish that they remarkably adapt to derivative orders. We show that the posterior measure of the regression function and its derivatives, with the same choice of hyperparameter that does not depend on the order of derivatives, converges at the minimax optimal rate up to a logarithmic factor for functions in certain classes. We analyze a data-driven hyperparameter tuning method based on empirical Bayes, and show that it satisfies the optimal rate condition while maintaining computational efficiency. This article to the best of our knowledge provides the first positive result for plug-in GPs in the context of inferring derivative functionals, and leads to a practically simple nonparametric Bayesian method with optimal and adaptive hyperparameter tuning for simultaneously estimating the regression function and its derivatives. Simulations show competitive finite sample performance of the plug-in GP method. A climate change application for analyzing the global sea-level rise is discussed., Comment: This paper supersedes the second part of the technical report available at arXiv:2011.13967v1. That technical report has been split: The first part on equivalence theory will be extended and become 2011.13967v2. The results on Bayesian inference for function derivatives have evolved into this paper. arXiv admin note: text overlap with arXiv:2011.13967

Deep convolutional neural networks have achieved remarkable progress in recent years. However, the large volume of intermediate results generated during inference poses a significant challenge to the accelerator design for resource-constraint FPGA. Due to the limited on-chip storage, partial results of intermediate layers are frequently transferred back and forth between on-chip memory and off-chip DRAM, leading to a non-negligible increase in latency and energy consumption. In this paper, we propose block convolution, a hardware-friendly, simple, yet efficient convolution operation that can completely avoid the off-chip transfer of intermediate feature maps at run-time. The fundamental idea of block convolution is to eliminate the dependency of feature map tiles in the spatial dimension when spatial tiling is used, which is realized by splitting a feature map into independent blocks so that convolution can be performed separately on individual blocks. We conduct extensive experiments to demonstrate the efficacy of the proposed block convolution on both the algorithm side and the hardware side. Specifically, we evaluate block convolution on 1) VGG-16, ResNet-18, ResNet-50, and MobileNet-V1 for ImageNet classification task; 2) SSD, FPN for COCO object detection task, and 3) VDSR for Set5 single image super-resolution task. Experimental results demonstrate that comparable or higher accuracy can be achieved with block convolution. We also showcase two CNN accelerators via algorithm/hardware co-design based on block convolution on memory-limited FPGAs, and evaluation shows that both accelerators substantially outperform the baseline without off-chip transfer of intermediate feature maps., Comment: Accepted to IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems (TCAD), 2021. This is an extended version of the conference paper published on DATE'18

There is a wide range of applications where the local extrema of a function are the key quantity of interest. However, there is surprisingly little work on methods to infer local extrema with uncertainty quantification in the presence of noise. By viewing the function as an infinite-dimensional nuisance parameter, a semiparametric formulation of this problem poses daunting challenges, both methodologically and theoretically, as (i) the number of local extrema may be unknown, and (ii) the induced shape constraints associated with local extrema are highly irregular. In this article, we build upon a derivative-constrained Gaussian process prior recently proposed by Yu et al. (2023) to derive what we call an encompassing approach that indexes possibly multiple local extrema by a single parameter. We provide closed-form characterization of the posterior distribution and study its large sample behavior under this unconventional encompassing regime. We show that the posterior measure converges to a mixture of Gaussians with the number of components matching the underlying truth, leading to posterior exploration that accounts for multi-modality. Point and interval estimates of local extrema with frequentist properties are also provided. The encompassing approach leads to a remarkably simple, fast semiparametric approach for inference on local extrema. We illustrate the method through simulations and a real data application to event-related potential analysis.

BERT is the most recent Transformer-based model that achieves state-of-the-art performance in various NLP tasks. In this paper, we investigate the hardware acceleration of BERT on FPGA for edge computing. To tackle the issue of huge computational complexity and memory footprint, we propose to fully quantize the BERT (FQ-BERT), including weights, activations, softmax, layer normalization, and all the intermediate results. Experiments demonstrate that the FQ-BERT can achieve 7.94x compression for weights with negligible performance loss. We then propose an accelerator tailored for the FQ-BERT and evaluate on Xilinx ZCU102 and ZCU111 FPGA. It can achieve a performance-per-watt of 3.18 fps/W, which is 28.91x and 12.72x over Intel(R) Core(TM) i7-8700 CPU and NVIDIA K80 GPU, respectively.

We study the posterior contraction rates of a Bayesian method with Gaussian process priors in nonparametric regression and its plug-in property for differential operators. For a general class of kernels, we establish convergence rates of the posterior measure of the regression function and its derivatives, which are both minimax optimal up to a logarithmic factor for functions in certain classes. Our calculation shows that the rate-optimal estimation of the regression function and its derivatives share the same choice of hyperparameter, indicating that the Bayes procedure remarkably adapts to the order of derivatives and enjoys a generalized plug-in property that extends real-valued functionals to function-valued functionals. This leads to a practically simple method for estimating the regression function and its derivatives, whose finite sample performance is assessed using simulations. Our proof shows that, under certain conditions, to any convergence rate of Bayes estimators there corresponds the same convergence rate of the posterior distributions (i.e., posterior contraction rate), and vice versa. This equivalence holds for a general class of Gaussian processes and covers the regression function and its derivative functionals, under both the $L_2$ and $L_{\infty}$ norms. In addition to connecting these two fundamental large sample properties in Bayesian and non-Bayesian regimes, such equivalence enables a new routine to establish posterior contraction rates by calculating convergence rates of nonparametric point estimators. At the core of our argument is an operator-theoretic framework for kernel ridge regression and equivalent kernel techniques. We derive a range of sharp non-asymptotic bounds that are pivotal in establishing convergence rates of nonparametric point estimators and the equivalence theory, which may be of independent interest.

We study the problem of estimating the derivatives of a regression function, which has a wide range of applications as a key nonparametric functional of unknown functions. Standard analysis may be tailored to specific derivative orders, and parameter tuning remains a daunting challenge particularly for high-order derivatives. In this article, we propose a simple plug-in kernel ridge regression (KRR) estimator in nonparametric regression with random design that is broadly applicable for multi-dimensional support and arbitrary mixed-partial derivatives. We provide a non-asymptotic analysis to study the behavior of the proposed estimator in a unified manner that encompasses the regression function and its derivatives, leading to two error bounds for a general class of kernels under the strong $L_\infty$ norm. In a concrete example specialized to kernels with polynomially decaying eigenvalues, the proposed estimator recovers the minimax optimal rate up to a logarithmic factor for estimating derivatives of functions in H\"older and Sobolev classes. Interestingly, the proposed estimator achieves the optimal rate of convergence with the same choice of tuning parameter for any order of derivatives. Hence, the proposed estimator enjoys a \textit{plug-in property} for derivatives in that it automatically adapts to the order of derivatives to be estimated, enabling easy tuning in practice. Our simulation studies show favorable finite sample performance of the proposed method relative to several existing methods and corroborate the theoretical findings on its minimax optimality., Comment: Accepted by Journal of Machine Learning Research

Object detection has made impressive progress in recent years with the help of deep learning. However, state-of-the-art algorithms are both computation and memory intensive. Though many lightweight networks are developed for a trade-off between accuracy and efficiency, it is still a challenge to make it practical on an embedded device. In this paper, we present a system-level solution for efficient object detection on a heterogeneous embedded device. The detection network is quantized to low bits and allows efficient implementation with shift operators. In order to make the most of the benefits of low-bit quantization, we design a dedicated accelerator with programmable logic. Inside the accelerator, a hybrid dataflow is exploited according to the heterogeneous property of different convolutional layers. We adopt a straightforward but resource-friendly column-prior tiling strategy to map the computation-intensive convolutional layers to the accelerator that can support arbitrary feature size. Other operations can be performed on the low-power CPU cores, and the entire system is executed in a pipelined manner. As a case study, we evaluate our object detection system on a real-world surveillance video with input size of 512x512, and it turns out that the system can achieve an inference speed of 18 fps at the cost of 6.9W (with display) with an mAP of 66.4 verified on the PASCAL VOC 2012 dataset., Comment: Accepted by ICCV 2019 Low-Power Computer Vision Workshop