Block Convolution: Towards Memory-Efficient Inference of Large-Scale CNNs on FPGA

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.

Semiparametric Bayesian Inference for Local Extrema of Functions in the Presence of Noise

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 address these challenges by suggesting an encompassing strategy that eliminates the need to specify the number of local extrema, which leads to a remarkably simple, fast semiparametric Bayesian approach for inference on local extrema. We provide closed-form characterization of the posterior distribution and study its large sample behaviors under this encompassing regime. We show a multi-modal Bernstein-von Mises phenomenon in which 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. We illustrate the method through simulations and a real data application to event-related potential analysis.

Hardware Acceleration of Fully Quantized BERT for Efficient Natural Language Processing

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.

Equivalence of Convergence Rates of Posterior Distributions and Bayes Estimators for Functions and Nonparametric Functionals

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.

On the Estimation of Derivatives Using Plug-in KRR Estimators

We study the problem of estimating the derivatives of the 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, 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 Holder class. 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 remarkable 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.