Convolutional neural networks (CNNs) are the core of most state-of-the-art deep learning algorithms specialized for object detection and classification. CNNs are both computationally complex and embarrassingly parallel. Two properties that leave room for potential software and hardware optimizations for embedded systems. Given a programmable hardware accelerator with a CNN oriented custom instructions set, the compiler's task is to exploit the hardware's full potential, while abiding with the hardware constraints and maintaining generality to run different CNN models with varying workload properties. Snowflake is an efficient and scalable hardware accelerator implemented on programmable logic devices. It implements a control pipeline for a custom instruction set. The goal of this paper is to present Snowflake's compiler that generates machine level instructions from Torch7 model description files. The main software design points explored in this work are: model structure parsing, CNN workload breakdown, loop rearrangement for memory bandwidth optimizations and memory access balancing. The performance achieved by compiler generated instructions matches against hand optimized code for convolution layers. Generated instructions also efficiently execute AlexNet and ResNet18 inference on Snowflake. Snowflake with @math processing units was synthesized on Xilinx's Zynq XC7Z045 FPGA. At @math MHz, AlexNet achieved in @math frames s and @math GB s of off-chip memory bandwidth, and @math frames s and @math GB s for ResNet18. Total on-chip power is @math W.
is a @math D convolution of an input volume with a group of @math D kernels that result in extracted features from the input. Each @math D kernel is associated with a bias value. Number channels is the z-axis of input volume. Input volume is called maps and a slice of it is a map. A window is the size of one kernel convolved with part of input volume. Operations in a compute window are independent, hence it is well suited to multi-core processors: GPUs @cite_20 and other designs using ASIC @cite_2 @cite_16 and FPGAs @cite_7 @cite_17 .
@cite_7 @cite_2 @cite_16 @cite_20 @cite_17
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We investigate the minimization of Newton's functional for the problem of the body of minimal resistance with maximal height @math cite butt in the class of convex developable functions defined in a disc. This class is a natural candidate to find a (non-radial) minimizer in accordance with the results of cite lrp2. We prove that the minimizer in this class has a minimal set in the form of a regular polygon with @math sides centered in the disc, and numerical experiments indicate that the natural number @math is a non-decreasing function of @math . The corresponding functions all achieve a lower value of the functional than the optimal radially symmetric function with the same height @math . We study the problem of distribution to real-value regression, where one aims to regress a mapping @math that takes in a distribution input covariate @math (for a non-parametric family of distributions @math ) and outputs a real-valued response @math . This setting was recently studied, and a "Kernel-Kernel" estimator was introduced and shown to have a polynomial rate of convergence. However, evaluating a new prediction with the Kernel-Kernel estimator scales as @math . This causes the difficult situation where a large amount of data may be necessary for a low estimation risk, but the computation cost of estimation becomes infeasible when the data-set is too large. To this end, we propose the Double-Basis estimator, which looks to alleviate this big data problem in two ways: first, the Double-Basis estimator is shown to have a computation complexity that is independent of the number of of instances @math when evaluating new predictions after training; secondly, the Double-Basis estimator is shown to have a fast rate of convergence for a general class of mappings @math . Conventional convolutional neural networks use either a linear or a nonlinear filter to extract features from an image patch (region) of spatial size @math (typically, @math is small and is equal to @math , e.g., @math is 5 or 7). Generally, the size of the filter is equal to the size @math of the input patch. We argue that the representational ability of equal-size strategy is not strong enough. To overcome the drawback, we propose to use subpatch filter whose spatial size @math is smaller than @math . The proposed subpatch filter consists of two subsequent filters. The first one is a linear filter of spatial size @math and is aimed at extracting features from spatial domain. The second one is of spatial size @math and is used for strengthening the connection between different input feature channels and for reducing the number of parameters. The subpatch filter convolves with the input patch and the resulting network is called a subpatch network. Taking the output of one subpatch network as input, we further repeat constructing subpatch networks until the output contains only one neuron in spatial domain. These subpatch networks form a new network called the cascaded subpatch network (CSNet). The feature layer generated by CSNet is called the csconv layer. For the whole input image, we construct a deep neural network by stacking a sequence of csconv layers. Experimental results on five benchmark data sets demonstrate the effectiveness and compactness of the proposed CSNet. For example, our CSNet reaches a test error of 5.68 on the CIFAR10 data set without model averaging. To the best of our knowledge, this is the best result ever obtained on the CIFAR10 data set. Chen's data for the raw frequency of use of 138 physics journals in the science library at M I T are re‐examined and converted to densities of use‐per‐metre of shelf. Other units of size for obtaining densities, and their measurement, are discussed. There is no evidence for synchronous obsolescence in the 1955 to 1968 volumes of these journals: instead there is some statistically significant evidence of greater density of use with greater age. Similar evidence elsewhere is cited. The ranking order for heaviness of use is also radically altered by converting raw frequencies to densities of use. It is suggested that, for comparing the relative values of different journals, or age groups, in library use or citation studies, analyses of raw frequencies are valueless, and indeed potentially dangerously misleading, until they are converted to allow for the numbers of available items in each group examined.