Convolutional neural networks (CNNs) require high computation and memory demand for training. This paper presents the design of a frequency-domain accelerator for energy-efficient CNN training. With Fourier representations of parameters, we replace convolutions with simpler pointwise multiplications. To eliminate the Fourier transforms at every layer, we train the network entirely in the frequency domain using approximate frequency-domain nonlinear operations. We further reduce computation and memory requirements using sinc interpolation and Hermitian symmetry. The accelerator is designed and synthesized in 28nm CMOS, as well as prototyped in an FPGA. The simulation results show that the proposed accelerator significantly reduces training time and energy for a target recognition accuracy.

https://dl.acm.org/doi/pdf/10.1145/3061639.3062228

Design of an Energy-Efficient Accelerator for Training of Convolutional Neural Networks using Frequency-Domain Computation

The purpose of the current work is the theoretical and computational comparison of selected models for the energetics of dislocation dissociation resulting in stacking fault and partial dislocation (core) formation in fcc crystals as based on the (generalized) Peierls–Nabarro (GPN: e.g., Xiang et al., 2008 , Shen et al., 2014 ), and phase-field (PF: e.g., Shen and Wang, 2004 , Hunter et al., 2011 , Hunter et al., 2013 , Mianroodi and Svendsen, 2015 ), methodologies (e.g., Wang and Li, 2010 ). More specifically, in the current work, the GPN-based model of Xiang et al. (2008) is compared theoretically with the PF-based models of Shen and Wang (2004) , Hunter et al., 2011 , Hunter et al., 2013 , and Mianroodi and Svendsen (2015) . This is carried out here with the help of a unified formulation for these models via a generalization of the approach of Cahn and Hilliard (1958) to mechanics. Differences among these include the model forms for the free energy density ψ ela of the lattice and the free energy density ψ sli associated with dislocation slip. In the PF-based models, for example, ψ ela is formulated with respect to the residual distortion H R due to dislocation slip (e.g., Khachaturyan, 1983 , Mura, 1987 ), and with respect to the dislocation tensor curl H R in the GPN model (e.g., Xiang et al., 2008 ). As shown here, both model forms for ψ ela are in fact mathematically equal and so physically equivalent. On the other hand, model forms for ψ sli differ in the assumed dependence on the phase or disregistry fields ϕ , whose spatial variation represents the transition from unslipped to slipped regions in the crystal. In particular, Xiang et al. (2008) and Hunter et al., 2011 , Hunter et al., 2013 work with ψ sli ( ϕ ) . On the other hand, Shen and Wang (2004) and Mianroodi and Svendsen (2015) employ ψ sli ( ϕ , ∇ ϕ ) . To investigate the consequences of these differences for the modeling of the dislocation core, dissociation, and stacking fault formation, predictions from the models of Hunter et al., 2011 , Hunter et al., 2013 and Mianroodi and Svendsen (2015) are compared with results from molecular statics (MS) for the deformation field of dissociated edge and screw dipoles in Al and Au. Particularly notable is the agreement of the MS and PF strain field results for the case of perfect screw dissociation which, in contrast to the edge case, are characterized by asymmetric displacement and strain fields. The degree of this asymmetry is apparently related to the corresponding anisotropy ratio. As well, comparison of MS and PF disregistry fields implies that the gradient dependence of ψ sli results in a broadening of the (otherwise too narrow) disregistry profile to the form predicted by MS.

Theoretical and computational comparison of models for dislocation dissociation and stacking fault/core formation in fcc crystals

Large-scale convolutional neural network is a fundamental algorithmic building block in many computer vision and artificial intelligence applications that follow the deep learning principle. However, a typically-sized CNN is well known to be computationally intensive. This work presents a novel stochastic-based and scalable hardware architecture and circuit design that computes a large-scale CNN with FPGA. The key idea is to implement all key components of a deep learning CNN, including multi-dimensional convolution, activation, and pooling layers, completely in the probabilistic computing domain in order to achieve high computing robustness, high performance, and low hardware usage. Our approach has three advantages. First, it can achieve significantly lower algorithmic complexity for any given accuracy requirement. For a $N$ dimensional image feature map, we have theoretically proven that a random sample size of $k^* \log (N)$ is sufficient to achieve no more than 0.05 error at 95 percent confidence level, where $k^*$ is a constant of 510. This computing complexity, when compared with that of conventional multiplier-based architecture, represents on average 8.97 $\times$ and 6.98 $\times$ performance improvement for SCNN and Deep SCNN, respectively. Second, this proposed stochastic-based architecture is highly fault-tolerant because the information to be processed is encoded with a large ensemble of random samples. As such, the local perturbations of its computing accuracy will be dissipated globally, thus becoming inconsequential to the final overall results. More interestingly, our measured results have shown that 0.1 percent degradation in computing accuracy of CNN can actually mitigate the well-known overfitting problem. Overall, being highly scalable and energy efficient, our stochastic-based convolutional neural network architecture is well-suited for a modular vision engine with the goal of performing real-time detection, recognition, and segmentation of mega-pixel images, especially those perception-based computing tasks that are inherently fault-tolerant, while still requiring high energy efficiency.

Stochastic-Based Deep Convolutional Networks with Reconfigurable Logic Fabric

A rational approximation of the Dawsons integral for efficient computation of the complex error function

The Chang’E-2 digital elevation model (DEM, named CE2TMap2015), which is the highest resolution DEM product in China, was released with global coverage of the lunar surface. A detailed geometric quality assessment of the product is desirable for wider applications by users. A novel procedure for evaluating DEM geometric quality, which investigates both the global geometric uncertainty and local gross errors, is proposed in this paper. First, the DEM was divided into regular blocks and matched with the reference DEM. Then, the characteristics of errors were investigated using the statistical information of the matched tie points. Next, the local outlier factor (LOF) algorithm was performed to locate the gross errors. In our experiment, CE2TMap2015 was evaluated using the proposed method, with SLDEM2015 as the reference DEM. The results show that there were widespread geometric inconsistencies with an area-weighted average of 183.1 m horizontally (with the standard deviation being 101.2 m) and 2.3 m vertically (with the standard deviation being 15.4 m). Gross errors were detected automatically and were excluded in the statistical analysis. The periodic errors were extracted in the frequency domain using a Fourier transform. Our research results provide instructional information for the utilization of CE2TMap2015 by world-wide users. The proposed method can be used in the assessment of other planetary DEMs.

Geometric Quality Assessment of Chang’E-2 Global DEM Product

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The Fourier Transform And Its Application