Hartley Stochastic Computing For Convolutional Neural Networks

Energy consumption and the latency of convolutional neural networks (CNNs) are two important factors that limit their applications specifically for embedded devices. Fourier-based frequency domain (FD) convolution is a promising low-cost alternative to conventional implementations in the spatial domain (SD) for CNNs. FD convolution performs its operation with point-wise multiplications. However, in CNNs, the overhead for the Fourier-based FD-convolution surpasses its computational saving for small filter sizes. In this work, we propose to implement convolutional layers in the FD using the Hartley transformation (HT) instead of the Fourier transformation. We show that the HT can reduce the convolution delay and energy consumption even for small filters. With the HT of parameters, we replace convolution with point-wise multiplications. HT lets us compress input feature maps, in all convolutional layer, before convolving them with filters. To optimize the hardware implementation of our method, we utilize stochastic computing (SC) to perform the point-wise multiplications in the FD. In this regard, we re-formalize the HT to better match with SC. We show that, compared to conventional Fourier-based convolution, Hartley SC-based convolution can achieve 1.33x speedup, and 1.23x energy saving on a Virtex 7 FPGA when we implement AlexNet over CIFAR-10.