HexCNN: A Framework for Native Hexagonal Convolutional Neural Networks

Abstract

Hexagonal CNN models have shown superior performance in applications such as IACT data analysis and aerial scene classification due to their better rotation symmetry and reduced anisotropy. In order to realize hexagonal processing, existing studies mainly use the ZeroOut method to imitate hexagonal processing, which causes substantial memory and computation overheads. We address this deficiency with a novel native hexagonal CNN framework named HexCNN. HexCNN takes hexagon-shaped input and performs forward and backward propagation on the original form of the input based on hexagonshaped filters, hence avoiding computation and memory overheads caused by imitation. For applications with rectangle-shaped input but require hexagonal processing, HexCNN can be applied by padding the input into hexagon-shape as preprocessing. In this case, we show that the time and space efficiency of HexCNN still outperforms existing hexagonal CNN methods substantially. Experimental results show that compared with the state-ofthe-art models, which imitate hexagonal processing but using rectangle-shaped filters, HexCNN reduces the training time by up to 42.2%. Meanwhile, HexCNN saves the memory space cost by up to 25% and 41.7% for loading the input and performing convolution, respectively.

Rotation-Invariant Convolution Networks with Hexagon-Based Kernels

“…These features can be used in the field of map coordinate positioning [10]. Using the convolution neural network, the hexagonal representation can store a large amount of data on the same sampling points and reduce calculation time and quantization error [11], [12]. Zhao et al also prove that CNN with the hexagonal kernel has the same back-propagation as standard CNN [12].…”

“…Using the convolution neural network, the hexagonal representation can store a large amount of data on the same sampling points and reduce calculation time and quantization error [11], [12]. Zhao et al also prove that CNN with the hexagonal kernel has the same back-propagation as standard CNN [12]. Luo et al and Hoogeboom et al describe a set of construction methods for hexagonal structures that enable lossless rotation of hexagonal images and propose that hexagonal kernels could be used for G-CNN [4], [13], [14].…”

Biologically inspired deep residual networks for computer vision applications

“…They define the size of kernel based on the number of levels of neighbouring elements. These hexagonal convolutions achieve higher efficiency than ZeroOut method [40] due to its divide-and-conquer approach. Increasing the number of learnable parameters along the skip connection of residual network architecture will again lead to vanishing gradient problem as mentioned in Sec.…”