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Convolutional neural networks (CNNs) have been used in many machine learningfields. In practical applications, the computational cost of convolutionalneural networks is often high with the deepening of the network and the growthof data volume, mostly due to a large amount of multiplication operations offloating-point numbers in convolution operations. To reduce the amount ofmultiplications, we propose a new type of CNNs called Tropical ConvolutionalNeural Networks (TCNNs) which are built on tropical convolutions in which themultiplications and additions in conventional convolutional layers are replacedby additions and min/max operations respectively. In addition, since tropicalconvolution operators are essentially nonlinear operators, we expect TCNNs tohave higher nonlinear fitting ability than conventional CNNs. In theexperiments, we test and analyze several different architectures of TCNNs forimage classification tasks in comparison with similar-sized conventional CNNs.The results show that TCNN can achieve higher expressive power than ordinaryconvolutional layers on the MNIST and CIFAR10 image data set. In differentnoise environments, there are wins and losses in the robustness of TCNN andordinary CNNs.

An Alternative Practice of Tropical Convolution to Traditional Convolutional Neural Networks