  Convolutional neural networks (CNNs) have been used in many machine learning
fields. In practical applications, the computational cost of convolutional
neural networks is often high with the deepening of the network and the growth
of data volume, mostly due to a large amount of multiplication operations of
floating-point numbers in convolution operations. To reduce the amount of
multiplications, we propose a new type of CNNs called Tropical Convolutional
Neural Networks (TCNNs) which are built on tropical convolutions in which the
multiplications and additions in conventional convolutional layers are replaced
by additions and min/max operations respectively. In addition, since tropical
convolution operators are essentially nonlinear operators, we expect TCNNs to
have higher nonlinear fitting ability than conventional CNNs. In the
experiments, we test and analyze several different architectures of TCNNs for
image classification tasks in comparison with similar-sized conventional CNNs.
The results show that TCNN can achieve higher expressive power than ordinary
convolutional layers on the MNIST and CIFAR10 image data set. In different
noise environments, there are wins and losses in the robustness of TCNN and
ordinary CNNs.
