  We present a new model of neural networks called Min-Max-Plus Neural Networks
(MMP-NNs) based on operations in tropical arithmetic. In general, an MMP-NN is
composed of three types of alternately stacked layers, namely linear layers,
min-plus layers and max-plus layers. Specifically, the latter two types of
layers constitute the nonlinear part of the network which is trainable and more
sophisticated compared to the nonlinear part of conventional neural networks.
In addition, we show that with higher capability of nonlinearity expression,
MMP-NNs are universal approximators of continuous functions, even when the
number of multiplication operations is tremendously reduced (possibly to none
in certain extreme cases). Furthermore, we formulate the backpropagation
algorithm in the training process of MMP-NNs and introduce an algorithm of
normalization to improve the rate of convergence in training.
