  Deep neural networks (DNNs) have been employed for designing wireless systems
in many aspects, say transceiver design, resource optimization, and information
prediction. Existing works either use the fully-connected DNN or the DNNs with
particular architectures developed in other domains. While generating labels
for supervised learning and gathering training samples are time-consuming or
cost-prohibitive, how to develop DNNs with wireless priors for reducing
training complexity remains open. In this paper, we show that two kinds of
permutation invariant properties widely existed in wireless tasks can be
harnessed to reduce the number of model parameters and hence the sample and
computational complexity for training. We find special architecture of DNNs
whose input-output relationships satisfy the properties, called permutation
invariant DNN (PINN), and augment the data with the properties. By learning the
impact of the scale of a wireless system, the size of the constructed PINNs can
flexibly adapt to the input data dimension. We take predictive resource
allocation and interference coordination as examples to show how the PINNs can
be employed for learning the optimal policy with unsupervised and supervised
learning. Simulations results demonstrate a dramatic gain of the proposed PINNs
in terms of reducing training complexity.
