  We propose to employ the hierarchical coarse-grained structure in the
artificial neural networks explicitly to improve the interpretability without
degrading performance. The idea has been applied in two situations. One is a
neural network called TaylorNet, which aims to approximate the general mapping
from input data to output result in terms of Taylor series directly, without
resorting to any magic nonlinear activations. The other is a new setup for data
distillation, which can perform multi-level abstraction of the input dataset
and generate new data that possesses the relevant features of the original
dataset and can be used as references for classification. In both cases, the
coarse-grained structure plays an important role in simplifying the network and
improving both the interpretability and efficiency. The validity has been
demonstrated on MNIST and CIFAR-10 datasets. Further improvement and some open
questions related are also discussed.
