  Despite the superior performance of deep learning in many applications,
challenges remain in the area of regression on function spaces. In particular,
neural networks are unable to encode function inputs compactly as each node
encodes just a real value. We propose a novel idea to address this shortcoming:
to encode an entire function in a single network node. To that end, we design a
compact network representation that encodes and propagates functions in single
nodes for the distribution regression task. Our proposed Distribution
Regression Network (DRN) achieves higher prediction accuracies while being much
more compact and uses fewer parameters than traditional neural networks.
