A Compact Network Model for Distribution Regression

Despite the superior performance of deep neural networks, they are not efficient for regressing 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 encode an entire function in a single network node. We design a network that encodes and propagates functions in single nodes for the distribution regression task. Our proposed distribution regression network achieves higher prediction accuracies and more compact models compared to traditional neural networks.