Towards a Deep Network Architecture for Structured Smoothness

We propose the Fixed Grouping Layer (FGL); a novel feedforward layer designed to incorporate the inductive bias of structured smoothness into a deep learning model. FGL achieves this goal by connecting nodes across layers based on spatial similarity. The use of structured smoothness, as implemented by FGL, is motivated by applications to structured spatial data, which is, in turn, motivated by domain knowledge. The proposed model architecture outperforms conventional neural network architectures across a variety of simulated and real datasets with structured smoothness.