  Modern methods for learning over graph input data have shown the fruitfulness
of accounting for relationships among elements in a collection. However, most
methods that learn over set input data use only rudimentary approaches to
exploit intra-collection relationships. In this work we introduce Deep Message
Passing on Sets (DMPS), a novel method that incorporates relational learning
for sets. DMPS not only connects learning on graphs with learning on sets via
deep kernel learning, but it also bridges message passing on sets and
traditional diffusion dynamics commonly used in denoising models. Based on
these connections, we develop two new blocks for relational learning on sets:
the set-denoising block and the set-residual block. The former is motivated by
the connection between message passing on general graphs and diffusion-based
denoising models, whereas the latter is inspired by the well-known residual
network. In addition to demonstrating the interpretability of our model by
learning the true underlying relational structure experimentally, we also show
the effectiveness of our approach on both synthetic and real-world datasets by
achieving results that are competitive with or outperform the state-of-the-art.
