  Neural Processes (NPs) are powerful and flexible models able to incorporate
uncertainty when representing stochastic processes, while maintaining a linear
time complexity. However, NPs produce a latent description by aggregating
independent representations of context points and lack the ability to exploit
relational information present in many datasets. This renders NPs ineffective
in settings where the stochastic process is primarily governed by neighbourhood
rules, such as cellular automata (CA), and limits performance for any task
where relational information remains unused. We address this shortcoming by
introducing Message Passing Neural Processes (MPNPs), the first class of NPs
that explicitly makes use of relational structure within the model. Our
evaluation shows that MPNPs thrive at lower sampling rates, on existing
benchmarks and newly-proposed CA and Cora-Branched tasks. We further report
strong generalisation over density-based CA rule-sets and significant gains in
challenging arbitrary-labelling and few-shot learning setups.
