  We introduce the Convolutional Conditional Neural Process (ConvCNP), a new
member of the Neural Process family that models translation equivariance in the
data. Translation equivariance is an important inductive bias for many learning
problems including time series modelling, spatial data, and images. The model
embeds data sets into an infinite-dimensional function space as opposed to a
finite-dimensional vector space. To formalize this notion, we extend the theory
of neural representations of sets to include functional representations, and
demonstrate that any translation-equivariant embedding can be represented using
a convolutional deep set. We evaluate ConvCNPs in several settings,
demonstrating that they achieve state-of-the-art performance compared to
existing NPs. We demonstrate that building in translation equivariance enables
zero-shot generalization to challenging, out-of-domain tasks.
