  We introduce a novel encoder-decoder architecture to embed functional
processes into latent vector spaces. This embedding can then be decoded to
sample the encoded functions over any arbitrary domain. This autoencoder
generalizes the recently introduced Conditional Neural Process (CNP) model of
random processes. Our architecture employs the latest advances in graph neural
networks to process irregularly sampled functions. Thus, we refer to our model
as Conditional Graph Neural Process (CGNP). Graph neural networks can
effectively exploit `local' structures of the metric spaces over which the
functions/processes are defined. The contributions of this paper are twofold:
(i) a novel graph-based encoder-decoder architecture for functional and process
embeddings, and (ii) a demonstration of the importance of using the structure
of metric spaces for this type of representations.
