Neural Processes (NPs) are a family of conditional generative models that are able to model a distribution over functions, in a way that allows them to perform predictions at test time conditioned on a number of context points. A recent addition to this family, Convolutional Conditional Neural Processes (ConvCNP), have shown remarkable improvement in performance over prior art, but we find that they sometimes struggle to generalize when applied to time series data. In particular, they are not robust to distribution shifts and fail to extrapolate observed patterns into the future. By incorporating a Gaussian Process into the model, we are able to remedy this and at the same time improve performance within distribution. As an added benefit, the Gaussian Process reintroduces the possibility to sample from the model, a key feature of other members in the NP family.

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.