Convolutional Conditional Neural Processes

TL;DR

The paper introduces ConvCNP, a neural model that leverages translation equivariance for improved modeling of spatial and temporal data, achieving state-of-the-art results and zero-shot generalization.

Contribution

It extends neural processes with convolutional structures to incorporate translation equivariance, enabling better out-of-domain generalization.

Findings

Achieves state-of-the-art performance on several benchmarks.

Enables zero-shot generalization to out-of-domain tasks.

Models translation equivariance effectively in neural processes.

Abstract

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.