Conditional Graph Neural Processes: A Functional Autoencoder Approach

TL;DR

This paper presents Conditional Graph Neural Processes, a new autoencoder architecture that embeds and decodes functional processes using graph neural networks, emphasizing the importance of metric space structures for process representations.

Contribution

Introduces a novel graph-based encoder-decoder architecture for functional process embeddings, leveraging metric space structures, extending the Conditional Neural Process framework.

Findings

Effective embedding and decoding of functions over arbitrary domains.

Utilization of graph neural networks to exploit local structures.

Demonstrates the importance of metric space structures in process representations.

Abstract

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.