Set-Structured Latent Representations

Unstructured data often has latent component structure, such as the objects in an image of a scene. In these situations, the relevant latent structure is an unordered collection or \emph{set}. However, learning such representations directly from data is difficult due to the discrete and unordered structure. Here, we develop a framework for differentiable learning of set-structured latent representations. We show how to use this framework to naturally decompose data such as images into sets of interpretable and meaningful components and demonstrate how existing techniques cannot properly disentangle relevant structure. We also show how to extend our methodology to downstream tasks such as set matching, which uses set-specific operations. Our code is available at https://github.com/CUVL/SSLR.