HATS: A Hierarchical Sequence-Attention Framework for Inductive Set-of-Sets Embeddings

In many complex domains, the input data are often not suited for the typical vector representations used in deep learning models. For example, in relational learning and computer vision tasks, the data are often better represented as sets (e.g., the neighborhood of a node, a cloud of points). In these cases, a key challenge is to learn an embedding function that is invariant to permutations of the input. While there has been some recent work on principled methods for learning permutation-invariant representations of sets, these approaches are limited in their applicability to set-of-sets (SoS) tasks, such as subgraph prediction and scene classification. In this work, we develop a deep neural network framework to learn inductive SoS embeddings that are invariant to SoS permutations. Specifically, we propose HATS, a hierarchical sequence model with attention mechanisms for inductive set-of-sets embeddings. We develop stochastic optimization and inference methods for learning HATS, and our experiments demonstrate that HATS achieves superior performance across a wide range of set-of-sets tasks.