Title: The Set Autoencoder: Unsupervised Representation Learning for Sets. Abstract: We propose the set autoencoder, a model for unsupervised representation learning for sets of elements. It is closely related to sequence-to-sequence models, which learn fixed-sized latent representations for sequences, and have been applied to a number of challenging supervised sequence tasks such as machine translation, as well as unsupervised representation learning for sequences.
In contrast to sequences, sets are permutation invariant. The proposed set autoencoder considers this fact, both with respect to the input as well as the output of the model. On the input side, we adapt a recently-introduced recurrent neural architecture using a content-based attention mechanism. On the output side, we use a stable marriage algorithm to align predictions to labels in the learning phase.
We train the model on synthetic data sets of point clouds and show that the learned representations change smoothly with translations in the inputs, preserve distances in the inputs, and that the set size is represented directly. We apply the model to supervised tasks on the point clouds using the fixed-size latent representation. For a number of difficult classification problems, the results are better than those of a model that does not consider the permutation invariance. Especially for small training sets, the set-aware model benefits from unsupervised pretraining.