Title: Leveraging affinity cycle consistency to isolate factors of variation in learned representations. Abstract: Identifying the dominant factors of variation across a dataset is a central goal of representation learning. Generative approaches lead to descriptions that are rich enough to recreate the data, but often only a partial description is needed to complete downstream tasks or to gain insights about the dataset.  In this work, we operate in the setting where limited information is known about the data in the form of groupings, or set membership, and the task is to learn representations which isolate the factors of variation that are common across the groupings.  Our key insight is the use of affinity cycle consistency (ACC) between the learned embeddings of images belonging to different sets. In contrast to prior work, we demonstrate that ACC can be applied with significantly fewer constraints on the factors of variation, across a remarkably broad range of settings, and without any supervision for half of the data. By curating datasets from Shapes3D, we quantify the effectiveness of ACC through mutual information between the learned representations and the known generative factors. In addition, we demonstrate the applicability of ACC to the tasks of digit style isolation and synthetic-to-real object pose transfer and compare to generative approaches utilizing the same supervision.