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Cycle-consistent training is widely used for jointly learning a forward andinverse mapping between two domains of interest without the cumbersomerequirement of collecting matched pairs within each domain. In this regard, theimplicit assumption is that there exists (at least approximately) aground-truth bijection such that a given input from either domain can beaccurately reconstructed from successive application of the respectivemappings. But in many applications no such bijection can be expected to existand large reconstruction errors can compromise the success of cycle-consistenttraining. As one important instance of this limitation, we considerpractically-relevant situations where there exists a many-to-one or surjectivemapping between domains. To address this regime, we develop a conditionalvariational autoencoder (CVAE) approach that can be viewed as convertingsurjective mappings to implicit bijections whereby reconstruction errors inboth directions can be minimized, and as a natural byproduct, realistic outputdiversity can be obtained in the one-to-many direction. As theoreticalmotivation, we analyze a simplified scenario whereby minima of the proposedCVAE-based energy function align with the recovery of ground-truth surjectivemappings. On the empirical side, we consider a synthetic image dataset withknown ground-truth, as well as a real-world application involving naturallanguage generation from knowledge graphs and vice versa, a prototypicalsurjective case. For the latter, our CVAE pipeline can capture such many-to-onemappings during cycle training while promoting textural diversity forgraph-to-text tasks. Our code is available at github.com/QipengGuo/CycleGT  *A condensed version of this paper has been accepted to AISTATS 2021. Thisversion contains additional content and updates.

Fork or Fail: Cycle-Consistent Training with Many-to-One Mappings