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Data for pretraining machine learning models often consists of collections ofheterogeneous datasets. Although training on their union is reasonable inagnostic settings, it might be suboptimal when the target domain -- where themodel will ultimately be used -- is known in advance. In that case, one wouldideally pretrain only on the dataset(s) most similar to the target one. Insteadof limiting this choice to those datasets already present in the pretrainingcollection, here we explore extending this search to all datasets that can besynthesized as `combinations' of them. We define such combinations asmulti-dataset interpolations, formalized through the notion of generalizedgeodesics from optimal transport (OT) theory. We compute these geodesics usinga recent notion of distance between labeled datasets, and derive alternativeinterpolation schemes based on it: using either barycentric projections oroptimal transport maps, the latter computed using recent neural OT methods.These methods are scalable, efficient, and -- notably -- can be used tointerpolate even between datasets with distinct and unrelated label sets.Through various experiments in transfer learning in computer vision, wedemonstrate this is a promising new approach for targeted on-demand datasetsynthesis.

Generating Synthetic Datasets by Interpolating along Generalized Geodesics