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Delta lenses are an established mathematical framework for modelling anddesigning bidirectional model transformations. Following the recentobservations by Fong et al, the paper extends the delta lens framework with a anew ingredient: learning over a parameterized space of model transformationsseen as functors. We define a notion of an asymmetric learning delta lens withamendment (ala-lens), and show how ala-lenses can be organized into a symmetricmonoidal (sm) category. We also show that sequential and parallel compositionof well-behaved ala-lenses are also well-behaved so that well-behavedala-lenses constitute a full sm-subcategory of ala-lenses.

General supervised learning as change propagation with delta lenses