General supervised categorical learning as change propagation with delta lenses
share
Delta lenses are an established mathematical framework for modelling and designing bidirectional model transformations. Following the recent observations by Fong et al, the paper extends the delta lens framework with a a new ingredient: learning over a parameterized space of model transformations seen as functors. We define a notion of an asymmetric learning delta lens with amendment (ala-lens), and show how ala-lens can be organized into a symmetric monoidal (sm) category. We also show that sequential and parallel composition of well-behaved ala-lenses are also well-behaved so that well-behaved ala-lenses constitute a full sm-subcategory of ala-lenses.
READ FULL TEXT