General supervised learning as change propagation with delta lenses
arXiv:1911.12904 · doi:10.1007/978-3-030-45231-5_10
Abstract
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-lenses 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.
An extended version of paper with the same title published at FOSSACS 2020. Unfortunately, both the paper and the previous version of the extended version uploaded to arxiv on Feb 26, 2020, had bad typos in Definition 4 and Fig.4, which are now fixed