Further reading

The categorical background begins with standard introductions such as Mac Lane [ 1998 ] and Riehl [ 2017 ] . For the presentation of mathematical theories by sketches, the classical line runs from Ehresmann’s original program through categorical model theory and accessible categories [ Ehresmann , 1968 , Barr and Wells , 1999 , Makkai and Paré , 1989 , Adámek and Rosický , 1994 ] . These sources explain why a diagram can specify a theory before any numerical objective is chosen.

For readers interested in compositional learning itself, Fong et al. [ 2019 ] treats backpropagation functorially, while Cruttwell et al. [ 2022 ] develops categorical foundations for gradient-based learning. The more recent categorical-deep-learning program argues for an algebraic bridge between architectural constraints and their implementations [ Gavranović et al. , 2024 ] . LINCS is closest to this literature in its insistence on typed composition, but differs by making failed factorization and guarded repair the central learning event.

The interventionist contrast is developed by Pearl [ 2009b , 2018 ] . Those works motivate the need for models that support action rather than association alone. LINCS adopts that discipline at the level of the learning system while retaining a strict boundary between a general structural edit and a causally grounded intervention.