Further reading

Kock exemplifies the strategy of beginning a differential theory from one generative axiom; LINCS borrows the organization, not the algebraic content [ Kock , 2006 ] . A neighboring program explicitly called Synthetic Machine Learning develops a synthetic approach through categorical probability and statistics, Markov categories, information geometry, and noncommutative information geometry [ Sepúlveda-Jiménez , 2025 ] . LINCS shares its synthetic ambition but takes declared compositional failure, typed obstruction, and controlled repair as its organizing primitives. Pearl develops do-calculus and the causal critique of association-only learning [ Pearl , 2009b , 2018 ] . Sketches as categorical theories originate with Ehresmann [ 1968 ] ; Barr and Wells [ 1999 ] connects them to categorical logic and model theory. Tangent categories supply the infinitesimal substrate [ Cockett and Cruttwell , 2014b , 2017 ] , while Riehl [ 2017 ] provides background on universal constructions, localization, and descent. Generalized gradients and nonsmooth backpropagation are treated by Rockafellar [ 1980 ] , Bolte et al. [ 2022 ] .