arXiv:1902.05465cs.LO
Change Actions: Models of Generalised Differentiation
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Abstract
Cai et al. have recently proposed change structures as a semantic framework for incremental computation. We generalise change structures to arbitrary cartesian categories and propose the notion of change action model as a categorical model for (higher-order) generalised differentiation. Change action models naturally arise from many geometric and computational settings, such as (generalised) cartesian differential categories, group models of discrete calculus, and Kleene algebra of regular expressions. We show how to build canonical change action models on arbitrary cartesian categories, reminiscent of the Fàa di Bruno construction.
Thanks for checking out our project! Completely understand where you're coming from, I also struggled with imagining how differentiable programs could work, after all, computer programs implement discrete functions! When building it, I learned two surprising facts: (1) We can…
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