7 citations · 13 across the 7 of their papers we have counts for
7 papers
Functorial String Diagrams for Reverse-Mode Automatic Differentiation
Mario Alvarez-Picallo, Dan R. Ghica, David Sprunger +1
We enhance the calculus of string diagrams for monoidal categories with hierarchical features in order to capture closed monoidal (and cartesian closed) structure. Using this new s…
The Difference Lambda-Calculus: A Language for Difference Categories
Mario Alvarez-Picallo, C. -H. Luke Ong
Cartesian difference categories are a recent generalisation of Cartesian differential categories which introduce a notion of "infinitesimal" arrows satisfying an analogue of the Ko…
Cartesian Difference Categories
Mario Alvarez-Picallo, Jean-Simon Pacaud Lemay
Cartesian differential categories are categories equipped with a differential combinator which axiomatizes the directional derivative. Important models of Cartesian differential ca…
Change actions: from incremental computation to discrete derivatives
Mario Alvarez-Picallo
The goal of this thesis is threefold: first, to provide a general semantic setting for reasoning about incremental computation. Second, to establish and clarify the connection betw…
Cartesian Difference Categories: Extended Report
Mario Alvarez-Picallo, Jean-Simon Pacaud Lemay
Cartesian differential categories are categories equipped with a differential combinator which axiomatizes the directional derivative. Important models of Cartesian differential ca…
Change Actions: Models of Generalised Differentiation
Mario Alvarez-Picallo, C. -H. Luke Ong
Cai et al. have recently proposed change structures as a semantic framework for incremental computation. We generalise change structures to arbitrary cartesian categories and propo…
Fixing Incremental Computation: Derivatives of Fixpoints, and the Recursive Semantics of Datalog
Mario Alvarez-Picallo, Alex Eyers-Taylor, Michael Peyton Jones +1
Incremental computation has recently been studied using the concepts of change structures and derivatives of programs, where the derivative of a function allows updating the output…