mlsanityData to 7 Oct 2026

Functorial String Diagrams for Reverse-Mode Automatic Differentiation

arXiv 2107.13433 ↗First posted 28 Jul 2021cs.PL cs.LGcited by 2

Not on the map. Why?

Abstract (arXiv)

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 syntax we formulate an automatic differentiation algorithm for (applied) simply typed lambda calculus in the style of [Pearlmutter and Siskind 2008] and we prove for the first time its soundness. To give an efficient yet principled implementation of the AD algorithm we define a sound and complete representation of hierarchical string diagrams as a class of hierarchical hypergraphs we call hypernets.

Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 16 of its 64 references that are in the map. First posted on arXiv 28 Jul 2021.

Builds on

16 of 64 references.

References · 16

  1. 2015Automatic differentiation in machine learning: a surveycited by 846
  2. 2018The simple essence of automatic differentiationcited by 22
  3. 2019Reverse derivative categoriescited by 15
  4. 2018Demystifying Differentiable Programming: Shift/Reset the Penultimate Backpropagatorcited by 14
  5. 2020Correctness of Automatic Differentiation via Diffeologies and Categorical Gluingcited by 11
  6. 2016Rewriting modulo symmetric monoidal structurecited by 4
  7. 2019Backpropagation in the Simply Typed Lambda-calculus with Linear Negationcited by 4
  8. 2016DiffSharp: An AD Library for .NET Languagescited by 3
  9. 2017Diagrammatic Semantics for Digital Circuitscited by 3
  10. 2020Reverse AD at Higher Types: Pure, Principled and Denotationally Correctcited by 3
  11. 2018Normalization for planar string diagrams and a quadratic equivalence algorithmcited by 2
  12. 2013Proof nets and the call-by-value lambda-calculuscited by 1
4 more
  1. 2016Efficient Implementation of a Higher-Order Language with Built-In ADcited by 1
  2. 2016Globular: an online proof assistant for higher-dimensional rewritingcited by 1
  3. 2018The Dynamic Geometry of Interaction Machine: A Token-Guided Graph Rewritercited by 1
  4. 2021Operational Semantics with Hierarchical Abstract Syntax Graphscited by 1

Built on by

Cited by year

Citing papers per year: 2024: 1; 2025: 1.

2 papers.

  1. 2024Position: Categorical Deep Learning is an Algebraic Theory of All Architecturescited by 32
  2. 2025Graph Lineages and Skeletal Graph Productscited by 0