@misc{discovery10132859,
           month = {July},
         address = {Ithaca, NY, USA},
            note = {This version is the version of record. For information on re-use, please refer to the publisher's terms and conditions.},
       publisher = {ArXiv},
            year = {2021},
           title = {Functorial String Diagrams for Reverse-Mode Automatic Differentiation},
         journal = {arXiv.org},
          author = {Alvarez-Picallo, M and Ghica, DR and Sprunger, D and Zanasi, F},
        abstract = {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.},
             url = {https://doi.org/10.48550/arXiv.2107.13433},
        keywords = {string diagrams, automatic differentiation, graph rewriting, hierarchical hypergraphs}
}