BibTeX
@INPROCEEDINGS{
         Bosse2025ADa,
       author = "T. Bosse and H. M. B{\"u}cker",
       title = "Algorithmic Differentiation and Vertex Elimination on Computational Hypergraphs",
       booktitle = "2025 Proceedings of the Conference on Applied and Computational Discrete
         Algorithms (ACDA), July~30--August~1, 2025",
       editor = "A. Conway and A. Pothen and M. Farach-Colton and B. U{\c{c}}ar",
       pages = "196--207",
       address = "Philadelphia, PA, USA",
       publisher = "SIAM",
       url = "https://doi.org/10.1137/1.9781611978759.15",
       doi = "10.1137/1.9781611978759.15",
       abstract = "Algorithmic differentiation is a numerical method for computing derivatives of
         functions defined by computer codes. It systematically applies the chain rule to the operations
         executed during a program evaluation, typically represented by a directed acyclic graph. The
         vertices of this graph correspond to intermediate scalar values computed and stored during the
         program execution, and edges represent the data dependencies between these values. The process of
         accumulating derivatives involves successively eliminating vertices in a specific order within this
         graph. While the graph model captures perfectly the situation where the program executes
         scalar-valued operations with one or two input scalars, it does not immediately allow for raising
         the abstraction to a coarser level. The major contribution of this article is a novel combinatorial
         model that is capable of representing algorithmic differentiation for more general operations.
         Specifically, the model accommodates operations with multiple-input and multiple-output relations as
         well as intermediate values that are non-scalar. The new combinatorial model is based on
         computational hypergraphs, a novel class of directed hypergraphs where vertices represent non-scalar
         intermediate values and hyperedges correspond to operations involving multiple inputs and
         outputs---essentially, subroutines. Accumulating derivatives then corresponds to vertex elimination
         within these computational hypergraphs. In contrast to the graph model, the new elimination rules in
         the hypergraph model differ.",
       year = "2025",
       ad_theotech = "Computational Graph"
}