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Flip Graphs for Matrix Multiplication

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arxiv 2212.01175 v1 pith:ILD4ZK2R submitted 2022-12-02 cs.SC

Manuel Kauers , Jakob Moosbauer This is my paper · ORCID
classification cs.SC
keywords matrixflipgraphmethodmultiplicationablearbitrarycall
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We introduce a new method for discovering matrix multiplication schemes based on random walks in a certain graph, which we call the flip graph. Using this method, we were able to reduce the number of multiplications for the matrix formats (4, 4, 5) and (5, 5, 5), both in characteristic two and for arbitrary ground fields.

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  1. Depth-first search for tensor rank and border rank over finite fields

    cs.CC 2024-11 conditional novelty 6.0 of 10

    An exact algorithm with O*(|F|^{(R-max_d n_d)(sum_d n_d)+max_d n_d}) time decides tensor rank over finite fields, with a border-rank variant over F[x]/(x^H).

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