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Jakob Moosbauer

Publications and source records attributed to Jakob Moosbauer.

9 recordsLinked to original sources
arXiv2026

Exploiting the Structure in Tensor Decompositions for Matrix Multiplication

We present a new algorithm for fast matrix multiplication using tensor decompositions which have special features. Thanks to these features we obtain exponents lower than what the rank of the tensor decomposition suggests. In particular for $6\times 6$ matrix multiplication we reduce the exponent of the recent algorithm by Moosbauer and Poole from $2.8075$ to $2.8019$, while retaining a reasonable leading coefficient.

cs.SC↗
arXiv2025

Strassen's algorithm via orbit flip graphs

We give a short proof for Strassen's result that the rank of the 2 by 2 matrix multiplication tensor is at most 7. The proof requires no calculations and also no pattern matching or other type of nontrivial verification, and is based solely on properties of a specific order 6 group action. Our proof is based on the recent combination of flip graph algorithms and symmetries.

cs.DS↗
arXiv2025

Flip Graphs with Symmetry and New Matrix Multiplication Schemes

The flip graph algorithm is a method for discovering new matrix multiplication schemes by following random walks on a graph. We introduce a version of the flip graph algorithm for matrix multiplication schemes that admit certain symmetries. This significantly reduces the size of the search space, allowing for more efficient exploration of the flip graph. The symmetry in the resulting schemes also facilitates the process of lifting solutions from $F_2$ to $\mathbb{Z}$. Our results are new schemes for multiplying $5\times 5$ matrices using $93$ multiplications and $6\times 6$ matrices using $153$ multiplications over arbitrary ground fields.

cs.SC↗
arXiv2022

Flip Graphs for Matrix Multiplication

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.

cs.SC↗
arXiv2022

A Normal Form for Matrix Multiplication Schemes

Schemes for exact multiplication of small matrices have a large symmetry group. This group defines an equivalence relation on the set of multiplication schemes. There are algorithms to decide whether two schemes are equivalent. However, for a large number of schemes a pairwise equivalence check becomes cumbersome. In this paper we propose an algorithm to compute a normal form of matrix multiplication schemes. This allows us to decide pairwise equivalence of a larger number of schemes efficiently.

cs.CC↗
arXiv2020

Good pivots for small sparse matrices

For sparse matrices up to size $8 \times 8$, we determine optimal choices for pivot selection in Gaussian elimination. It turns out that they are slightly better than the pivots chosen by a popular pivot selection strategy, so there is some room for improvement. We then create a pivot selection strategy using machine learning and find that it indeed leads to a small improvement compared to the classical strategy.

cs.SC↗
arXiv2019

Chevalley Warning type results on abelian groups

We develop a notion of degree for functions between two abelian groups that allows us to generalize the Chevalley Warning Theorems from fields to noncommutative rings or abelian groups of prime power order.

math.GR↗