Exploring the Meta Flip Graph for Matrix Multiplication
Manuel Kauers, Isaac Wood
TL;DR
This paper investigates the meta flip graph structure to improve tensor rank bounds for matrix multiplication across various formats, advancing theoretical understanding in computational complexity.
Contribution
It introduces improved tensor rank bounds for approximately thirty matrix formats using flip graph analysis, building on recent tensor rank bounding methods.
Findings
Enhanced tensor rank bounds for multiple matrix formats
Advances in understanding the structure of flip graphs
Improved theoretical limits for matrix multiplication complexity
Abstract
Continuing recent investigations of bounding the tensor rank of matrix multiplication using flip graphs, we present here improved rank bounds for about thirty matrix formats.
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Taxonomy
TopicsTensor decomposition and applications · Complexity and Algorithms in Graphs · Sparse and Compressive Sensing Techniques