Re: maths - with an S
"Moreover either matrix multiplication has been improved or it hasn't."
It's not quite as straightforward as that, at least for multiplication of non-square matrices, where the scaling of computational complexity depends also on the shape of the matrices in questions, so comparison becomes difficult. Furthermore, the practical scaling of efficiency of an algorithm, even for square matrix multiplication, depends on the hardware on which it's run (e.g., CPU, GPU, FPGA, etc.), and how the algorithm is implemented on the hardware (e.g., to exploit parallelism, cache sizes, memory access, and so on).
I had a skim through the paper, and it's actually pretty impressive (albeit, as they say, a work-in-progress). They achieve real reductions of multiplication operations on small matrices—which become building-blocks for large matrix multiplications—against state-of-the-art known algorithms. Perhaps more importantly, they are also able to optimise algorithms for specific hardware.
Biting the hand that feeds IT
