making computers multiply FASTER! (matrix hacking)

Matrix Multiplication is critical to everything from AI training to computer graphics. With clever mathematical hacks, it's possible to outperform traditional methods by a significant margin!

In this video we go over some of the latest research in matrix algorithm development, specifically the improvements to Strassen found by Johannes Kepler University in May 2025.

I also write some code to convert the tensors into an easily runnable form, so you can try it out on your own CPU!

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Papers Cited:

Consequences of the Moosbauer-Poole Algorithms:
https://arxiv.org/pdf/2505.05896

Strassens Matrix Multiplication on GPUs:
https://www.cise.ufl.edu/~sahni/papers/strassen.pdf

Flip Graphs with Symmetry and New Matrix Multiplication Schemes:
https://arxiv.org/pdf/2502.04514

AlphaEvolve:
https://storage.googleapis.com/deepmind-media/DeepMind.com/Blog/alphaevolve-a-gemini-powered-coding-agent-for-designing-advanced-algorithms/AlphaEvolve.pdf

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Timestamps
00:00 Intro
01:23 Naive Method
03:03 Strassen
05:28 Benchmarking Time Complexity
07:53 Johannes Kepler Research
10:30 New Method in Action
14:53 Rank Improvements
16:19 Limitations and Caching