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!

---

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

---

Follow LaurieWired on Social Media:
►https://linktr.ee/lauriewired

---

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

Laurie Wired's resource offers insights, tutorials, and resources for technology enthusiasts, DIYers, and makers. Readers can learn about electronics projects, hardware hacking, and DIY gadgets. With articles, tutorials, and project guides, Laurie Wired provides resources for learning and experimenting with technology.

LaurieWired

Matrix multiplication optimization has evolved from the naive O(n³) approach to more efficient algorithms like Strassen's method, which reduces complexity to O(n^2.807). New research from Austria's Institute for Algebra introduces novel optimization techniques using flip graph search algorithms to find minimal multiplication operations for specific matrix dimensions. These optimizations are crucial for applications in machine learning, graphics, and high-frequency trading, though their effectiveness depends on factors like matrix size, hardware architecture, and whether computation or memory bandwidth is the limiting factor.

making computers multiply FASTER! (matrix hacking)