Matrix Multiplication: Coppersmith-Winograd and Beyond

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" summary

Describes a concrete route from tensors to matrix multiplication exponent: use border rank q+2 bounds on a specific Coppersmith‑Winograd family, symmetrize and take tensor powers, then apply blocking and zeroing‑out combinatorics to extract many small matrix‑products and lower‑bound a value function via multinomial counts and Stirling approximations. That pipeline produces numerical exponents (CW square gives 2.376, higher powers inch down toward the current ~2.373) and also exposes a provable barrier: the standard merging/zeroing framework cannot push omega to 2 without new tensors or restrictions.

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" chapters (17)

1. 0:00Intro
2. 0:49Tensors and matrix multiplication
3. 5:52Border Rank
4. 8:34Restrictions of tensors
5. 10:48Zeroing out - a special restriction
6. 14:39Value of a tensor
7. 23:20The CW tensor
8. 25:38Blocking of a tensor
9. 31:16Zeroing out blocks
10. 33:18Fractions for block triples
11. 38:36When the linear system doesn't have full rank
12. 41:36Example
13. 45:07Blockings and tensor powers
14. 49:24Computational issues
15. 50:05Summary
16. 51:00Questions?
17. 51:35Limitations