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Results tagged with algebraic-complexity
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user 23100
3
votes
What is the best known bound for the bilinear complexity of $4\times 4$ matrices product
In the paper you mention, Bläser improves the lower bound to 34.
To my knowledge, there was no progress on this specific problem.
The recent Nature paper which used machine learning to solve the usual …
- 561
5
votes
How far is the slice rank of a tensor from its CP rank
No.
For $n \times n \times n$ tensors slice rank does not exceed $n$, while tensor rank can be as large as $\frac{n^3}{3n - 2} \sim \frac{n^2}{3}$ by dimension count.
- 561
9
votes
What is expected (border) rank of the knonecker product of 3-tensors
We don't know.
There are formats in which the equality is false for generic tensors: take $F^{n \times n \times 1}$ and $F^{n \times n \times n^2}$. Generic tensors in both formats are isomorphic to m …
- 561