Lower Bounds for Depth-4 Formulas Computing Iterated Matrix Multiplication

SIAM: SIAM Journal on Computing, Volume 44, Issue 5, 2015.

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Abstract:

We study the arithmetic complexity of iterated matrix multiplication. We show that any multilinear homogeneous depth-4 arithmetic formula computing the product of $d$ generic matrices of size $n times n$, $mathrm{IMM}_{n,d}$, has size $n^{Omega(sqrt{d})}$ as long as $d = n^{O(1)}$. This improves the result of Nisan and Wigderson [Comput. ...More

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