Theoretical computer science · Oct 6, 2026

Homogeneous depth-five lower bounds for iterated matrix multiplication

Over every characteristic-zero field, the (1,1)(1,1) entry of a product of n independent n×nn\times n variable matrices requires nΘ(n)n^{\Theta(\sqrt n)} gates in homogeneous depth-five sum–product circuits. This sharp bound allows shared gates and bottom linear forms involving all variables.

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