Over every characteristic-zero field, for all sufficiently large n every syntactically homogeneous depth-five ΣΠΣΠΣ circuit computing the (1,1) entry of n independent n×n matrix products has at least n^(√n/400) gates.
Over every characteristic-zero field, for all sufficiently large n every syntactically homogeneous depth-five ΣΠΣΠΣ circuit computing the (1,1) entry of n independent n×n matrix products has at least n^(√n/400) gates.
Over every characteristic-zero field, for all sufficiently large n every syntactically homogeneous depth-five ΣΠΣΠΣ circuit computing the (1,1) entry of n independent n×n matrix products has at least n^(√n/400) gates.
If correct, establishes a superpolynomial lower bound for a natural polynomial at homogeneous depth five.
Does iterated matrix multiplication require superpolynomial homogeneous depth-five circuit size?
Publication dates and editorial changes.
OpenAI reports a depth-five lower bound for iterated matrix multiplication
Allow optional Google Analytics to help improve AIProofWatch? Privacy details.
