Homogeneous depth-five lower bounds for iterated matrix multiplication with unrestricted bottom fan-in (Bera-Chakrabarti question, balanced regime)

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Bera and Chakrabarti, A Depth-Five Lower Bound for Iterated Matrix Multiplication (CCC 2015) evidence for this event

Claims that over every field of characteristic zero every syntactically homogeneous $\Sigma\Pi\Sigma\Pi\Sigma$ circuit computing $\mathrm{IMM}_{n,n}$ has at least $n^{\sqrt n/400}$ gates for large $n$, with gate sharing, arbitrary fan-in and bottom linear forms of arbitrary support allowed, and a block construction gives $n^{\sqrt n+4}$ over every field, so the gate complexity is $n^{\Theta(\sqrt n)}$. The measure is the rank of a partial-derivative-times-multiplication operator. It does NOT treat the Bera-Chakrabarti regime $\mathrm{IMM}_{n^q,n}$ directly, positive characteristic, non-homogeneous circuits, or depths beyond five. parent of this event

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Homogeneous depth-five lower bounds for iterated matrix multiplication with unrestricted bottom fan-in (Bera-Chakrabarti question, balanced regime) parent of this event

Homogeneous depth-five lower bounds for iterated matrix multiplication with unrestricted bottom fan-in (Bera-Chakrabarti question, balanced regime) evidence for this event

VibeMathed record: Homogeneous depth-five lower bounds for iterated matrix multiplication with unrestricted bottom fan-in (Bera-Chakrabarti question, balanced regime) evidence for this event

Lean formalization: depth-five lower and upper bounds for IMM evidence for this event

Lean comparator statement: DepthFive evidence for this event