Ankit Gupta, Neeraj Kayal, Satyanarayana V. Lokam

We present a randomized algorithm for reconstructing multilinear depth-4 arithmetic circuits with fan-in 2 at the top + gate. The algorithm is given blackbox access to a multilinear polynomial f in F[x_1,..,x_n] computable by a multilinear Sum-Product-Sum-Product(SPSP) circuit of size s and outputs an equivalent multilinear SPSP circuit, runs ... more >>>

Mrinal Kumar, Rafael Mendes de Oliveira, Ramprasad Saptharishi

We show that any $n$-variate polynomial computable by a syntactically multilinear circuit of size $\mathop{poly}(n)$ can be computed by a depth-$4$ syntactically multilinear ($\Sigma\Pi\Sigma\Pi$) circuit of size at most $\exp\left({O\left(\sqrt{n\log n}\right)}\right)$. For degree $d = \omega(n/\log n)$, this improves upon the upper bound of $\exp\left({O(\sqrt{d}\log n)}\right)$ obtained by Tavenas (MFCS ... more >>>