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We study coded distributed matrix multiplication from an approximate recoveryviewpoint. We consider a system of $P$ computation nodes where each node stores$1/m$ of each multiplicand via linear encoding. Our main result shows that thematrix product can be recovered with $\epsilon$ relative error from any $m$ ofthe $P$ nodes for any $\epsilon > 0$. We obtain this result through a carefulspecialization of MatDot codes -- a class of matrix multiplication codespreviously developed in the context of exact recovery ($\epsilon=0$). Sinceprior results showed that MatDot codes achieve the best exact recoverythreshold for a class of linear coding schemes, our result shows that allowingfor mild approximations leads to a system that is nearly twice as efficient asexact reconstruction. As an additional contribution, we develop an optimizationframework based on alternating minimization that enables the discovery of newcodes for approximate matrix multiplication.

$\epsilon$-Approximate Coded Matrix Multiplication is Nearly Twice as Efficient as Exact Multiplication