On Multilinear Forms: Bias, Correlation, and Tensor Rank

Electronic Colloquium on Computational Complexity (ECCC), Volume 25, 2018, Pages 81

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Abstract:

In this paper, we prove new relations between the bias of multilinear forms, the correlation between multilinear forms and lower degree polynomials, and the rank of tensors over $GF(2)= {0,1}$. We show the following results for multilinear forms and tensors. 1. Correlation bounds : We show that a random $d$-linear form has exponentially l...More

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