On Multilinear Forms: Bias, Correlation, and Tensor Rank

  title={On Multilinear Forms: Bias, Correlation, and Tensor Rank},
  author={Abhishek Bhrushundi and Prahladh Harsha and Pooya Hatami and Swastik Kopparty and Mrinal Kumar},
  booktitle={Electron. Colloquium Comput. Complex.},
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 low correlation with low-degree polynomials. More precisely, for $d \ll 2^{o(k)}$, we show that a random $d$-linear form $f(X_1,X_2, \dots, X_d) : \left(GF(2… 
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