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arXiv · 2609.28839

Exponential Correlation Bounds for Polynomials

Eshan Chattopadhyay·Pooya Hatami·Chin Ho Lee·Shachar Lovett·Avishay Tal·Emanuele Viola
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Abstract

We prove that the XOR of $k$ majorities on disjoint blocks of \(\ell\) bits has correlation at most \((2d/\sqrt{\ell})^k\) with every degree-\(d\) polynomial over \(\mathbb F_2\). By known techniques, this implies pseudorandom generators with polylogarithmic seed length for low-degree polynomials over $\mathbb F_2$ and for alternating circuits with parity gates.

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Eshan Chattopadhyay, Pooya Hatami, Chin Ho Lee, Shachar Lovett, Avishay Tal, Emanuele Viola. 2026-09-23. Exponential Correlation Bounds for Polynomials. https://arxiv.org/abs/2609.28839

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