AI & ML
On the most informative Boolean function under noise
arXiv math.IT0 views
arXiv:2611.05430v1 Announce Type: new Abstract: Let $X$ be a uniform random bit string and $Y$ be obtained by flipping each bit of $X$ independently with probability $p$. Let $C$ be a random bit obtained as a function of $Y$. We show that $\mathbf{I}(C:X)\le \mathbf{I}(Y_1:X)$ for all $p\in[0,1]$, which resolves a conjecture posed by Courtade and Kumar in 2013.
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