probability-statistics / Boolean functions; information theory
The Courtade-Kumar conjecture (2014) posits that dictatorship functions maximize mutual information between a Boolean function's output and a noisy input. The paper resolves an open question posed by Courtade and Kumar themselves - a sharp bound of $1-H(\alpha)$ on the sum of coordinate-wise mutual informations for arbitrary bias - and extends the proven high-noise range of the main conjecture via optimal entropy bounds.
Temporal state
No reconciled state yet.
Append-only history
Fully resolves the posed coordinate-wise question; the main Courtade-Kumar conjecture itself remains open outside the extended high-noise range.
Research memory
The Courtade-Kumar conjecture (2014) posits that dictatorship functions maximize mutual information between a Boolean function's output and a noisy input. The paper resolves an open question posed by Courtade and Kumar themselves - a sharp bound of $1-H(\alpha)$ on the sum of coordinate-wise mutual informations for arbitrary bias - and extends the proven high-noise range of the main conjecture via optimal entropy bounds.
Fully resolves the posed coordinate-wise question; the main Courtade-Kumar conjecture itself remains open outside the extended high-noise range.
Evidence graph
No public relationships recorded yet.