← 研踪 PaperTrailarXiv:2610.39355 · v1
A Sharp Fisher-Information Inequality for Boolean Pairs: Proof of the Amari--Kobayashi Conjecture
首次提交 2026-10-29 12:48
版本更新 2026-10-29 12:48
雷达观测 2026-10-30 11:25
摘要
Consider two terminals that observe correlated uniform binary vectors and separately compress their observations to one bit. We prove that, for every blocklength and every correlation parameter in $(-1,1)$, the Fisher information retained by the resulting pair of bits is maximized by matching parity functions of an appropriate degree, thereby resolving a conjecture of Amari and Kobayashi. The proof combines a Fourier-based bound on the derivative of the normalized covariance with a scalar inequality for signed polynomials subject to a global range constraint.
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v1 · 2026-10-29 12:48 · 最新观测版本
A Sharp Fisher-Information Inequality for Boolean Pairs: Proof of the Amari--Kobayashi Conjecture
Consider two terminals that observe correlated uniform binary vectors and separately compress their observations to one bit. We prove that, for every blocklength and every correlation parameter in $(-1,1)$, the Fisher information retained by the resulting pair of bits is maximized by matching parity functions of an appropriate degree, thereby resolving a conjecture of Amari and Kobayashi. The proof combines a Fourier-based bound on the derivative of the normalized covariance with a scalar inequality for signed polynomials subject to a global range constraint.
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