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A Sharp Fisher-Information Inequality for Boolean Pairs: Proof of the Amari--Kobayashi Conjecture — arXiv:2610.39355

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.39355
License (as archived): CC0-1.0
Archived: 2026-11-01T02:39:43.049Z
SHA-256 of the archived text: 0e503422c26edf00b67b1afd7b0c5b00fe688a5df0f9acb1d595590211a57f52
Stable URL of this page: https://metraipolis.com/documento/dc_bfa498ff3d71

How to cite

A Sharp Fisher-Information Inequality for Boolean Pairs: Proof of the Amari--Kobayashi Conjecture — arXiv:2610.39355 — arXiv (en), https://arxiv.org/abs/2610.39355 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_bfa498ff3d71 (Metraipolis archive dc_bfa498ff3d71, sha256 0e503422c26edf00b67b1afd7b0c5b00fe688a5df0f9acb1d595590211a57f52)

BibTeX

@misc{dcbfa498ff3d71,
  title = {A Sharp Fisher-Information Inequality for Boolean Pairs: Proof of the Amari--Kobayashi Conjecture — arXiv:2610.39355},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.39355},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_bfa498ff3d71; sha256 0e503422c26edf00b67b1afd7b0c5b00fe688a5df0f9acb1d595590211a57f52},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.39355. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.IT, nuovi lavori del giorno).
Categorie arXiv: Information Theory (cs.IT).
Pagina del lavoro: https://arxiv.org/abs/2610.39355 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-01T02:15:43.727Z dalla pagina https://arxiv.org/list/math.IT/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).