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News/The Banach-Butterfly Invariant: Influence-Adaptive Walsh Geometry for Ternary Polynomial Threshold Functions
arxiv
PublishedMay 5, 2026 at 4:00 AM

The Banach-Butterfly Invariant: Influence-Adaptive Walsh Geometry for Ternary Polynomial Threshold Functions

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arXiv:2605.01637v1 Announce Type: new Abstract: We introduce the Banach-Butterfly Invariant (BBT), an influence-adaptive Banach geometry on the Walsh-Hadamard butterfly factorization. For a Boolean function $f:\{-1,+1\}^n\to\{-1,+1\}$ with coordinate influences $\mathrm{Inf}_\ell(f)$, BBT assigns ex

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