TL;DR
A fully non-adaptive protocol whose query list is fixed before any bit is observed and whose sample complexity matches the adaptive one-bit minimax rate in every moment regime.
A randomized fully non-adaptive protocol is constructed that fixes all queries before observing the data and matches the optimal adaptive sample complexity, giving a negative answer to the COLT 2026 open problem asking whether interaction is necessary for order-optimal one-bit mean estimation.
It is shown that cells with low average distortion cover constant measure, that each such cell has exponentially small measure, and that Gaussian-profile isoperimetry forces total boundary Ω( p k ) .
This work identifies the minimum interval budget needed to retain the unrestricted 1-bit minimax sample rate and determines the minimax sample complexity among non-adaptive 1-bit estimators when every one-set $Q^{-1}(1)$ is restricted to a union of at most $s$ intervals.
A fully non-adaptive public-coin protocol that fixes every measurable 1-bit query before communication is constructed, and rates answer the Lau--Scarlett open problem for arbitrary measurable 1-bit queries in the affirmative.
Low-Pathwidth GRAND (LP-GRAND) is developed for binary phase-shift keying (BPSK) with precision matrix $Q, and induces an ML codeword for any nonempty binary codebook with equiprobable codewords.
A one-shot (finite-blocklength) channel-coding framework based on the pairwise error probability (PEP) of a decoder with randomized tie-breaking that recovers several classical one-shot bounds, including the random-coding union bound and minimax meta-converse of Polyanskiy-Poor-Verdu, the information-spectrum bounds of...
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