Interaction Is Not Necessary for Order-Optimal 1-Bit Mean Estimation

What the math gives to ML

The paper constructs a randomized, fully non-adaptive one-bit measurement scheme that estimates a mean without first localizing it and then adapting later queries. The transferable asset is a multiscale public-randomness protocol: fixed binary measurements at geometrically separated resolutions can cover a large dynamic range, while finite-moment assumptions control clipping and tail bias. This is relevant to federated or distributed neural training, where clients communicate gradient information under severe bit budgets and cannot afford interactive threshold refinement. The most direct experiment is to replace floating-point gradient communication with a fixed multiscale threshold sketch and measure optimization quality at equal communication cost.