Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 140-02. Posterior replicas and conditional information in Gaussian regression
Manuscript map · lines 5105–5114
OpenAI@2026-10-07#rem:oai-p-140-02
Authors: OpenAI. Family 140.
Title: Posterior replicas and conditional information in Gaussian regression.
Abstract: For a signal with density bounded by L relative to uniform probability on $S{}{d-1}$, we bound the information in a finite message W formed from exact Gaussian measurements, conditional on an independent projection revealed only to the analyst. For explicit row counts proportional to d, the bound is $O(H(W)/d+d+{}log(2+{}log L))$. Consequently, a finite-state learner with $o(d{}2)$ persistent bits and a deterministic sample horizon needs ${}Omega(d{}log(1/{}epsilon))$ fresh noiseless Gaussian measurements for constant-probability angular accuracy $0{}lt {}epsilon{}le1/10$ under the uniform spherical prior.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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