Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 140-01. Memory and precision in noiseless Gaussian regression
Manuscript map · lines 5095–5104
OpenAI@2026-10-07#rem:oai-p-140-01
Authors: OpenAI. Family 140.
Title: Memory and precision in noiseless Gaussian regression.
Abstract: For every fixed A > 0, a learner that retains at most $Ad{}2$ bits between fresh exact Gaussian linear measurements needs ${}Omega_A(d{}log(1/{}epsilon))$ measurements to estimate a uniformly random unit vector to angular error at most ϵ, for any $0{}lt {}epsilon{}le 1/10$, with probability at least 2/3. The constant is absolute for $o(d{}2)$ memory.
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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