Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 140-06. Subsphere methods for memory-sample lower bounds in noiseless Gaussian regression
Manuscript map · lines 5145–5154
OpenAI@2026-10-07#rem:oai-p-140-06
Authors: OpenAI. Family 140.
Title: Subsphere methods for memory-sample lower bounds in noiseless Gaussian regression.
Abstract: Let a finite-state streaming learner estimate a uniformly random unit vector from independent exact Gaussian linear measurements. We prove that $o(d{}2)$ bits of persistent memory and angular success probability at least 2/3 require at least $2{}{-16}d{}log_2(1/{}epsilon)$ samples for all sufficiently large d, uniformly for $0{}lt {}epsilon{}le1/10$. The proof conditions each batch on its observed projection and controls the resulting random residual subsphere.
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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