{"id":"openai-math/Memory-and-precision-in-noiseless-Gaussian-regression","pdf":"https://github.com/openai/math/blob/main/preprints/Memory-and-precision-in-noiseless-Gaussian-regression-September-27-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Memory-and-precision-in-noiseless-Gaussian-regression-September-27-2026","tags":["learning-theory","memory-constraints","gaussian-regression","sample-complexity"],"score":0,"title":"Memory and precision in noiseless Gaussian regression","domain":"Theoretical computer science","family":"140","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"cs.CC","summary":"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.","category":"research","comments":0,"disputed":false,"division":"cs","mentions":0,"discussed":0,"published":"2026-09-27","reactions":{},"formalized":true,"family_title":"Memory–sample lower bounds for noiseless Gaussian regression"}