{"id":"openai-math/Localization-costs-and-information-growth-for-exact-Gaussian-observations","pdf":"https://github.com/openai/math/blob/main/preprints/Localization-costs-and-information-growth-for-exact-Gaussian-observations-September-27-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Localization-costs-and-information-growth-for-exact-Gaussian-observations-September-27-2026","tags":["information-theory","high-dimensional-probability","gaussian-measurements"],"score":0,"title":"Localization costs and information growth for exact Gaussian observations","domain":"Theoretical computer science","family":"140","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"cs.CC","summary":"For the image of a uniform cube under a spherical coordinate map, we prove that finite messages from t blocks of $`\\Theta(d)`$ exact Gaussian measurements reveal only $`O_A(dt)`$ information when each message has at most $`\\exp(Ad^2)`$ values, for fixed A . The same bound holds when each message is supplemented with a nested cell that restores the required geometric spread.","category":"research","comments":0,"disputed":false,"division":"cs","mentions":0,"discussed":0,"published":"2026-09-27","reactions":{},"formalized":false,"family_title":"Memory–sample lower bounds for noiseless Gaussian regression"}