For every fixed A>0 and sufficiently large dimension d, a one-pass learner retaining at most Ad² bits between independent exact Gaussian linear measurements needs at least c_A d log(1/ε) measurements to estimate a uniformly random unit vector to angular error ε≤1/10 with success probability at least 2/3.
For every fixed A>0 and sufficiently large dimension d, a one-pass learner retaining at most Ad² bits between independent exact Gaussian linear measurements needs at least c_A d log(1/ε) measurements to estimate a uniformly random unit vector to angular error ε≤1/10 with success probability at least 2/3.
For every fixed A>0 and sufficiently large dimension d, a one-pass learner retaining at most Ad² bits between independent exact Gaussian linear measurements needs at least c_A d log(1/ε) measurements to estimate a uniformly random unit vector to angular error ε≤1/10 with success probability at least 2/3.
If correct, establishes a precision-driven sample lower bound even though every observation is noiseless.
How many noiseless Gaussian measurements are needed when a learner remembers at most O(d²) bits?
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OpenAI reports a memory–sample lower bound for noiseless Gaussian regression
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