Replacing Gaussian observations in memory-constrained inference
Replacing the Gaussian rows used to select a finite message by independent rows increases the remaining conditional information by at most $Cd$, for a uniform spherical signal, message entropy at most d 2 , and the specified row dimensions proportional to d . As an application, we prove that learners with $M=o(d^2)$ persistent bits need $T=\Omega(d\log(1/\epsilon))$ exact observations to attain uniform-sphere angular success at least 3/5, for $0\lt \epsilon\le1/10$ and a deterministic finite horizon.
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