Noiseless Gaussian regression estimates a fixed vector 
from independent standard Gaussian feature vectors 
and exact labels 
. For a unit signal and a unit estimate, angular
accuracy 
means 
.
If all raw observations can be retained, 
rows in dimension 
determine 
almost surely.
In a finite-state streaming model, at most 
states are retained between observations. The learner reads
each pair once, cannot choose or revisit rows, and may perform unrestricted computation
on the current pair using fresh randomness. Its rules may use a data-independent
shared random seed, and the complete experiment must be jointly measurable. It stops
by a prescribed deterministic horizon 
; its output uses only its terminal state, stopping index,
and fresh randomness. Thus memory is measured in bits, and even the last pair can
affect the output only through that state.
