Why it is a question
THEORY-293 now states two things separately: an optimal learner whose capacity is bounded learns none of a set of equally frequent facts below a threshold set by the mixing ratio, and all of them once capacity exceeds it by the facts’ total entropy; and Pythia models trained on synthetic biographies mixed into web text show a threshold in model size and in mixing ratio. That the second is an instance of the first is asserted by Gu et al. (LIT-984) and supported only by the shape of the curves and one exponent, 1.152 against a predicted 1.283, with no interval (NOTE-796). Below the threshold, much longer training barely helps. That fits an allocation that never reaches the facts, and also a dynamical wall the static theory does not see.
What would answer it
Thresholds predicted in advance from the measured loss-versus-size curve of the second domain and the facts’ total entropy, matched by networks trained to convergence over several seeds and several mixing ratios, with recall rising over a width of about the facts’ entropy past the threshold, would answer it yes. Thresholds departing systematically from (1/(r·p))^(1/(α+1)), or networks below the threshold that learn the facts given enough further training, would answer it no. More sigmoid-shaped curves in r or in size do not settle it: they show a threshold, not that capacity allocation sets it.