Why it is a question
THEORY-270 now states the upper bound of LIT-941’s common-nonsense model: maximum likelihood with a plausibility prior and no parallel data has error O(log|Θ| / (α·min(m, |T|))) when source and prior are uniform over sets from which shared random nonsense is removed and the translators are one-to-one. The bound is proved, and was re-derived. The models are uniform and random by design and, in the paper’s words, “not intended to accurately capture natural language”. Whether the exchange between common ground, source size and samples survives outside them is open.
What would answer it
A proof of the same kind of bound for non-uniform (for instance Zipfian) source languages, or for lossy translators, with an error that still falls in the common ground and the size of the source language and a lower bound to match, would answer it yes. So would an experiment on real corpora in which the error of prior-scored translation without parallel data falls with measured common ground at the predicted rate. A non-uniform model in which richer source languages do not reduce the common ground needed would answer it no. Further synthetic runs in the paper’s two models cannot settle it: they only confirm the proofs.