Why it is a question
THEORY-238 states Theorem 4 of LIT-245: the expected generalization error of an encoder–decoder learner is at most 2√((2B + K + 2)/n) + ε, where B is the KL divergence of the encoder’s train-and-ghost latents to a prior symmetric under label-preserving permutations. The theorem holds for any decoder, and its constants were re-checked in the audit. Nobody has computed it. The paper lists evaluating it “analytically in simple setups” as future work. The prior it allows may depend on the ghost set, which a learner never sees, and the experiment approximates it by moving averages that are only approximately symmetric. A floor of 2√((K+2)/n) remains however compressible the latents are.
So whether this quantity accounts for generalization in practice, rather than only in principle, is open.
What would answer it
A numerical evaluation of the bound for a trained encoder, with a prior built without the ghost data and checked to be type-III symmetric, showing whether the bound is below 1 for 0–1 loss, and how close it is to the measured gap. A bound that is vacuous at realistic n and K would answer it no for that setting. Test accuracies of regularizers built from the bound, such as CDVIB, cannot settle it: a better regularizer does not show that the bound is tight.