Why it is a question
THEORY-614 (Xie et al., LIT-797) states Theorem 1 for a mixture of hidden Markov models under exact fit. A prompt of concatenated examples moves the posterior onto the prompt’s concept, and the in-context predictor becomes Bayes-optimal as examples accumulate, provided each example’s evidence outweighs the cost of the transitions between examples. Its title ends: “whether trained networks learn in context this way is not shown”. Its promotion condition asked for evidence about trained networks. That is the disclaimed clause, not the title’s claim, so on 2026-10-19 the promotion audit (batch 026) moved it here and pointed THEORY-614’s condition at the proof of Theorem 1.
The question is open because the analysis is of the distribution, not of a network. The only experiments, on GINC, use data built to satisfy the assumptions (NOTE-633).
What would answer it
The condition formerly on THEORY-614, unchanged. Evidence about a trained language model, not about the data distribution. Either a demonstration that its in-context predictions track the posterior predictive of an explicit latent-concept mixture fitted to its pretraining data, across prompt lengths and example lengths, including the order and zero-shot effects the account predicts from mismatch. Or a measured posterior over concepts, read from the network, that concentrates as the theorems say. Further results on synthetic data built to satisfy the assumptions, such as GINC, cannot settle it, and neither can a gain of under one point on a natural benchmark.