Attribution Ambiguity Can Make Target Bayes Rules Non-Identifiable in EEG Transfer

Reliable unsupervised domain adaptation (UDA) for electroencephalography (EEG) decoding depends on information constraining how source and target domains may differ. We ask how far such knowledge can take us: if the laws governing how latent neural components transform across domains were fully specified, would that be enough to determine the optimal target classifier? We examine this question in an idealized Oracle setting in which the full source distribution of observations and labels, the target observation marginal, and the corresponding component-specific operators are known exactly, while other common sources of uncertainty are removed. Yet a simple Gaussian construction yields a negative answer. We trace this failure to attribution ambiguity: scalp EEG observations reflect aggregate neural activity but not how predictive activity is partitioned across component types. Although each type's cross-domain operator is known, allocations indistinguishable in the source domain can remain consistent with different target observation–label relationships that require conflicting optimal decisions. To characterize the resulting learning barrier, we derive an information-theoretic lower bound showing that it cannot be overcome by algorithmic choice alone. With additional structure, a complementary upper bound shows that the target decision can be learned without full latent-attribution recovery. Finally, EEG simulations instantiate the theoretical mechanism, while real-EEG experiments provide complementary evidence for its learner-side predictive implications.