Abduction-Deduction Entanglement: Domain Adaptation via Representation Transplants

In domain adaptation, unobserved confounding can make prediction rules change across populations even when the response mechanism remains invariant. We show how source data can nevertheless constrain target prediction without identifying the underlying mechanisms. In each domain, the optimal prediction factorizes into abduction, which infers a distribution over unobserved variables from the input, and deduction, which predicts the response given both. Although these maps may not be identifiable, they must jointly reproduce the source predictions. When deduction is shared across domains, this abduction–deduction entanglement allows the sources to restrict the optimal target prediction rule. We assume that objects of abduction are linearly expressed given a pretrained representation, and under further support assumptions, we implicitly parametrize the source and target causal models, and enforce constraints on them via representation transplants – a linear transformation over the representation space that swaps the abduction component between the domains while preserving the deduction content of the representation. Unlabeled target data adds additional restrictions by informing the support of the target representations. We use this parametrization in Causal Robust Optimization (CRO), where a learner minimizes worst-case loss on transplanted data from different sources against an adversary searching the space of valid abduction–deduction maps. Experiments show improvement over Colored-MNIST, attaining 60% accuracy on the hard target domain where association between color and digits is reversed. We also evaluate the method in tasks involving language representations, and a real-world Vision benchmark.