Abduction-Deduction Entanglement: Domain Generalization via Representation Transplants

2026-05-24

AI Summary

This work addresses the challenge of poor generalization from a source domain to unseen target domains by proposing a causal mechanism–based abductive–deductive decomposition framework. It decomposes optimal prediction into an abductive mapping that infers latent variables from observations and a deductive mapping that combines these latents with observations for prediction. The method constrains the set of feasible mapping pairs using source-domain data and searches for effective predictors in the target domain via representation transplantation—adjusting only the abductive component in the representation space while keeping the deductive component fixed. Theoretically, the approach converges to a minimax optimal predictor under ideal optimization. Empirically, it achieves competitive performance on domain generalization benchmarks. The key innovation lies in introducing the notion of abductive–deductive entanglement and the representation transplantation mechanism, which together reveal the partial identifiability of source-domain information for target-domain prediction.

Abstract

Prediction models trained under the source distribution do not generalize well to a different target distribution. A valid inference about an unseen data distribution must be anchored by the invariance of certain causal mechanisms that generate the source and target data, however, these structural invariances are non-identifiable from the source data alone. Under mild causal assumptions about the data, we show that the optimal prediction in the target is in fact partially identifiable by the source distribution. The result rests on a simple observation: In any domain, the optimal prediction can be factorized into what we call a pair of abduction and deduction maps, where the abduction map makes inference about some unobserved variables (possibly confounders) from the observed variables and the deduction map predicts the label using both the observed and inferred quantities. Access to large source data pins down the optimal prediction, thus constrains the valid abduction-deduction ensembles that produce it -- a non-identifiability that we call the abduction-deduction entanglement. To leverage this, we parameterize the constrained family using what we call a representation transplant, that is a specific linear transformation in the representation space that manipulates the abduction content of the representation while retaining the deduction component. Invariance of the causal mechanism generating the label implies existence of an invariant deduction map between source and target. Thus, we can search the space of plausible target distributions via a parametric transplant. We use this scheme in a learner-adversary game that, under an idealistic optimization, provably terminates with the learner having the minimax-optimal target prediction. Evaluations verify the theory, showing that the method is competitive in DG benchmarks.

Problem

• domain generalization
• causal invariance
• distribution shift
• abduction-deduction entanglement
• representation learning

Innovation

• abduction-deduction entanglement
• representation transplant
• domain generalization
• causal invariance
• minimax optimization