Adapting, Fast and Slow: On Few-Shot Transportability of Compositions

Rules learned from source sequences can be composed to learn new computations from few target samples. We study the conditions and sample requirements for this form of compositional generalization in finite sequential causal models without unobserved confounding. Causal structure and knowledge of shared mechanisms identify local conditional distributions that can be reused across domains. We give a sufficient condition under which their estimates, called gates, can be composed by Circuit-TR to estimate the target concept—the output conditional given the inputs—without target samples. When the target composition and its source correspondences are unknown, we prove that Circuit-AD competes with this oracle by minimizing empirical log loss with a circuit-size penalty. The excess-risk bound separates source estimation error from composition selection; the selection cost decreases with target sample size and adapts to the comparator's size without requiring it in advance. Different compositions can compute the same noiseless function yet incur different risks when their gates are noisy. Neural-AD learns compositions of frozen source gates, allowing us to examine these distinctions experimentally. The results show how the available source operations affect adaptation and how process supervision reduces the samples needed to learn a composition.