Title: Transferability of Compositionality. Abstract: Compositional generalization is the algebraic capacity to understand and produce large amount of novel combinations from known components. It is a key element of human intelligence for out-of-distribution generalization. To equip neural networks with such ability, many algorithms have been proposed to extract compositional representations from the training distribution. However, it has not been discussed whether the trained model can still extract such representations in the test distribution. In this paper, we argue that the extraction ability does not transfer naturally, because the extraction network suffers from the divergence of distributions. To address this problem, we propose to use an auxiliary reconstruction network with regularized hidden representations as input, and optimize the representations during inference. The proposed approach significantly improves accuracy, showing more than a 20% absolute increase in various experiments compared with baselines. To our best knowledge, this is the first work to focus on the transferability of compositionality, and it is orthogonal to existing efforts of learning compositional representations in training distribution. We hope this work will help to advance compositional generalization and artificial intelligence research.