In visual domain adaptation, separating the domain-specific characteristics from the domain-invariant representations is an ill-posed problem. Existing methods apply different kinds of priors or direct domain discrepancy minimization to address this problem, which lack flexibility in handling real-world situations. Other research pipeline expresses the domain-specific information as a gradually transferring process, which tends to be suboptimal in accurately removing the domain-specific properties. In this paper, we address the modeling of domain-invariant and domain-specific information from the heuristic search perspective. We identify the characteristics in the existing representations that lead to larger domain discrepancy as the heuristic representations. With the guidance of heuristic representations, we formulate a principled framework of Heuristic Domain Adaptation (HDA), with well-founded theoretical guarantees. To satisfy HDA, the cosine similarity scores and independence measurements between domain-invariant and domain-specific representations result in the constraints at the initial and final states during the learning procedure. Similar to the final condition of heuristic search, we further derive a constraint enforcing the final range of heuristic network output to be small. Accordingly, we propose Heuristic Domain Adaptation Network (HDAN), to explicitly leverage heuristic representations. Extensive experiments show that HDAN has exceeded state-of-the-art on unsupervised DA, multi-source DA and semi-supervised DA.
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