  In visual domain adaptation (DA), separating the domain-specific
characteristics from the domain-invariant representations is an ill-posed
problem. Existing methods apply different kinds of priors or directly minimize
the domain discrepancy to address this problem, which lack flexibility in
handling real-world situations. Another research pipeline expresses the
domain-specific information as a gradual 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 perform HDA, the
cosine similarity scores and independence measurements between domain-invariant
and domain-specific representations are cast into 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), which explicitly learns the
domain-invariant and domain-specific representations with the above mentioned
constraints. Extensive experiments show that HDAN has exceeded state-of-the-art
on unsupervised DA, multi-source DA and semi-supervised DA. The code is
available at https://github.com/cuishuhao/HDA.
