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Title: The Role of Embedding Complexity in Domain-invariant Representations

Paper content:
Unsupervised domain adaptation aims to generalize the hypothesis trained in a source domain to an unlabeled target domain.
One popular approach to this problem is to learn a domain-invariant representation for both domains.
In this work, we study, theoretically and empirically, the explicit effect of the embedding on generalization to the target domain.
In particular, the complexity of the class of embeddings affects an upper bound on the target domain's risk.
This is reflected in our experiments, too.
Domain adaptation is critical in many applications where collecting large-scale supervised data is prohibitively expensive or intractable, or conditions at prediction time can change.
For instance, self-driving cars must be robust to various conditions such as different weather, change of landscape and traffic.
In such cases, the model learned from limited source data should ideally generalize to different target domains.
Specifically, unsupervised domain adaptation aims to transfer knowledge learned from a labeled source domain to similar but completely unlabeled target domains.One popular approach to unsupervised domain adaptation is to learn domain-invariant representations BID7 BID5 , by minimizing a divergence between the representations of source and target domains.
The prediction function is learned on the latent space, with the aim of making it domain-independent.
A series of theoretical works justifies this idea BID9 BID1 BID3 .Despite
the empirical success of domain-invariant representations, exactly matching the representations of source and target distribution can sometimes fail to achieve domain adaptation. For example
, BID13 show that exact matching may increase target error if label distributions are different between source and target domain, and propose a new divergence metric to overcome this limitation. BID14 establish
lower and upper bounds on the risk when label distributions between source and target domains differ. BID6 point out
the information lost in non-invertible embeddings, and propose different generalization bounds based on the overlap of the supports of source and target distribution.In contrast to previous analyses that focus on changes in the label distributions or on joint support, we here study the effect of the complexity of the joint representation. In particular,
we show a general bound on the target risk that reflects a tradeoff between the embedding complexity and the divergence of source and target in the latent representation space. In particular,
a too powerful class of embedding functions can result in overfitting the source data and the distribution matching, leading to arbitrarily high target risk. Hence, a restriction
(taking into account assumptions about correspondences and invariances) is needed. Our experiments reflect
these trends empirically, too.
The experiments show that the complexity of the encoder can have a direct effect on the target error.
A more complex encoder class leads to larger theoretical bound on the target error, and, indeed, aligned with the theory, we see a significant performance drop in target domain.
Moreover, the experiments suggest that inductive bias is important too.
With a suitable inductive bias such as CNNs, DANN achieves higher performance than the with the MLP encoder, even if the CNN encoder has twice the number of layers.
CNNs are standard for many vision tasks, such as digit recognition.
However, explicit supervision may be required to identify the encoder class when we have less prior knowledge about the task BID10 BID2 .
In this work, we study the role of embedding complexity for domain-invariant representations.
We theoretically and empirically show that restricting the encoder is necessary for successful adaptation, a fact that has mostly been overlooked by previous work.
In fact, without carefully selecting the encoder class, learning domain invariant representations might even harm the performance.
Our observations motivate future research on identifying eappropriate encoder classes for various tasks.

assistant: text: A general upper bound on the target domain's risk that reflects the role of embedding-complexity.