Domain-invariant Learning using Adaptive Filter Decomposition

Domain shifts are frequently encountered in real-world scenarios. In this paper, we consider the problem of domain-invariant deep learning by explicitly modeling domain shifts with only a small amount of domain-specific parameters in a Convolutional Neural Network (CNN). By exploiting the observation that a convolutional filter can be well approximated as a linear combination of a small set of basis elements, we show for the first time, both empirically and theoretically, that domain shifts can be effectively handled by decomposing a regular convolutional layer into a domain-specific basis layer and a domain-shared basis coefficient layer, while both remain convolutional. An input channel will now first convolve spatially only with each respective domain-specific basis to "absorb" domain variations, and then output channels are linearly combined using common basis coefficients trained to promote shared semantics across domains. We use toy examples, rigorous analysis, and real-world examples to show the framework's effectiveness in cross-domain performance and domain adaptation. With the proposed architecture, we need only a small set of basis elements to model each additional domain, which brings a negligible amount of additional parameters, typically a few hundred. 1 Introduction Training supervised deep networks requires large amount of labeled training data; however, well-trained deep networks often degrade dramatically on testing data from a significantly different domain. In real-world scenarios, such domain shifts are introduced by many factors, such as different illumination, viewing angles, and resolutions. Research topics such as transfer learning and domain adaptation are studied to promote invariant representations across domains with different levels of availabilities of annotated data. Recent efforts on learning cross-domain invariant representations using deep networks generally fall into two categories. The first one is to learn a common network with constraints encouraging invariant feature representations across different domains [11, 14, 26].