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.