  Deep learning techniques often perform poorly in the presence of domain
shift, where the test data follows a different distribution than the training
data. The most practically desirable approach to address this issue is Single
Domain Generalization (S-DG), which aims to train robust models using data from
a single source. Prior work on S-DG has primarily focused on using data
augmentation techniques to generate diverse training data. In this paper, we
explore an alternative approach by investigating the robustness of linear
operators, such as convolution and dense layers commonly used in deep learning.
We propose a novel operator called XCNorm that computes the normalized
cross-correlation between weights and an input feature patch. This approach is
invariant to both affine shifts and changes in energy within a local feature
patch and eliminates the need for commonly used non-linear activation
functions. We show that deep neural networks composed of this operator are
robust to common semantic distribution shifts. Furthermore, our empirical
results on single-domain generalization benchmarks demonstrate that our
proposed technique performs comparably to the state-of-the-art methods.
