Title: LASSO: Latent Sub-spaces Orientation for Domain Generalization. Abstract: To achieve a satisfactory generalization performance on prediction tasks in an unseen domain, existing domain generalization (DG) approaches often rely on the strict assumption of fixed domain-invariant features and common hypotheses learned from a set of training domains. While it is a natural and important premise to ground generalization capacity on the target domain, we argue that this assumption could be overly strict and sub-optimal. It is particularly evident when source domains share little information or the target domains leverages information from selective source domains in a compositional way instead of relying on a unique invariant hypothesis across all source domains. Unlike most existing approaches, instead of constructing a single hypothesis shared among domains, we propose a LAtent Sub-Space Orientation (LASSO) method that explores diverse latent sub-spaces and learning individual hypotheses on those sub-spaces. Moreover, in LASSO, since the latent sub-spaces are formed by the label-informative features captured in source domains, they allow us to project target examples onto appropriate sub-spaces, while preserving crucial label-informative features for the label prediction. Finally, we empirically evaluate our method on several well-known DG benchmarks, where it achieves state-of-the-art results.