<p>The absence of a specific target domain in the context of domain generalization (DG) poses significant challenges in formal modeling, often resulting in a theoretical lag behind algorithmic developments. Traditional approaches have sought to address this challenge by positing that target distributions can be represented as convex combinations of source distributions. However, this convex combination assumption exhibits limited efficacy for broader domain generalization (DG) when the availability of source domains is insufficient. In our work, we advance DG theory by moving beyond this restrictive assumption. To highlight the limitation of the convex combination assumption, we demonstrate the feasibility of deriving and further tightening the original domain generalization error bound without this assumption. Based on the above analysis, we derive an interpretable domain generalization error bound without the convex combination assumption. This bound comprises two main terms: one representing the dispersion of the source domain and the other reflecting the minimum discrepancy between the target and source distributions. Through these terms, we elucidate the domain-invariant representation learning algorithms and quantify the concept of ‘generalizability’ respectively, thereby enriching the theoretical landscape of domain generalization. Finally, to illustrate the practicality of our interpretable bound, we conduct simulation experiments across a variety of datasets.</p>