Abstract
Domain generalization aims to learn a reliable predictor on unseen target domains from source domains alone. Traditional empirical risk minimization (ERM), which relies on spurious correlations such as backgrounds and textures, tends to fail under distribution shift. Methods based on feature-statistic mixing (MixStyle, DSU) and weight averaging (SWAD) have proven effective, yet they have long been regarded as independent heuristics lacking a unified theoretical characterization, and the boundary of their effectiveness has not been systematically studied. Existing causal invariant transformation (CIT), though an ideal formal framework for characterizing invariant predictors, only covers input-space transformations such as rotations and flips; it neither accounts for feature-statistic perturbations at intermediate layers nor connects to weight averaging in parameter space. This paper extends CIT to feature moments and establishes a unified causal-invariance framework under the content–style assumption, with three theoretical results connecting feature space, distribution space, and parameter space, based on which we design the plug-and-play, target-free Content-Conditioned Invariant Feature-Statistic Augmentation (CIFA) operator. Paired-seed experiments on ResNet-50 across four DomainBed benchmarks show CIFA is statistically equivalent to SWAD and four classic baselines. Component ablations validate the framework’s predictions about each component’s role: weight averaging dominates accuracy, while the benefit of feature-moment mixing is constrained by content–style separability, providing an empirical characterization of the validity boundary for this class of methods. The core contribution lies not in accuracy improvement, but in offering a unified theoretical perspective for two families of empirically effective methods and delineating the validity boundary of such invariance methods through systematic experiments.