Content-Conditioned Invariant Feature-Statistic Augmentation: Unifying Robustness and Weight Averaging for Domain Generalization

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 and 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 on par with SWAD, with no statistically significant difference; the reference-batch gain of +0.99 did not replicate, and an independent unified-code re-run places CIFA within the same accuracy range as four classic baselines on PACS. Component ablations and stress tests delineate, rather than validate, the roles of the components: weight averaging accounts for the measured accuracy gain, the content-preservation gate is activatable but provides no measurable accuracy gain in the standard regime (a dormant safety mechanism), and feature-moment mixing is associated with content–style separability without that separability being established as necessary. CIFA matches the strongest baseline on PACS while showing no significant gain on the other benchmarks, and the exploratory worst-domain direction is not stable. Because the coverage gap is not identifiable without target access, all guarantees are presented as conditional bounds, and the effectiveness boundary is characterized empirically rather than as a guaranteed improvement. 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 effectiveness boundary of such invariance methods through systematic experiments.