Feature re-sampled detached learning balances each attribute without distorting the label priors of co-occurring attributes. Gradient-oriented augment translating further addresses feature noise and semantic imbalance, combining independent balancing and augmentation with minimal computational overhead.

Attribute-disentangled feature learning minimizes information shared across attribute-specific representations. This journal study extends the co-occurrence-bias framework with improved feature-space exploration, treatment of imbalance, and flexibility to preserve selected causal dependencies.

A quadruplet domain-translation analysis characterizes the limitations of reconstruction error as an OOD signal. Semantic reconstruction, certainty decomposition, and distance normalization improve detection without additional data or sacrificing known-class classification accuracy.

Feature-level re-sampling makes independent label balancing feasible despite image-level attribute co-occurrence. Bayesian feature augmentation adds in-distribution diversity for under-represented attributes, addressing label imbalance and semantic imbalance together.

Mutual-information minimization discourages attribute representations from encoding other attributes. Efficient feature transformation and recombination reduce reliance on dataset-specific co-occurrences and improve robustness under identity and scene shifts.

This work separates statistical identification from computational recovery in invariant learning through a conditional computational barrier. It also quantifies how environment diversity controls identifiability, estimation difficulty, and phase transitions, connecting theoretical limits with empirical diversity diagnostics.

Counterfactual pairing cycles reuse the same two images and two captions while changing only their assignment. The balanced contrast cancels image-only, text-only, and additive component shortcuts exactly, providing an evaluation primitive, a training loss, and a diagnostic for relational OOD.

Labels identify a posterior quotient, rather than an arbitrary semantic/background decomposition. This motivates quotient-first auditing and editing of frozen representations. A structured second-order specialization yields dual-moment decomposition; residual editing is useful only in regimes with sufficient residual signal, support, and split stability.

Source labels do not reveal how different sources orient their coordinates. In a sparse Gaussian model, relative-gauge metadata enables synchronization and changes the learning problem from sparse PCA to sparse mean recovery. Aligned mass quantifies the statistical value of calibration, with computational consequences under sparse-PCA hardness assumptions.