A Stationary (and Therefore Compatible) Representation is All You Need

Stationary representations learned via d-Simplex fixed classifiers formally satisfy compatibility, meaning feature vectors from different model versions can be used interchangeably in retrieval systems without re-indexing. The paper shows cross-entropy training with this classifier aligns first-order feature statistics but may miss higher-order dependencies across sequential fine-tuning steps. The result provides a theoretical grounding for backward-compatible representation learning in evolving deployment pipelines.