WTN: Low-Rank Invertible Adapters for Low-Bit Embedding Cache Migration

Updating low-bit embedding caches for new tasks can disrupt services that depend on earlier representations. We introduce Wasserstein Transport Networks (WTN), a constrained family of low-rank convex-gradient residual maps designed to support both task adaptation and historical recovery. WTN learns a flexible set of transport directions under joint constraints that ensure a fixed residual Lipschitz bound, global bijectivity, and stable inversion. The non-expansive inverse allows the same learned maps used for adaptation to recover historical representations, with recovery errors bounded by accumulated quantization and numerical inversion errors. As a result, WTN requires only the latest cache rather than storing historical representations. Across four hierarchical vision datasets and multiple 3-bit migrations, WTN maintains strong latest-task performance while limiting degradation on historical tasks and preserving the neighborhood structure of older representations.