Conformal Routing of Partially Transferable Experts

Transferability need not be a property of an entire source model; useful computations can coexist with source-specific shortcuts, and their value can vary across target inputs. We introduce ROUTECP (Conformal Routing of Partially Transferable Experts), which aligns reusable source experts to a target representation and learns a sparse input-dependent route over them. Training directly targets conformal efficiency under a compute budget, while a finite-partition safety certificate suppresses expert contributions that cannot be certified as nonharmful. An untouched target calibration split forms a calibration firewall, preserving finite-sample marginal target coverage under calibration-test exchangeability despite adaptive source training, routing, selection, and certification. We derive an oracle inequality for sparse local routing, prove a separation from whole-source transfer under partial sharing, and establish simultaneous cell-average safety over a finite target partition. Simulations and real-data experiments show smaller prediction sets, improved low-resource transfer, reduced negative transfer, and favorable compute-efficiency tradeoffs at nominal coverage across heterogeneous target domains.