Learning How to Share: Optimal Transport for Medical Multi-Task Learning

We present ASK-OT (**AS**ymmetric **K**nowledge sharing via **O**ptimal **T**ransport), an innovative framework for multi-task learning that formulates knowledge sharing as a resource allocation problem. ASK-OT learns a set of knowledge modules from a shared representation and allocates them to tasks according to their representational needs. We formulate this allocation as an optimal transport problem, allowing task-specific and asymmetric sharing patterns to emerge from the learned representations rather than being imposed by predefined task groups. To account for the distinct roles of modules and tasks, we introduce a module-capacity constraint and task constraint relaxation, which respectively allow modules to be shared across tasks while allowing tasks to draw different amounts of knowledge. We theoretically characterize the resulting asymmetric sharing and demonstrate experimentally that ASK-OT outperforms representative baselines. Code will be available upon acceptance.