Capacity and Redundancy Trade-offs in Multi-Task Learning

In multi-task learning (MTL), jointly training on multiple tasks often produces negative transfer, where adding tasks degrades performance instead of improving it. We introduce a Capacity--Redundancy (CR) inequality showing that the total predictive information extractable from a shared latent is upper-bounded by the capacity of representation plus the redundancy among tasks. For related tasks, redundancy allows the shared information to support multiple predictions. For unrelated tasks, the bound certifies an unavoidable trade-off, explaining negative transfer and motivating a need for private task-specific features. We extend the CR framework to shared–private architectures in parameter-efficient finetuning approaches and derive implications for error lower bounds which can be a useful tool for practical design decisions.