JIVEAdapter: A Multi-Task Additive Low-Rank Adapter via Joint and Individual Variation Explained (JIVE)

Parameter-efficient fine-tuning adapts pretrained models at a fraction of the cost of full fine-tuning, yet most low-rank adapters are single-task and represent each weight update multiplicatively, leaving no explicit account of what is shared across tasks and what is task-specific. We introduce JIVEAdapter, a multi-task additive low-rank adapter inspired by statistical Joint and Individual Variation Explained (JIVE). JIVEAdapter decomposes every weight update into a Joint structure shared across all tasks plus a per-task Individual structure, penalizes the Individual structures to be near-orthogonal to the Joint so shared and task-specific signal stay interpretable and separated, and allocates rank adaptively across a shared Joint pool and a per-task Individual pool. The Joint is learned once, jointly over a task group or incrementally, one task at a time, then frozen and reused as a prior for new tasks without retraining the shared part. On GLUE and SuperGLUE with DeBERTaV3-base, \method is competitive with strong single-task and multi-task low-rank baselines at a matched per-task effective rank, without extra modules such as MoE, and when a related held-in task exists its frozen Joint serves a held-out task by reusing that task's Individual with only a cheap per-direction scale, otherwise training a small new one.