Geofield-LoRA: Reading Task-Specific Adapters from a Shared Gaussian Primitive Field

Low-Rank Adaptation (LoRA) provides an efficient way to adapt large language models, but multi-task adaptation must capture both the commonalities and differences across task-specific updates. Existing conditional LoRA methods typically address this through learned mixing, routing, or parameter-generation functions. In practice, such functions can concentrate most tasks on a few shared components. We instead formulate multi-task adaptation from a multi-view perspective, where different tasks obtain related but distinct updates from a shared parameter field. We introduce Geofield-LoRA, which represents shared low-rank updates as Gaussian primitives in a high-dimensional task-view space. A task condition defines a view of this shared field, and ray-based Gaussian responses determine how the primitive-specific low-rank updates are combined into a task-specific LoRA residual. This allows different tasks to reuse the same low-rank component bank while forming distinct task-specific updates through different combinations. Extensive and controlled studies show that Geofield-LoRA makes effective use of shared low-rank capacity: tasks with related adaptation requirements share primitives while retaining distinct updates, highlighting view-conditioned parameter fields as a promising direction for multi-task adaptation.