Compositional Learnware Identification and Gradient-Guided Assembly

Tasks and query batches often require diverse capabilities, motivating complementary model reuse from growing repositories. The learnware paradigm—Learnware = Model + Specification—provides reusable capability representations, supporting such reuse without evaluating every candidate on the target task. PAVE (Parameter Vector) specifications encode model capabilities and user requirements as parameter updates in a common space. However, independently ranking models by PAVE similarity can favor overlapping capabilities, while collection-level PAVEs provide limited evidence for assigning individual inputs. We address these challenges through complementary identification and gradient-guided sample-level assignment. Inspired by task arithmetic, we formulate identification as sparse PAVE reconstruction, using the unexplained user-PAVE residual to guide complementary model selection. For assignment, we exploit sample gradients as local adaptation signals, calibrated using collection-level statistics, to match individual inputs with selected model PAVEs. Under a local update approximation, our analysis relates gradient–PAVE matching to average gradient-kernel similarity between a sample and a specification's fitting distribution. Across 72 mixed LLM batches, 720 mixed CV/NLP runs, and 41 single-dataset benchmarks, our method consistently improves model reuse without training a parametric selector. It exceeds the strongest compared learning-based router by 1.06 points on mixed LLM workloads and improves over hindsight Best-Single by 10.62/2.52 points on mixed CV/NLP tasks, while invoking one candidate per input. Extensive controlled ablations further validate the contributions of complementary identification and gradient-guided assembly, as well as the effects of gradient calibration and common-direction removal.