Separating Common and Unique Directions for Model Merging

Model merging combines multiple fine-tuned models without additional training, and arithmetic methods have emerged as a simple yet effective way to merge models without data. However, existing arithmetic methods treat task vectors in parameter space and apply a single element-wise rule to directions that can differ in mergeability. In a shared directional basis, we find a consistent two-regime structure: a low-dispersion common bulk shared across tasks and a high-dispersion task-dominated tail that carries disproportionate energy. These findings motivate Common-Unique Subspace Decomposition (CUSD), a data-free pre-merging method that separates task vectors into common and unique directional components, merges the common components with downstream arithmetic operator, and retains unique residuals separately. Experiments across 11 base models, four model families, and four arithmetic-based merging operators show that CUSD improves 42 of 44 model-operator combinations and achieves up to 22.5% improvement over the corresponding baselines.