Geometry-Aware Directional Alignment for Coherent Model Merging

Model merging has emerged as a practical paradigm for integrating multiple independently trained models into a single model without joint retraining. Prior work shows that parameter fusion techniques, such as parameter decomposition, coefficient optimization, and subspace learning, can achieve strong performance while avoiding the cost of joint training. However, these approaches largely treat merging as a parameter aggregation problem, implicitly assuming compatibility in the underlying directional structures. We argue that this assumption rarely holds. In practice, independently trained models often exhibit misaligned dominant directions in both parameter and feature spaces. Naïve merging can therefore disrupt structural coherence, leading to significant performance degradation, especially in heterogeneous settings such as healthcare, where models trained on tasks like medical QA or clinical text understanding develop distinct representational geometries. Moreover, coefficient-based methods rely on well-aligned feature directions, an assumption contradicted by insights from Neural Collapse, which suggest that class features follow structured yet model-specific directional patterns. In this work, we identify directional alignment as the key principle for effective model merging. We propose Merging with Directional Alignment (\method{}), a unified geometric framework that explicitly enforces consistency in directional structures across both parameter and feature spaces. Our analysis shows that directional alignment preserves structural coherence during merging, and extensive experiments across multiple benchmarks, including healthcare QA, demonstrate consistent improvements across model scales and task settings.