Model Merging on Loss Landscape: A Geometry Perspective

• URL: http://arxiv.org/abs/2605.26693v1
• Date: Tue, 26 May 2026 08:33:30 GMT
• Title: Model Merging on Loss Landscape: A Geometry Perspective
• Abstract summary: EpiMer is a framework that casts model merging as solving the Fréchet mean on a Riemannian manifold.<n>Our theoretical analysis decomposes the merging error bound into the subspace Fréchet variance and the residual energy.<n>Merging fine-tuned CLIP-ViT models on eight image classification tasks, Epistemic Merging strictly outperforms the baselines on all three CLIP-ViT backbones at matched rank.
• Score: 2.2624434825206543
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Model merging offers a promising avenue for knowledge integration and parallel development without retraining. Yet, existing methods either ignore the geometry of the loss landscape or rely on intractable full-space Hessian approximations. We propose EpiMer, a framework that casts model merging as solving the Fréchet mean on a Riemannian manifold and restricts the computation to a low-rank subspace spanned by the task vectors. With the expected Hessian as the metric, we reveal a connection between local curvature and epistemic uncertainty of the parameters. Our theoretical analysis decomposes the merging error bound into the subspace Fréchet variance and the residual energy, and provides a closed-form characterization of when curvature-aware merging provably outperforms flat-geometry methods. In addition, our framework unifies both curvature-aware methods and recent spectral methods as special cases of the subspace Fréchet mean with different geometric metrics. Merging fine-tuned CLIP-ViT models on eight image classification tasks, Epistemic Merging strictly outperforms the baselines on all three CLIP-ViT backbones at matched rank, improving the across-task average accuracy and worst-task accuracy on every backbone.

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