EpiMer: A Geometry-Based Framework for Model Merging
Researchers propose EpiMer, a framework that redefines model merging as solving the Fréchet mean on a Riemannian manifold. By restricting computations to a low-rank subspace spanned by task vectors and using the expected Hessian as a metric, EpiMer connects local curvature with epistemic uncertainty. Theoretical analysis decomposes merging error into subspace Fréchet variance and residual energy, providing conditions where curvature-aware merging outperforms flat-geometry methods. The framework unifies curvature-aware and spectral methods as special cases of subspace Fréchet mean.
Key facts
- Model merging integrates knowledge without retraining.
- Existing methods ignore loss landscape geometry or rely on intractable Hessian approximations.
- EpiMer casts merging as Fréchet mean on a Riemannian manifold.
- Computation is restricted to a low-rank subspace spanned by task vectors.
- Expected Hessian serves as the metric.
- Local curvature is linked to epistemic uncertainty of parameters.
- Merging error bound is decomposed into subspace Fréchet variance and residual energy.
- Curvature-aware merging provably outperforms flat-geometry methods under specific conditions.
Entities
Institutions
- arXiv