AlignMerge: Alignment-preserving large language model merging via Fisher-guided geometric constraints

Researchers propose AlignMerge, a geometry-aware framework that treats alignment as an explicit invariant when merging large language models, addressing the problem that standard schemes such as linear weight soups, task vectors, and Fisher-weighted averaging may silently break alignment while preserving loss. The method estimates an alignment subspace in the local Fisher graph of an instruction-tuned base model using a projection matrix P_A, optimizes a combined objective of a geometric term, an alignment-direction penalty, and a soft alignment budget, and uses the decoding-invariant alignment quality index AQI, a latent-space criterion, as the alignment functional.