@inproceedings{bibcite_146,
  author = {Dongzhe Zheng and Christine Allen-Blanchette},
  title = {Beyond Pairwise: Diagnosing Higher-Order Merge Failures via Hodge Decomposition},
  abstract = {<p>Model merging typically chooses a reference model, aligns all other models to it, and interpolates their weights. This star-shaped pipeline treats mergeability as pairwise: if each model can be merged with the reference, then larger collections are assumed to be mergeable as well. We show that this assumption can fail even in a controlled setting. For 24 weight-matched PlainCNNs trained on CIFAR-10, more than 90\% of triples whose pairs are individually mergeable are not jointly mergeable. We diagnose this failure by representing mergeability as a simplicial complex and decomposing merge barriers into gradient, curl, and harmonic components. These components capture reference-dependent effects, local inconsistencies around triples, and global obstructions that persist under fixed alignment. The mergeability complex exposes substantial higher-order obstruction: its first Betti number, counting cycles of pairwise-mergeable models that do not bound jointly mergeable triples, reaches 122. Under standard star-topology alignment, 25.5\% of barrier energy remains harmonic, a component not directly targeted by existing merging methods. Re-aligning models along a minimum spanning tree weighted by harmonic energy reduces this fraction to 1.8\% and decreases the first Betti number from 75 to 5, though the total merge barrier increases by 15\%. Thus, alignment topology is not merely an implementation detail: it determines which merge barriers are visible, removable, or hidden as global obstructions.</p>},
  year = {2026},
  journal = {ICML 2026 Workshop on Weight-Space Symmetries},
}