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Model merging aims to cheaply combine individual task-specific models into asingle multitask model. In this work, we view past merging methods asleveraging different notions of a ''task subspace'' in which models are matchedbefore being merged. We connect the task subspace of a given model to its losslandscape and formalize how this approach to model merging can be seen assolving a linear system of equations. While past work has generally beenlimited to linear systems that have a closed-form solution, we consider usingthe conjugate gradient method to find a solution. We show that using theconjugate gradient method can outperform closed-form solutions, enables mergingvia linear systems that are otherwise intractable to solve, and flexibly allowschoosing from a wide variety of initializations and estimates for the ''tasksubspace''. We ultimately demonstrate that our merging framework called''Matching Models in their Task Subspace'' (MaTS) achieves state-of-the-artresults in multitask and intermediate-task model merging. We release all of thecode and checkpoints used in our work at https://github.com/r-three/mats.

Merging by Matching Models in Task Subspaces