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I'm the author of several model merging libraries, so perhaps I can explain.
It's quite straightforward. When you finetune a LLM (or PEFT), you are taking a fixed base and tuning it against a dataset. Pretraining already fixed our parameters in a pretty solid matrix; so all changes must operate around this as the basis.
Training can't perturbate the base model outside of a certain range without the model collapsing, so viable changes will follow allowable patterns. This is why the resulting models are homomorphic. These trainings create kernels that are commonly known as 'task vectors'.
As long as these models remain homomorphic, and you only attempt to merge parts of the parameter space that are in the same alignment, two kernels can be interpolated to adjust the parameter space to have relative changes that assume the properties of both.
The alignment issue - this is where sign agreement comes in. Since merging generally compares the delta weights, it is possible that kernels may train out of phase. One kernel may have been trained in a positive phase alignment with the base model, and the other developed a negative phase alignment. Since they are out of phase with each other, their kernels would interfere.
I don't know if that's as clear as I would like it to be, but it's late.
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