Improving model merging by respecting rotary position embeddings in attention
MeRoTune: RoPE-Safe Merging with a Tunable Dial
Computation and Language
Summary
When combining two versions of a language model that were trained separately, the usual method is to average their internal settings. This only works well if certain parts of the models stay aligned. The authors point out that a common method to fix alignment fails when models use a technique called rotary position embeddings (RoPE). They find the exact kind of adjustment needed to maintain proper alignment with RoPE and introduce a new way to merge models that respects this. Their method lets users smoothly blend two models after training using a kind of dial instead of being stuck with a fixed combination.
model mergingweight averagingattention mechanismrotary position embeddingsRoPEquery and key projectionsinvertible correction matrixfine-tuningblend ratioLoRA
Authors
Salman Faroz
Abstract
When you merge two fine-tuned models from the same base checkpoint by simply averaging their weights, you implicitly assume their attention subspaces are still aligned. Recent work attempts to fix misalignments by learning an invertible correction matrix, $M$, for each model's query and key projections. This correction cancels out---using $M$ on the query side and $M^{-T}$ on the key side---right before the dot product. However, this cancellation is only exact if nothing sits between the projection and the dot product. In reality, almost all modern open-weight language models put a rotary position embedding (RoPE) exactly there. In this paper, we show that this cancellation is exact under RoPE if and only if $M$ commutes with RoPE's per-position rotation. We derive the specific class of matrices where this holds: a scaled rotation acting independently within each RoPE frequency pair. This forms a strict, low-dimensional subset of the unconstrained matrices that current methods normally train. Building on this, we turn this constrained matrix class into a new merging method. While keeping the base weights entirely frozen, two fine-tunes each learn their own RoPE-compliant correction matrices. We optimize these corrections against a chosen blend ratio so the final result can be adjusted post-hoc like a dial, rather than locked into a single fixed merge. Our default approach trains at one fixed blend ratio, similar to how LoRA sets its scaling hyperparameter in advance. We also experiment with resampling the blend ratio randomly at every training step, and we report the results of both approaches.