Model Merging by Output-Space Projection

• URL: http://arxiv.org/abs/2605.29101v1
• Date: Wed, 27 May 2026 21:01:29 GMT
• Title: Model Merging by Output-Space Projection
• Abstract summary: Model merging combines fine-tuned checkpoints into a single multi-task model without retraining.<n>We show that merging can be formulated as a convex programme over residual updates.<n>We extend to multi-layer merging via a sequential layer-wise algorithm and demonstrate consistent gains across language and vision benchmarks.
• Score: 6.752805486904705
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Model merging combines fine-tuned checkpoints into a single multi-task model without retraining. Existing methods - such as task arithmetic, model soups, TIES, and DARE - are computationally efficient and empirically successful, but rely on heuristic design choices and lack formal optimality guarantees. We show that merging can be formulated as a convex quadratic programme over residual updates, yielding weights that minimise a squared-output calibration objective using calibration inputs and fine-tuned model outputs, and subsuming existing methods as special cases. Our framework yields a closed-form diagnostic - the fraction of residual energy captured by a chosen basis - that predicts downstream merge quality using only the calibration set. Empirically, the QP matches or outperforms existing methods in the single-layer setting, and we characterise when the optimal basis provides significant gains over the cheaper diagonal QP. We extend to multi-layer merging via a sequential layer-wise algorithm and demonstrate consistent gains across language and vision benchmarks.

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