Model Merging by Output-Space Projection
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911726080884736 |
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| author | Evans, Bethan Etheridge, Benjamin Roberts, Stephen Tanner, Jared |
| author_facet | Evans, Bethan Etheridge, Benjamin Roberts, Stephen Tanner, Jared |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_29101 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Model Merging by Output-Space Projection Evans, Bethan Etheridge, Benjamin Roberts, Stephen Tanner, Jared Machine Learning Information Theory 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. |
| title | Model Merging by Output-Space Projection |
| topic | Machine Learning Information Theory |
| url | https://arxiv.org/abs/2605.29101 |