提出一种基于输出空间投影的模型合并方法，可精准预测合并效果并提升性能。
Model Merging by Output-Space Projection
- 将模型合并建模为输出空间的凸二次规划问题，以最小化输出校准误差。
- 在单层和多层设置下均优于或相当现有方法，且能准确预测合并质量。
- 适合需要高效合并多个微调模型的研究者，尤其在语言与视觉任务中表现优异。
模型合并可在不重新训练的情况下，将多个微调检查点整合为一个多功能模型。现有方法如任务算术、模型汤、TIES 和 DARE 虽计算高效且实证成功，但依赖启发式设计，缺乏形式上的最优性保证。本文将合并问题形式化为残差更新上的凸二次规划，通过校准输入和微调模型输出最小化平方输出校准目标，可涵盖现有方法作为特例。该框架提供闭式诊断指标——选定基底捕捉的残差能量比例，仅用校准集即可预测下游合并质量。实验表明，该方法在单层设置中表现匹配或超越现有方法，并刻画了最优基底带来显著增益的条件。通过分层顺序算法扩展至多层合并，在语言与视觉基准上均实现一致提升。
原文摘要 · Abstract (English)
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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