Model merging combines several independently fine-tuned experts into a single multi-task model without any training data, reducing the storage, serving, and decentralized-development costs of large foundation models. State-of-the-art merging methods formulate merging as a layer-wise quadratic interference minimization problem. Although this problem admits an exact closed-form pseudoinverse solution, that solution underperforms hundreds of iterations of gradient descent in practice. The iterative loop dominates the cost of the pipeline, yet its effectiveness has remained unexplained. We revisit this regime and show that the iterative solver does not primarily act as an optimizer; rather, it serves as an implicit spectral regularizer for an ill-posed normal equation, where small-eigenvalue directions of the per-layer interference operator amplify proxy noise. Building on this finding, we formalize multi-task model merging as a noisy linear inverse problem and propose a spectral filtering estimator parameterized by a per-direction filter. We instantiate this estimator with SWUDI, a closed-form method that combines a soft exponential filter, which matches the gradient-flow trajectory of iterative descent, with a hard top-K truncation that suppresses noise-amplifying small-eigenvalue directions. Furthermore, we propose SWUDI-A, an adaptive variant that replaces the global rank hyperparameter with per-layer rank rules, further improving robustness across architectures. Both variants share a single symmetric eigendecomposition per linear layer and require no training data or optimizer state. Across four general benchmarks and a multimodal merging benchmark spanning VQA, Geometry, Chart, OCR, Grounding, and modality merging, our proposed spectral solvers match or outperform state-of-the-art merging methods. Crucially, they reduce wall-clock time by 28-72x and peak GPU memory by up to 50%.
Model merging aims to combine multiple fine-tuned models derived from a common pretrained model into a single multi-task model without additional joint training. Recent spectral merging methods improve over simple weight averaging by exploiting low-rank structures of task-specific updates, but they commonly assign the same rank capacity to every task. This uniform allocation ignores that task vectors can have heterogeneous spectral complexity, causing the shared merging space to be used suboptimally. In this paper, we propose Spectral Energy-proportional Rank Allocation (SERA), a simple task-adaptive strategy that allocates ranks according to the singular-value energy structure of each task vector. By assigning richer spectral capacity to complex or isolated tasks and fewer directions to compact tasks, SERA extends SVD-based model merging from uniform-capacity merging to task-dependent capacity allocation. Experiments under standard vision model merging protocols show that SERA improves multi-task merging performance while preserving the same total rank budget as existing spectral merging methods. Further analysis demonstrates that task-level spectral concentration is closely related to the per-task effect of adaptive rank allocation, providing insight into when and why SERA is effective.
Model merging has emerged as a promising paradigm for enabling multi-task capabilities without additional training. However, traditional basic merging methods often experience performance degradation due to parameter conflicts, even when applied to similar tasks. While recent personalized merging frameworks successfully preserve task-specific information to maintain performance, they typically incur storage overhead. In this paper, we propose Decomposition, Thresholding, and Scaling (DTS), an approximation-based personalized merging framework that pushes task-specific storage efficiency. DTS first applies singular value decomposition to the task-specific information and retains only a small subset of singular values and vectors. It then introduces a novel thresholding strategy that partitions singular vector elements into groups and assigns a scaling factor to each group. To enable generalization to unseen tasks, we further extend DTS with a variant that fuses task-specific information in a data-free manner based on the semantic similarity of task characteristics. Extensive experiments demonstrate that DTS consistently outperforms state-of-the-art baselines while requiring only 1% extra storage per task. Furthermore, experiments on unseen tasks show that the DTS variant achieves significantly better generalization performance. Our code is available at https://github.com/krumpguo/DTS.
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.
Bethan Evans, Benjamin Etheridge, Stephen Roberts +1