Beyond Uniform Subspaces: Spectrum-Aware and Depth-Adaptive Fusion for Multi-Task Model Merging

Model merging aims to consolidate multiple task-specific models fine-tuned on different datasets into a unified architecture that performs cross-domain proficiency. Current data-free model merging methods often struggle to scale as they rely on simple parameter-level heuristics that ignore inter-layer dependencies and non-uniform distribution of expertise. This work proposes SA-Merging, which is built upon connectivity-based saliency formulations from structural pruning (e.g., SynFlow) and extends them to the data-free model merging setting. We define a saliency score over task vectors relative to a shared base model, and further introduce merge-aware modulation that incorporates agreement across experts to mitigate task interference. Based on this formulation, an iterative saliency-aware merging procedure progressively removes non-informative updates while preserving end-to-end connectivity. Furthermore, we extend SA-Merging to introduce rank-wise saliency decomposition for LoRAs without compromising their structural integrity. Extensive experiments on vision and language tasks demonstrate the effectiveness of our saliency-based approach, further reducing the gap between data-free and test-time adaptation methods.

Model merging aims to enable multi-task learning by integrating the capabilities of multiple models fine-tuned from the same pre-trained checkpoint into a single model. Its core challenge is inter-task interference among task-specific parameter updates. In this paper, we analyze the output shifts induced by task updates and observe that their energy is concentrated in a small number of principal directions. We call the subspace spanned by these directions the essential subspace. In contrast, most remaining directions carry little task-relevant energy, but their accumulation across multiple task updates can cause severe interference during merging. Motivated by this observation, we propose Essential Subspace Decomposition (ESD), which decomposes each task update according to the principal components of its activation shift. Based on ESD, we introduce Essential Subspace Merging (ESM), a training-free static merging method that orthogonalizes and fuses essential components into one compact multi-task model. We further extend ESM to ESM++, a training-free dynamic merging method that decomposes task-specific residuals into low-rank experts and selects the most relevant expert through prototype-based routing during forward inference. Extensive experiments across multiple task sets and model scales demonstrate that ESM and ESM++ effectively preserves task knowledge while reducing inter-task interference. Code is available at https://github.com/kiddo127/ESM.

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.