Bridging Domains through Subspace-Aware Model Merging

Model merging aims to integrate multiple task-specific fine-tuned models derived from a shared pre-trained checkpoint into a single multi-task model without additional training. Despite extensive research, task interference remains a major obstacle that often undermines the performance of merged models. In this paper, we propose ESM (Essential Subspace Merging) , a robust framework for effective model merging. We begin by performing Principal Component Analysis (PCA) on feature shifts induced by parameter updates. The resulting principal directions span an essential subspace that dominantly influences feature representations. Each task's parameter update matrix is projected onto its respective essential subspace for low-rank decomposition before merging. This methodology mitigates inter-task interference while preserving core task-specific functionality. Furthermore, we introduce a multi-level polarized scaling strategy that amplifies parameters containing critical knowledge and suppresses redundant ones, preventing essential knowledge from being overwhelmed during fusion. Extensive experiments across multiple task sets and model scales demonstrate that our method achieves state-of-the-art performance in multi-task model merging. Code is available at https://github.com/kiddo127/ESM.

Learning across domains is challenging when data cannot be centralized due to privacy or heterogeneity, which limits the ability to train a single comprehensive model. Model merging provides an appealing alternative by consolidating knowledge from multiple specialized models into one, avoiding data sharing and reducing retraining cost. In this work, we present DMM, a data-free model merging framework designed to handle highly divergent models. DMM proceeds in three steps. First, domain-specific models are trained independently. Second, models with high similarity are merged using standard techniques to ensure stability. Third, we synthesize pseudo-data from normalization statistics and distill knowledge from divergent models into the merged model through a lightweight refinement guided by these samples. This approach preserves rare but critical knowledge while maintaining stability. Extensive experiments on unimodal and multimodal benchmarks show that DMM achieves state-of-the-art performance over existing merging methods.

Merging different models into a single model is highly desirable for multi-task deployment, particularly in regulated domains like healthcare. In such settings, models are often locally fine-tuned due to strict data privacy policies, necessitating that aggregation operates exclusively on the fine-tuned weights. Existing methods apply a uniform merge across all tasks, ignoring the geometric relationships among their learned subspaces. When task updates occupy misaligned subspaces, projecting them onto a shared low-rank basis discards task-relevant directions, a failure mode named subspace interference. Through this study, we show that the per-task projection error of a merged model is governed by the principal-angle alignment between each task and the shared subspace, so that grouping geometrically compatible tasks provably reduces this error within each group. Motivated by this observation, we propose Group-wise Rank-Aware Model Merging (GRAM), which uses the principal-angle geometry of task vectors to decide which tasks should be merged together and then performs a standard SVD-based merge within each coalition; the pipeline requires only the fine-tuned weights at merge time. With only one additional model ($\nK{=}2$), GRAM significantly mitigates subspace interference and consistently outperforms prior merging methods across language understanding (GLUE with Flan-T5), 8-task CLIP vision, and medical instruction tuning (Qwen2-7B-Instruct with four English/Chinese medical LoRAs).