GRAM: Group-wise Rank-Aware Model Merging via Subspace Alignment

Authors: Di Wu , Shuaidong Pan

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Abstract: 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 \emph{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 \textbf{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).

Subjects:

Artificial Intelligence (cs.AI) ; Computation and Language (cs.CL)

Cite as:

arXiv:2610.29110 [cs.AI]

(or

arXiv:2610.29110v1 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2610.29110

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arXiv-issued DOI via DataCite (pending registration)

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From: Shuaidong Pan [ view email ]

[v1]

Wed, 21 Oct 2026 02:50:46 UTC (11,262 KB)

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