Paper
Functionality-Oriented LLM Merging on the Fisher--Rao Manifold
Authors
Jiayu Wang, Zuojun Ye, Wenpeng Yin
Abstract
Weight-space merging aims to combine multiple fine-tuned LLMs into a single model without retraining, yet most existing approaches remain fundamentally parameter-space heuristics. This creates three practical limitations. First, linear averaging, task vectors, and related rules operate on Euclidean coordinates, even though the desired goal is to merge functionality, i.e., predictive behaviors across tasks. Second, when the source checkpoints are farther apart or more heterogeneous, Euclidean blends often trigger representation collapse, manifested as activation variance shrinkage and effective-rank degradation, which sharply degrades accuracy. Third, many geometry-inspired methods are most natural for two-model interpolation and do not extend cleanly to merging N>2 experts with a principled objective. We address these issues by formulating model merging as computing a weighted Karcher mean on the Fisher--Rao manifold, which is locally equivalent to minimizing a KL-based function distance between predictive distributions. We derive a practical fixed-point algorithm using a lightweight spherical proxy that preserves norms and generalizes directly to multi-expert merging. Across various benchmarks and collapse diagnostics, our method remains stable as the number and heterogeneity of merged models increase, consistently outperforming prior baselines.
Metadata
Related papers
Gen-Searcher: Reinforcing Agentic Search for Image Generation
Kaituo Feng, Manyuan Zhang, Shuang Chen, Yunlong Lin, Kaixuan Fan, Yilei Jian... • 2026-03-30
On-the-fly Repulsion in the Contextual Space for Rich Diversity in Diffusion Transformers
Omer Dahary, Benaya Koren, Daniel Garibi, Daniel Cohen-Or • 2026-03-30
Graphilosophy: Graph-Based Digital Humanities Computing with The Four Books
Minh-Thu Do, Quynh-Chau Le-Tran, Duc-Duy Nguyen-Mai, Thien-Trang Nguyen, Khan... • 2026-03-30
ParaSpeechCLAP: A Dual-Encoder Speech-Text Model for Rich Stylistic Language-Audio Pretraining
Anuj Diwan, Eunsol Choi, David Harwath • 2026-03-30
RAD-AI: Rethinking Architecture Documentation for AI-Augmented Ecosystems
Oliver Aleksander Larsen, Mahyar T. Moghaddam • 2026-03-30
Raw Data (Debug)
{
"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2603.04972v1</id>\n <title>Functionality-Oriented LLM Merging on the Fisher--Rao Manifold</title>\n <updated>2026-03-05T09:08:38Z</updated>\n <link href='https://arxiv.org/abs/2603.04972v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2603.04972v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>Weight-space merging aims to combine multiple fine-tuned LLMs into a single model without retraining, yet most existing approaches remain fundamentally parameter-space heuristics. This creates three practical limitations. First, linear averaging, task vectors, and related rules operate on Euclidean coordinates, even though the desired goal is to merge functionality, i.e., predictive behaviors across tasks. Second, when the source checkpoints are farther apart or more heterogeneous, Euclidean blends often trigger representation collapse, manifested as activation variance shrinkage and effective-rank degradation, which sharply degrades accuracy. Third, many geometry-inspired methods are most natural for two-model interpolation and do not extend cleanly to merging N>2 experts with a principled objective.\n We address these issues by formulating model merging as computing a weighted Karcher mean on the Fisher--Rao manifold, which is locally equivalent to minimizing a KL-based function distance between predictive distributions. We derive a practical fixed-point algorithm using a lightweight spherical proxy that preserves norms and generalizes directly to multi-expert merging. Across various benchmarks and collapse diagnostics, our method remains stable as the number and heterogeneity of merged models increase, consistently outperforming prior baselines.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='cs.LG'/>\n <category scheme='http://arxiv.org/schemas/atom' term='cs.CL'/>\n <published>2026-03-05T09:08:38Z</published>\n <arxiv:comment>9 pages, 2 figures</arxiv:comment>\n <arxiv:primary_category term='cs.LG'/>\n <author>\n <name>Jiayu Wang</name>\n </author>\n <author>\n <name>Zuojun Ye</name>\n </author>\n <author>\n <name>Wenpeng Yin</name>\n </author>\n </entry>"
}