Beyond the Permutation Symmetry of Transformers: The Role of Rotation for Model Fusion

• URL: http://arxiv.org/abs/2502.00264v1
• Date: Sat, 01 Feb 2025 01:44:55 GMT
• Title: Beyond the Permutation Symmetry of Transformers: The Role of Rotation for Model Fusion
• Authors: Binchi Zhang, Zaiyi Zheng, Zhengzhang Chen, Jundong Li,
• Abstract summary: We introduce rotation symmetry, a novel form of parameter space symmetry for transformers. Unlike permutation symmetry, rotation symmetry operates in a continuous domain, thereby significantly expanding the equivalence set for transformers. We propose a theoretically optimal matching algorithm as a plug-and-play module to enhance model fusion.
• Score: 43.299430093251736
• License:
• Abstract: Symmetry in the parameter space of deep neural networks (DNNs) has proven beneficial for various deep learning applications. A well-known example is the permutation symmetry in Multi-Layer Perceptrons (MLPs), where permuting the rows of weight matrices in one layer and applying the inverse permutation to adjacent layers yields a functionally equivalent model. While permutation symmetry fully characterizes the equivalence set for MLPs, its discrete nature limits its utility for transformers. In this paper, we introduce rotation symmetry, a novel form of parameter space symmetry for transformers that generalizes permutation symmetry by rotating parameter matrices in self-attention layers. Unlike permutation symmetry, rotation symmetry operates in a continuous domain, thereby significantly expanding the equivalence set for transformers. Based on this property, we propose a theoretically optimal parameter matching algorithm as a plug-and-play module to enhance model fusion. We evaluate our approach using pre-trained transformers across diverse natural language and vision tasks. Experimental results demonstrate that our rotation symmetry-based matching algorithm substantially improves model fusion, highlighting the potential of parameter space symmetry to facilitate model fusion. Our code is available on https://github.com/zhengzaiyi/RotationSymmetry.

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