Constructing 3D Rotational Invariance and Equivariance with Symmetric Tensor Networks
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915768088657920 |
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| author | Zhang, Meng Wang, Chao Zhang, Hao Dong, Shaojun He, Lixin |
| author_facet | Zhang, Meng Wang, Chao Zhang, Hao Dong, Shaojun He, Lixin |
| contents | Symmetry-aware architectures are central to geometric deep learning. We present a systematic approach for constructing continuous rotationally invariant and equivariant functions using symmetric tensor networks. The proposed framework supports inputs and outputs given as a tuple of Cartesian tensors of different rank as well as spherical tensors of different type. We introduce tensor network generators for invariant maps and obtain equivariant maps via differentiation. Specifically, we derive general continuous equivariant maps from vector inputs to Cartesian or spherical tensor output. Finally, we clarify how common equivariant primitives in geometric graph neural networks arise within our construction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_12596 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Constructing 3D Rotational Invariance and Equivariance with Symmetric Tensor Networks Zhang, Meng Wang, Chao Zhang, Hao Dong, Shaojun He, Lixin Machine Learning Symmetry-aware architectures are central to geometric deep learning. We present a systematic approach for constructing continuous rotationally invariant and equivariant functions using symmetric tensor networks. The proposed framework supports inputs and outputs given as a tuple of Cartesian tensors of different rank as well as spherical tensors of different type. We introduce tensor network generators for invariant maps and obtain equivariant maps via differentiation. Specifically, we derive general continuous equivariant maps from vector inputs to Cartesian or spherical tensor output. Finally, we clarify how common equivariant primitives in geometric graph neural networks arise within our construction. |
| title | Constructing 3D Rotational Invariance and Equivariance with Symmetric Tensor Networks |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2508.12596 |