Revisiting Transformation Invariant Geometric Deep Learning: An Initial Representation Perspective.

Journal: IEEE transactions on pattern analysis and machine intelligence
Published Date: Mar 1, 2026

Abstract

Deep neural networks have achieved great success in the last decade. When designing neural networks to handle the ubiquitous geometric data such as point clouds and graphs, it is critical that the model can maintain invariance towards various transformations such as translation, rotation, and scaling. Most existing graph neural network (GNN) approaches can only maintain permutation-invariance, failing to guarantee invariance with respect to other transformations. Besides GNNs, other works design sophisticated transformation-invariant layers, which are computationally expensive and difficult to be extended. In this paper, we revisit why general neural networks cannot maintain transformation invariance. Our findings show that transformation-invariant and distance-preserving initial point representations are sufficient to achieve transformation invariance rather than needing sophisticated neural layer designs. Motivated by these findings, we propose Transformation Invariant Neural Networks (TinvNet), a straightforward and general plug-in for geometric data. Specifically, we realize transformation invariant and distance-preserving initial point representations by modifying multi-dimensional scaling and feed the representations into existing neural networks. We prove that TinvNet can strictly guarantee transformation invariance, being general and flexible enough to be combined with the existing neural networks. Extensive experimental results on point cloud analysis and combinatorial optimization demonstrate the effectiveness and general applicability of our method. We also extend our method into equivariance cases. Based on the results, we advocate that TinvNet should be considered as an essential baseline for further studies of transformation-invariant geometric deep learning.

Authors

  • Ziwei Zhang
    College of Chemistry, Jilin University, Qianjin Street 2699, Changchun, Jilin, 130012, China. [email protected].
  • Xin Wang
    Key Laboratory of Bio-based Material Science & Technology (Northeast Forestry University), Ministry of Education, Harbin 150040, China.
  • Zeyang Zhang
  • Peng Cui
    School of Life Sciences and Biotechnology, Shanghai Jiao Tong University, 800 Dongchuan Rd., Minhang, Shanghai 200240. China.
  • Wenwu Zhu
    Zhejiang Center for Medical Device Evaluation, Hangzhou, 310009.

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