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

Area of Science:

• Geometric Deep Learning
• Computer Vision
• Machine Learning

Background:

• Deep neural networks excel but struggle with geometric data transformations (translation, rotation, scaling).
• Existing Graph Neural Networks (GNNs) offer limited permutation-invariance, not general transformation invariance.
• Sophisticated invariant layers are computationally expensive and hard to extend.

Purpose of the Study:

• To investigate why standard neural networks lack transformation invariance for geometric data.
• To propose a novel, general method for achieving transformation invariance in deep learning models.
• To develop a flexible plug-in applicable to diverse geometric deep learning tasks.

Main Methods:

• Revisiting neural network limitations in handling geometric transformations.
• Proposing Transformation Invariant Neural Networks (TinvNet) using modified multi-dimensional scaling for initial point representations.
• Integrating these representations into existing neural network architectures.

Main Results:

• TinvNet strictly guarantees transformation invariance, unlike many existing GNNs.
• The method is general, flexible, and computationally efficient.
• Experiments on point cloud analysis and combinatorial optimization confirm TinvNet's effectiveness and broad applicability.

Conclusions:

• Transformation-invariant and distance-preserving initial point representations are key to achieving invariance.
• TinvNet provides a straightforward and effective plug-in solution for geometric deep learning.
• TinvNet should serve as a foundational baseline for future research in transformation-invariant geometric deep learning.