SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks (2006.10503v3)

Abstract: We introduce the SE(3)-Transformer, a variant of the self-attention module for 3D point clouds and graphs, which is equivariant under continuous 3D roto-translations. Equivariance is important to ensure stable and predictable performance in the presence of nuisance transformations of the data input. A positive corollary of equivariance is increased weight-tying within the model. The SE(3)-Transformer leverages the benefits of self-attention to operate on large point clouds and graphs with varying number of points, while guaranteeing SE(3)-equivariance for robustness. We evaluate our model on a toy N-body particle simulation dataset, showcasing the robustness of the predictions under rotations of the input. We further achieve competitive performance on two real-world datasets, ScanObjectNN and QM9. In all cases, our model outperforms a strong, non-equivariant attention baseline and an equivariant model without attention.

• The paper presents the SE(3)-Transformer, which leverages self-attention under SE(3) equivariance to enhance 3D data processing.
• It employs equivariant attention weights, value messages, and self-interaction layers to remain stable under rotations and translations.
• Empirical evaluations on N-Body, ScanObjectNN, and QM9 datasets demonstrate its robust handling of diverse real-world 3D transformations.

SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks

The paper "SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks" introduces a sophisticated model designed to handle 3D point clouds and graphs with an emphasis on maintaining equivariance under continuous 3D roto-translations. This model, named the SE(3)-Transformer, extends the concept of self-attention to domains where data invariance to spatial transformations is paramount.

Model Architecture and Principles

The SE(3)-Transformer builds on the fundamental principles of self-attention mechanisms, which are known for their adaptability across diverse tasks such as language processing and image recognition. However, traditional self-attention mechanisms do not exploit specific structural properties inherent in certain data types, such as 3D point clouds, which can lead to inefficiency and instability. To address this, the authors introduce a model that adheres to SE(3) equivariance constraints, thereby improving robustness against transformations like rotations and translations.

The model itself comprises several key components:

1. Equivariant Attention Weights: These weights are invariant to changes in the input's global pose, ensuring that attention mechanisms respect the symmetries of the task.
2. Equivariant Value Messages: Inspired by tensor field networks, these messages facilitate the propagation of information between nodes in a way that is sensitive to their relative positions and orientations.
3. Self-Interaction Layer: Positioned as either linear or attentive, this layer manages intra-point interactions, ensuring continuity of information across layers.

Numerical Evaluation

The authors rigorously evaluate the SE(3)-Transformer across multiple datasets:

• N-Body Simulations: Here, the model demonstrates its capacity to handle equivariant tasks effectively. It predicts future states of particles with minimal error, even when the inputs undergo arbitrary rotational transformations.
• ScanObjectNN Dataset: The model’s application to real-world point cloud data (3D scans) reveals competitive performance, showcasing its ability to handle noise and imperfections inherent in real-world data acquisition.
• QM9 Dataset: In molecular property prediction tasks, the SE(3)-Transformer presents respectable efficacy, although not surpassing all other contemporary approaches, it reliably outperforms earlier tensor field networks.

Contributions and Implications

This paper contributes a novel methodology for handling 3D data architectures, combining self-attention with the geometrical rigour of SE(3) equivariance. The authors introduce a fast computation library for spherical harmonics and elaborate on theoretical underpinnings related to irreducible group representations and graph neural networks.

Theoretical implications of this paper extend to the development of neural network models that more accurately process 3D data by respecting inherent symmetries. Practically, these advancements have the potential to influence fields such as robotics, computer vision, and computational chemistry, where spatial transformations are frequently encountered.

Future developments may involve integration with other neural network structures to further enhance the model's adaptability and efficiency, possibly exploring broader applications in virtual reality and autonomous systems.

In conclusion, the SE(3)-Transformer delineates a concrete step forward in the intersection between deep learning and geometric invariance, offering a compelling approach to managing the complexities of 3D data more effectively.