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3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data (1807.02547v2)

Published 6 Jul 2018 in cs.LG and stat.ML

Abstract: We present a convolutional network that is equivariant to rigid body motions. The model uses scalar-, vector-, and tensor fields over 3D Euclidean space to represent data, and equivariant convolutions to map between such representations. These SE(3)-equivariant convolutions utilize kernels which are parameterized as a linear combination of a complete steerable kernel basis, which is derived analytically in this paper. We prove that equivariant convolutions are the most general equivariant linear maps between fields over R3. Our experimental results confirm the effectiveness of 3D Steerable CNNs for the problem of amino acid propensity prediction and protein structure classification, both of which have inherent SE(3) symmetry.

Citations (470)

Summary

  • The paper introduces a 3D CNN model that preserves rotational symmetry using analytically derived steerable kernel bases for robust volumetric data processing.
  • Experimental results show that the model outperforms conventional CNNs by achieving higher accuracy and greater data efficiency with fewer learnable parameters.
  • The theoretical framework extends Steerable G-CNNs, offering practical benefits for applications in medical imaging, molecular biology, and other 3D data domains.

3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data

The paper "3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data" introduces a new convolutional network model designed to achieve equivariance to rigid body motions in 3D space. This work is significant for tasks involving volumetric data, where inherent symmetries can be leveraged to improve model performance and efficiency.

Core Contributions

The authors present a convolutional neural network (CNN) architecture that processes data as scalar, vector, or tensor fields across 3D Euclidean space, ensuring that these representations are invariant to rotations. The central technique involves 3D-equivariant convolutions, which employ kernels parameterized by a steerable kernel basis. These kernels are developed analytically, maintaining equivariance and providing robust transformations across the network's layers. The paper proves that equivariant convolutions are the most general form of linear maps which preserve the symmetries of R3R^3.

Experimental Results

The model is evaluated on two key tasks: amino acid propensity prediction and protein structure classification. These tasks are inherently three-dimensional and involve symmetries related to R3R^3. Results show that 3D Steerable CNNs outperform baseline models, indicating that incorporating rotational symmetry can yield superior data efficiency and accuracy compared to conventional 3D CNNs. Notably, the model achieves higher accuracy with fewer learnable parameters, leveraging its ability to utilize symmetry constraints effectively.

Theoretical Implications

From a theoretical perspective, this work extends the framework of Steerable G-CNNs by adapting it for 3D data. The introduction of the steerable kernel basis in the convolution layers ensures that feature transformations within the network adhere to the necessary symmetry constraints. This establishes a foundation for more sophisticated models capable of leveraging rotational symmetries, akin to foundational principles in theoretical physics such as Einstein's general covariance.

Practical Implications and Future Directions

Practically, 3D Steerable CNNs enable more efficient processing of volumetric data, such as in medical imaging or molecular biology. The reduced parameter requirement makes these models suitable for applications with limited computational resources and potential for deployment in real-world scenarios where 3D rotational symmetries are prevalent.

Future work could focus on extending this framework to other symmetry groups or exploring equivariant networks that incorporate additional transformations, such as affine or projective groups. Moreover, integrating these techniques into existing machine learning pipelines could enhance model interpretability and robustness, particularly in domains requiring precision and accuracy.

In conclusion, this paper provides a detailed account of developing and evaluating 3D Steerable CNNs, offering insights into both the theoretical underpinnings and practical advantages of symmetry-aware neural networks in volumetric data analysis.

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