Equivariance with Learned Canonicalization Functions
This provides a flexible alternative to symmetry-based architectures for researchers and practitioners in machine learning, though it is incremental as it builds on existing equivariance concepts.
The paper tackles the problem of achieving equivariance in neural networks without architectural constraints by learning canonicalization functions, which are competitive with existing equivariant techniques across tasks like image classification and point cloud segmentation while being faster.
Symmetry-based neural networks often constrain the architecture in order to achieve invariance or equivariance to a group of transformations. In this paper, we propose an alternative that avoids this architectural constraint by learning to produce canonical representations of the data. These canonicalization functions can readily be plugged into non-equivariant backbone architectures. We offer explicit ways to implement them for some groups of interest. We show that this approach enjoys universality while providing interpretable insights. Our main hypothesis, supported by our empirical results, is that learning a small neural network to perform canonicalization is better than using predefined heuristics. Our experiments show that learning the canonicalization function is competitive with existing techniques for learning equivariant functions across many tasks, including image classification, $N$-body dynamics prediction, point cloud classification and part segmentation, while being faster across the board.