Learning Symmetries through Loss Landscape
Keywords: Unconstrained models, equivariant models, symmetries.
Abstract: Incorporating equivariance as an inductive bias into deep learning architectures, to take advantage of the data symmetry, has been successful in multiple applications such as chemistry and dynamical systems. The build of equivariance architecture, particularly w.r.t. roto-translations, is crucial for effectively modeling geometric graphs and molecules, where the understanding of 3D structures enhances generalization. However, despite their potential, equivariant models often pose challenges due to their high computational complexity. In this paper, we study the capabilities of unconstrained models (which do not build equivariance into the architecture) and how they generalize compared to equivariant models. We show that unconstrained models can learn approximate symmetries by minimizing additional simple equivariance loss. By formulating equivariance as a new learning objective, we can control the level of approximate equivariance in the model. Our method achieves competitive performance compared to equivariant baselines while being 10x faster at inference and 2.5x at training.
Primary Area: learning on graphs and other geometries & topologies
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Submission Number: 11077
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