Rethinking SO(3)-equivariance with Bilinear Tensor Networks

• URL: http://arxiv.org/abs/2303.11288v1
• Date: Mon, 20 Mar 2023 17:23:15 GMT
• Title: Rethinking SO(3)-equivariance with Bilinear Tensor Networks
• Authors: Chase Shimmin and Zhelun Li and Ema Smith
• Abstract summary: We show that by judicious symmetry breaking, we can efficiently increase the expressiveness of a network operating only on vector and order-2 tensor representations of SO$(2)$. We demonstrate the method on an important problem from High Energy Physics known as textitb-tagging, where particle jets originating from b-meson decays must be discriminated from an overwhelming QCD background.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Many datasets in scientific and engineering applications are comprised of objects which have specific geometric structure. A common example is data which inhabits a representation of the group SO$(3)$ of 3D rotations: scalars, vectors, tensors, \textit{etc}. One way for a neural network to exploit prior knowledge of this structure is to enforce SO$(3)$-equivariance throughout its layers, and several such architectures have been proposed. While general methods for handling arbitrary SO$(3)$ representations exist, they computationally intensive and complicated to implement. We show that by judicious symmetry breaking, we can efficiently increase the expressiveness of a network operating only on vector and order-2 tensor representations of SO$(2)$. We demonstrate the method on an important problem from High Energy Physics known as \textit{b-tagging}, where particle jets originating from b-meson decays must be discriminated from an overwhelming QCD background. In this task, we find that augmenting a standard architecture with our method results in a \ensuremath{2.3\times} improvement in rejection score.

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