Lie Neurons: A General Adjoint-Equivariant Neural Network for Semisimple Lie Algebras
Primary Area: learning on graphs and other geometries & topologies
Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.
Keywords: geometric learning, equivariance, representation learning, lie group
Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2024/AuthorGuide.
Abstract: In this paper, we propose an adjoint-equivariant neural network that takes Lie algebra data as input. Various types of equivariant neural networks have been proposed in the literature, which treat the input data as elements in a vector space carrying certain types of transformations. In comparison, we aim to process inputs that are transformations between vector spaces. The change of basis on transformation is described by conjugations, inducing the adjoint-equivariance relationship that our model is designed to capture. Leveraging the invariance property of the Killing form, the proposed network is a general framework that works for arbitrary semisimple Lie algebras. Our network possesses a simple structure that can be viewed as a Lie algebraic generalization of a multi-layer perceptron (MLP). This work extends the application of equivariant feature learning. As an example, we showcase its value in homography modeling using $\mathfrak{sl}(3)$ Lie algebra.
Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors' identity.
No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.
Submission Number: 8125
Loading