Discovering Group Structures via Unitary Representation Learning
Keywords: group theory, representation theory, representation learning, symmetry discovery, symbolic relationship
Abstract: Discovering group structures within data poses a fundamental challenge across diverse scientific domains. A key obstacle is the non-differentiable nature of group axioms, hindering their integration into deep learning frameworks. To address this, we introduce a novel differentiable approach leveraging the representation theory of finite groups. Our method features a unique network architecture that models interactions between group elements via matrix multiplication of their representations, along with a regularizer promoting the unitarity of these representations. The interplay between the network architecture and the unitarity condition implicitly encourages the emergence of valid group structures. Evaluations demonstrate our method's ability to accurately recover group operations and their unitary representations from partial observations, achieving significant improvements in sample efficiency and a $\times 1000$ speedup over the state of the art. This work lays the foundation for a promising new paradigm in automated algebraic structure discovery, with potential applications across various domains, including automatic symmetry discovery for geometric deep learning.
Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
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.
Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2025/AuthorGuide.
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: 13021
Loading