A Wigner-Eckart Theorem for Group Equivariant Convolution Kernels
Authors: Leon Lang, Maurice Weiler
ICLR 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | This work provides such a characterization for the practically relevant case of G being any compact group. Our investigation is motivated by a striking analogy between the constraints underlying steerable kernels on the one hand and spherical tensor operators from quantum mechanics on the other hand. By generalizing the famous Wigner-Eckart theorem for spherical tensor operators, we prove that steerable kernel spaces are fully understood and parameterized in terms of 1) generalized reduced matrix elements, 2) Clebsch Gordan coefficients, and 3) harmonic basis functions on homogeneous spaces. |
| Researcher Affiliation | Academia | Leon Lang AMLab, CSL University of Amsterdam l.lang@uva.nl Maurice Weiler AMLab, QUVA Lab University of Amsterdam m.weiler.ml@gmail.com |
| Pseudocode | No | The paper does not contain structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not provide concrete access to source code. |
| Open Datasets | No | The paper is theoretical and does not conduct experiments that would use a dataset for training. |
| Dataset Splits | No | The paper is theoretical and does not conduct experiments that would require dataset splits. |
| Hardware Specification | No | The paper focuses on theoretical contributions and does not describe experiments that would require hardware specifications. |
| Software Dependencies | No | The paper focuses on theoretical contributions and does not describe experiments that would require specific software dependencies with version numbers. |
| Experiment Setup | No | The paper focuses on theoretical contributions and does not describe experiments with setup details or hyperparameters. |