How Jellyfish Characterise Alternating Group Equivariant Neural Networks
Authors: Edward Pearce-Crump
ICML 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We provide a full characterisation of all of the possible alternating group (An) equivariant neural networks whose layers are some tensor power of Rn. In particular, we find a basis of matrices for the learnable, linear, An equivariant layer functions between such tensor power spaces in the standard basis of Rn. We also describe how our approach generalises to the construction of neural networks that are equivariant to local symmetries. The main contributions of this paper, which appear in Section 6 onwards, are as follows: 1. We are the first to show how the combinatorics underlying set partition diagrams, together with some jellyfish, serves as the theoretical foundation for constructing neural networks that are equivariant to the alternating group when the layers are some tensor power of Rn. 2. In particular, we find a basis for the learnable, linear, An equivariant layer functions between such tensor power spaces in the standard basis of Rn. 3. We extend our approach to show how to construct neural networks that are equivariant to local symmetries. |
| Researcher Affiliation | Academia | 1Department of Computing, Imperial College London, United Kingdom. Correspondence to: Edward Pearce Crump <ep1011@ic.ac.uk>. |
| Pseudocode | Yes | Algorithm 1 How to Calculate the Weight Matrix for an An Equivariant Linear Layer Mapping (Rn) k (Rn) l |
| Open Source Code | No | The paper discusses 'technical challenges when implementing Algorithm 1 given the current state of computer hardware' and 'significant engineering efforts will be needed', but does not provide any statement or link for open-source code for the methodology described. |
| Open Datasets | No | This paper is theoretical and does not involve training models on datasets. |
| Dataset Splits | No | This paper is theoretical and does not involve data splitting for validation. |
| Hardware Specification | No | The paper discusses the 'current state of computer hardware' as a general limitation for potential future implementation, but it does not specify any hardware used for experiments as it is a theoretical paper. |
| Software Dependencies | No | The paper provides theoretical characterizations and pseudocode, but does not list any specific software dependencies with version numbers for implementation. |
| Experiment Setup | No | This paper is theoretical and does not include an experimental setup with hyperparameters or training configurations. |