A Classification of $G$-invariant Shallow Neural Networks
Authors: Devanshu Agrawal, James Ostrowski
NeurIPS 2022 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Using a code implementation, we enumerate the G-SNN architectures for some example groups G and visualize their structure. Using our code implementation, we enumerated all irreducible G-SNN architectures for one permutation representation of every group G, |G| 8, up to isomorphism. We report the number of architectures, broken down by type, for each group in Table 1 (see Supp. C.1; a discussion is included there as well). Script execution time for each group was under 2 seconds. |
| Researcher Affiliation | Academia | Devanshu Agrawal & James Ostrowski Department of Industrial and Systems Engineering University of Tennessee Knoxville, TN 37996 dagrawa2@vols.utk.edu, jostrows@utk.edu |
| Pseudocode | No | The paper describes theoretical concepts, proofs, and a classification algorithm but does not include any explicitly labeled 'Pseudocode' or 'Algorithm' blocks. |
| Open Source Code | Yes | Code for our implementation and for reproducing all results in this paper is available at: https://github.com/dagrawa2/gsnn_classification_code. |
| Open Datasets | No | The paper focuses on theoretical classification and enumeration of neural network architectures, not on training models with specific datasets. Therefore, it does not mention the use of any publicly available or open datasets for training or evaluation. |
| Dataset Splits | No | The paper is primarily theoretical, focusing on the classification and enumeration of G-SNN architectures. It does not involve training machine learning models on datasets that would require explicit training, validation, or test splits. |
| Hardware Specification | No | The paper does not provide any specific details regarding the hardware used for running the code implementation, such as GPU models, CPU types, or cloud computing resources. |
| Software Dependencies | Yes | We implemented the enumeration algorithm using a combination of GAP and Python; our implementation currently supports, in principle, all finite permutation groups G < P(m). and GAP. GAP Groups, Algorithms, and Programming, Version 4.11.1. https://www.gap-system.org, 2021. |
| Experiment Setup | Yes | To visualize these architectures, we set w = [1, 0] , a = 1, b = 0.5, c = 0, and d = 0 in Thm. 4 (b). |