Equivariant Frames and the Impossibility of Continuous Canonicalization
Authors: Nadav Dym, Hannah Lawrence, Jonathan W. Siegel
ICML 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section, we provide experimental evidence showing the advantage of preserving both continuity and invariance using robust frames. We consider the action of the permutation group Sn on two dimensional point clouds and leave the investigation of other group actions to future work. |
| Researcher Affiliation | Academia | 1Faculty of Mathematics, Faculty of Computer Science, Technion, Israel 2Department of Electrical Engineering and Computer Science, MIT, MA, USA 3Department of Mathematics, Texas A&M University, TX, USA. |
| Pseudocode | No | No explicit pseudocode or algorithm blocks were found. |
| Open Source Code | Yes | Code for reproducing this experiment can be found at https://github.com/jwsiegel2510/Sn-invariant-weighted-frames |
| Open Datasets | Yes | Starting from the MNIST dataset, we processed the image of each digit into a two-dimensional point cloud containing 100 points, ordered randomly. |
| Dataset Splits | No | No explicit training/validation/test dataset splits (e.g., percentages or absolute counts) were provided. |
| Hardware Specification | No | No specific hardware specifications (e.g., GPU/CPU models, memory details, or cluster configurations) used for running the experiments were provided. |
| Software Dependencies | No | No specific software dependencies with version numbers (e.g., library names with their exact versions) were provided. |
| Experiment Setup | Yes | All models were trained for 60 epochs using SGD with momentum 0.9 and a step size of 0.01, dropping to 0.001 after 30 epochs. The network was an MLP with 3 hidden layers of sizes 150, 100, and 50, with an input size of 200 and output of size 10. |