Discovering Group Structures via Unitary Representation Learning
Authors: Dongsung Huh
ICLR 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | 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 1000 speedup over the state of the art. |
| Researcher Affiliation | Industry | Dongsung Huh IBM Research EMAIL |
| Pseudocode | Yes | The main implementation of Hyper Cube is shown below. 1 import torch 3 def Hyper Cube_product(A,B,C): 4 return torch.einsum( aij,bjk,cki->abc , A,B,C) / A.shape[0] 6 def Hyper Cube_regularizer(A,B,C): 7 def helper(M,N): 8 MM = torch.einsum( aim,aij->mj , M,M) 9 NN = torch.einsum( bjk,bmk->jm , N,N) 10 return torch.einsum( mj,jm-> , MM, NN) 11 return (helper(A,B) + helper(B,C) + helper(C,A) ) / A.shape[0] |
| Open Source Code | No | The paper includes a code snippet labeled "The main implementation of Hyper Cube is shown below" in Appendix A, but it does not provide a statement about releasing the full source code for the methodology or a link to a code repository. |
| Open Datasets | Yes | We evaluate Hyper Cube and Hyper Cube-SE on diverse BOC datasets from Power et al. (2022), encompassing a wide spectrum of group and non-group operations (details in Appendix B). |
| Dataset Splits | Yes | Figure 3 compares the effect of different regularization strategies on the model s learning dynamics on the symmetric group S3 with 60% of the Cayley table sampled as training data. |
| Hardware Specification | Yes | GPU execution time remains nearly constant with increasing n (up to n = 200, the maximum size that fits in the 16GB memory of a Tesla V100 GPU). |
| Software Dependencies | No | The paper mentions "PyTorch" in the context of `einsum` operations and shows `import torch` in the code snippet. However, it does not specify a version number for PyTorch or any other software dependency. |
| Experiment Setup | Yes | We employ full-batch gradient descent to optimize the regularized loss with learning rate of 0.5 and momentum of 0.5. For the small scale experiments in Section 6, the Hyper Cube regularizer coefficient is set to ϵ = 0.1. For the larger scale experiments in Section 7, we use ϵ = 0.05 for Hyper Cube and ϵ = 0.01 for Hyper Cube-SE. |