Optimal Transport with Cyclic Symmetry
Authors: Shoichiro Takeda, Yasunori Akagi, Naoki Marumo, Kenta Niwa
AAAI 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Experiments show the effectiveness of our algorithms for LOT and EROT in synthetic/real-world data that has a strict/approximate cyclic symmetry structure. To validate the effectiveness of our algorithms, we conducted experiments on synthetic/real-world data that satisfy Assumption 1 strictly/approximately. |
| Researcher Affiliation | Industry | NTT Corporation, 1-1 Hikari-no-oka, Yokosuka-Shi, Kanagawa, 239-0847, Japan |
| Pseudocode | Yes | Algorithm 1: Fast Algorithm for C-LOT, Algorithm 2: Cyclic Sinkhorn Algorithm for C-EROT, Algorithm 3: Two-Stage Sinkhorn Algorithm for C-EROT with Approximate Cyclic Symmetry |
| Open Source Code | No | The paper states 'All the codes were implemented in Python.' but does not provide any explicit statement about code availability or a link to a repository. |
| Open Datasets | Yes | We tested our algorithms on the real-world case of mirror symmetry (n = 2) in Example 1 with the NYU Symmetry Database (Cicconet et al. 2017). |
| Dataset Splits | No | The paper does not explicitly provide specific training/test/validation dataset splits or cross-validation details for their experiments. |
| Hardware Specification | Yes | These experiments were performed on a Windows laptop with Intel Core i7-10750H CPU, 32 GB memory. |
| Software Dependencies | No | The paper mentions 'All the codes were implemented in Python.' and 'The network simplex algorithm was implemented using LEMON (Dezs o, J uttner, and Kov acs 2011).' but does not provide specific version numbers for Python or LEMON. |
| Experiment Setup | Yes | We set λ = 0.5 for the regularizer (3). we first run the cyclic Sinkhorn algorithm until the marginal error || (diag(bp)Kdiag(bq)) 1m β||2 is below 1.0 10 3 and then run the Sinkhorn algorithm until the difference between its objective function value and the value obtained by directly solving C-EROT with the Sinkhorn algorithm is below 1.0 10 4. |