Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in [1].
Estimation of Local Geometric Structure on Manifolds from Noisy Data
Authors: Yariv Aizenbud, Barak Sober
JMLR 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | The code for the algorithm in this paper, along with examples, can be found in https://github.com/aizeny/manapprox. In the first toy case, the manifold M is a circle of radius 10 in R2. The dataset consists of 5000 points. We start with some sample (illustrated in red in Figure 6), project it onto the circle (in Figure 6, the circle is marked in blue, and the projected point in green), and than move the point in some direction, project it again (shown in another green point in Figure 6), etc. |
| Researcher Affiliation | Academia | Yariv Aizenbud EMAIL Department of Applied Mathematics School of Mathematical Sciences Tel Aviv University Tel Aviv 69978, Israel. Barak Sober EMAIL Department of Statistics and Data Science Center for Digital Humanities The Hebrew University of Jerusalem Mount Scopus, Jerusalem 91905, Israel |
| Pseudocode | Yes | Algorithm 1 Step 1: Find an initial coordinate system. Algorithm 2 Step 2: estimating the manifold from a good initial guess. Algorithm 3 Step 1: in practice. Algorithm 4 Step 2: in practice. |
| Open Source Code | Yes | The code for the algorithm in this paper, along with examples, can be found in https://github.com/aizeny/manapprox. |
| Open Datasets | Yes | In the second example, we took a 3d model of an airplane1, rotated it in the z-axis, and took 2000 snapshots. Each snapshot is an image of 290 209 gray-scale pixels. The input data set consist of the unsorted images, sampled from a one dimensional manifold embedded in R60,610. Several such images appear in Figure 7. Starting from some image, we create a movie of the rotating airplane. The movie can be found in https://youtu.be/a HYy Uvu1Q-8, and the code for generating it can be found in https://github.com/aizeny/manapprox. 1. http://3dmag.org/en/market/download/item/4740/ |
| Dataset Splits | No | The paper describes using a dataset of 5000 points for the circle example and 2000 snapshots for the airplane example, but it does not provide any specific information regarding training, testing, or validation splits for these datasets. |
| Hardware Specification | No | The paper does not provide any specific hardware details such as GPU/CPU models, processor types, or memory used for running its experiments. |
| Software Dependencies | No | The paper describes algorithms and refers to theoretical underpinnings but does not explicitly list any specific software dependencies or libraries with version numbers (e.g., Python 3.x, PyTorch 1.x) that were used for implementation or experimentation. |
| Experiment Setup | No | The paper describes application examples like a 'geodesic walk on a circle' and creating a 'movie of the rotating airplane.' While it outlines the iterative process, it does not provide specific experimental setup details such as hyperparameter values (e.g., learning rates, batch sizes, number of epochs) or other system-level training settings like the step size (epsilon) for the geodesic walk. |