Identifying latent distances with Finslerian geometry
Authors: Alison Pouplin, David Eklund, Carl Henrik Ek, Søren Hauberg
TMLR 2023 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We want to illustrate cases where these metrics differ in practice. For this, we use two synthetic datasets, consisting of pinwheel and concentric circles mapped to a sphere, and four real-world datasets... We trained a GPLVM... to learn a latent manifold. From the learnt model, we can access the Riemannian and Finsler metrics, and minimise their respective curve energies to obtain the corresponding geodesics. |
| Researcher Affiliation | Academia | Alison Pouplin EMAIL Technical University of Denmark, David Eklund EMAIL Research Institutes of Sweden, Carl Henrik Ek EMAIL University of Cambridge, Søren Hauberg EMAIL Technical University of Denmark |
| Pseudocode | No | The paper describes mathematical concepts, theorems, and proofs for Finslerian geometry and its application, but it does not contain any explicitly labeled pseudocode or algorithm blocks. |
| Open Source Code | Yes | Code availability The code used for the experiments in this study is available on Git Hub at https://github.com/a-pouplin/ latent_distances_finsler. |
| Open Datasets | Yes | For this, we use two synthetic datasets... and four real-world datasets: a font dataset (Campbell & Kautz, 2014), a dataset representing single-cells (Guo et al., 2010), MNIST (Le Cun, 1998) and fashion MNIST (Xiao et al., 2017). |
| Dataset Splits | No | The paper mentions training GPLVM models on various datasets (synthetic, font, q PCR, MNIST, Fashion MNIST) but does not provide specific details on how these datasets were split into training, validation, or test sets for experiment reproduction. |
| Hardware Specification | No | The paper discusses software tools and models used (Stochman, Pyro, GPLVM) but does not provide specific hardware details such as CPU/GPU models, memory, or accelerator types used for running the experiments. |
| Software Dependencies | No | The paper mentions Stochman (Detlefsen et al., 2021), Pyro (Bingham et al., 2019), and Pytorch. While publication years are provided for Stochman and Pyro, these are not specific software version numbers. No version is given for Pytorch. |
| Experiment Setup | Yes | Table 2: Description of the datasets trained with a GP-LVM. It includes parameters such as 'Number of steps', 'learning rate', 'lengthscale', 'variance', and 'noise' for various datasets like pinwheel, font data, and q PCR. |