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].
Diffeomorphism-based feature learning using Poincaré inequalities on augmented input space
Authors: Romain Verdière, Clémentine Prieur, Olivier Zahm
JMLR 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Numerical comparisons with existing methods from the literature (Bigoni et al., 2022; Zhang et al., 2019a; Teng et al., 2021) are presented. Our numerical demonstrations highlight the efficiency of our methodology in achieving accurate approximations across various high-dimensional test cases. Notably, in the small sample regime, employing dimension augmentation outperforms existing state-of-the-art methods. In Section 7, we compare numerically the proposed strategy with the existing nonlinear dimension reduction methods from the literature on several high dimensional functions, including a parametrized partial differential equation. |
| Researcher Affiliation | Academia | Romain Verdière EMAIL Univ. Grenoble Alpes, Inria, CNRS, Grenoble INP, LJK, 38000 Grenoble, France Clémentine Prieur EMAIL Univ. Grenoble Alpes, Inria, CNRS, Grenoble INP, LJK, 38000 Grenoble, France Olivier Zahm EMAIL Univ. Grenoble Alpes, Inria, CNRS, Grenoble INP, LJK, 38000 Grenoble, France |
| Pseudocode | No | The paper describes methods and algorithms using mathematical formulations and textual descriptions but does not include any explicitly labeled pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not contain an unambiguous sentence stating that code for the work described in this paper is being released, nor does it provide a direct link to a source-code repository. |
| Open Datasets | No | We consider the following benchmark functions u1(x), u2(x), u3(x)... The training points {xi}ntrain i=1 are sampled through a latin hypercube sampling optimized with maximin criterion, using the scikit-optimize library (Head et al., 2022). We generate this submanifold with the following application: ΨQ : Rmint Rd Z 7 (Z Q1Z, . . . , Z Qd Z) where Q = (Q1, . . . , Qd) (Zmint mint)d. In this setup, each component of ΨQ is a quadratic function. For a given Q, Z is sampled according to the probability distribution πZ and we compute X = ΨQ(Z) to generate the dataset. |
| Dataset Splits | Yes | The cost functions are minimized with the ADAM optimizer, a multi-start procedure is applied with 8 different randomly chosen starting points, after 300 ADAM steps the best candidate is selected and then optimized for 3000 additional steps. All this procedure is done with a learning rate of 0.01. f is also trained with the ADAM optimizer but without multi-start. The same learning rate is used and the learning process is stopped after 5000 ADAM steps or when the loss function reduces to 10 8. |
| Hardware Specification | Yes | All the simulations have been implemented with Py Torch 2.01 and tested on a laptop with a 4.7 GHz Intel Core i7 CPU and 32GB of DRAM memory. |
| Software Dependencies | Yes | All the simulations have been implemented with Py Torch 2.01 and tested on a laptop with a 4.7 GHz Intel Core i7 CPU and 32GB of DRAM memory. |
| Experiment Setup | Yes | The cost functions are minimized with the ADAM optimizer, a multi-start procedure is applied with 8 different randomly chosen starting points, after 300 ADAM steps the best candidate is selected and then optimized for 3000 additional steps. All this procedure is done with a learning rate of 0.01. f is also trained with the ADAM optimizer but without multi-start. The same learning rate is used and the learning process is stopped after 5000 ADAM steps or when the loss function reduces to 10 8. |