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 Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
Nonlinear Laplacians: Tunable principal component analysis under directional prior information
Authors: Yuxin Ma, Dmitriy Kunisky
NeurIPS 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We find both theoretically and empirically that, if σ is chosen appropriately, then nonlinear Laplacian spectral algorithms substantially outperform direct spectral algorithms, while retaining the conceptual simplicity of spectral methods compared to broader classes of computations like approximate message passing or general first order methods. The other columns show the empirical eigenvalue distributions for various signal strengths β. The maximum eigenvalue is indicated with an arrow to highlight outliers, and the analytic prediction of the limiting eigenvalue density is plotted in red. |
| Researcher Affiliation | Academia | Yuxin Ma Applied Mathematics & Statistics Johns Hopkins University Baltimore, MD 21211 EMAIL Dmitriy Kunisky Applied Mathematics & Statistics Johns Hopkins University Baltimore, MD 21211 EMAIL |
| Pseudocode | No | The paper describes algorithms in prose and mathematical notation (e.g., Definition 2.2 for σ-Laplacian spectral algorithms) but does not include a distinct block labeled "Pseudocode" or "Algorithm". |
| Open Source Code | Yes | The code used to generate the results presented in this paper is also available online anonymously at https://github.com/yuxinma98/Nonlinear Laplacian. |
| Open Datasets | No | To find the optimized σ, we generate a dataset of i.i.d. pairs (Yi, yi) according to the following procedure: We fix parameters n0 and β0. |
| Dataset Splits | Yes | For the method of optimizing σ using an MLP to learn from data, the neural network was implemented with the Py Torch framework and trained on a randomly generated dataset of size n = 5000, split into training, validation, and test sets in a ratio of 0.6 : 0.1 : 0.3. |
| Hardware Specification | Yes | Training was conducted for 350 epochs on a single NVIDIA A5000 GPU. |
| Software Dependencies | No | The neural network was implemented with the Py Torch framework. We compute the integrals above using the standard numerical integration methods built into the Num Py library. We use the implementation of Brent s method in the Sci Py library. |
| Experiment Setup | Yes | We use L = 8, h = 20, and the tanh activation function. Training was performed by minimizing the binary cross-entropy loss using the Adam W optimizer with an initial learning rate of 0.01 and weight decay of 0.01. The learning rate was automatically halved if the validation loss did not improve for 10 consecutive epochs. Training was conducted for 350 epochs. |