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..
Hessian Eigenspectra of More Realistic Nonlinear Models
Authors: Zhenyu Liao, Michael W. Mahoney
NeurIPS 2021 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We also demonstrate our results empirically by showing that: 4. for a given response model (1), the Hessian eigenvalue distribution depends on the choice of loss function and the data/feature statistics in an intrinsic manner, e.g., bounded versus unbounded support and singleversus multi-bulk in Fig 2; and 5. there may exist two qualitatively different spikes one due to data signal µ and the other due to w or w and thus the underlying model which may appear on different sides of the main bulk, and their associated phase transition behaviors are characterized (Fig 4 versus 5). |
| Researcher Affiliation | Academia | Zhenyu Liao School of Electronic Information and Communications Huazhong University of Science and Technology, China EMAIL Michael W. Mahoney ICSI and Department of Statistics University of California, Berkeley, USA EMAIL |
| Pseudocode | No | The paper does not contain pseudocode or a clearly labeled algorithm block. |
| Open Source Code | No | The paper does not provide an unambiguous statement or link for the open-source code of the methodology described. |
| Open Datasets | No | The paper uses synthetic data generated with parameters such as 'xi i.i.d. N(µ, C)' and specified dimensions (e.g., 'p = 800, n = 6 000'), but does not mention or provide access information for a publicly available or open dataset in the traditional sense. |
| Dataset Splits | No | The paper does not explicitly provide training/test/validation dataset splits, as its empirical components are demonstrations based on theoretical models and generated data rather than typical machine learning experiments with distinct data splits. |
| Hardware Specification | No | The paper does not explicitly describe the hardware used to run its experiments. |
| Software Dependencies | No | The paper does not provide a reproducible description of ancillary software with specific version numbers. |
| Experiment Setup | Yes | Fig 1: 'eigenspectral properties of the Hessian of G-GLMs with p = 800, n = 6 000 and C = Ip.' Fig 2: 'p = 800, n = 6 000, logistic model in (2) with µ = 0, C = Ip, w = 0 and w = [ 1p/2, 1p/2]/ p.' Fig 4: 'p = 512 and n = 2 048.' Fig 5: 'p = 800 and n = 8 000.' |