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..
Escaping saddle points without Lipschitz smoothness: the power of nonlinear preconditioning
Authors: Alexander Bodard, Panagiotis Patrinos
NeurIPS 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | 4 Numerical validation Lastly, we illustrate some merits of nonlinear preconditioning, and validate the complexity result of Theorem 3.6 numerically. The source code is publicly available.2 Nonlinear preconditioning for symmetric matrix factorization For the symmetric matrix factorization problem (5) with n = 2 and r = 1, Fig. 2 presents a 2D visualization of the level curves of the objective, along with the iterates of both vanilla gradient descent (GD) and the preconditioned variant (P-GD) with ϕ(x) = cosh( x ) 1. ... Fast avoidance of saddle points Fig 3 validates the fast escape of saddle points by Algorithm 1. We consider the octopus objective [13] which was constructed such that GD takes exponential time to escape saddle points. We select all hyperparameters as in [13, 5], and set the only additional hyperparameter L = 1. We compare against vanilla GD and perturbed vanilla GD [13, Alg 1], and vary the constant L {1, 1.5, 2, 3} and dimension n {5, 10}, thus creating counterparts to [11, Figs 3 and 4]. We observe that algorithm 1 performs similar to perturbed vanilla GD, and also scales in a similar way with respect to n and L. This validates the complexity result from Theorem 3.6. |
| Researcher Affiliation | Academia | Alexander Bodard ESAT-STADIUS & Leuven.AI KU Leuven EMAIL Panagiotis Patrinos ESAT-STADIUS & Leuven.AI KU Leuven EMAIL |
| Pseudocode | Yes | Algorithm 1 Perturbed preconditioned gradient descent REQUIRE: x0 Rn, γ, λ > 0, perturbation radius r > 0, time interval T > 0, tolerance G > 0 |
| Open Source Code | Yes | The source code is publicly available.2 https://github.com/alexanderbodard/escaping_saddles_with_preconditioning |
| Open Datasets | No | No specific publicly available dataset is provided. The paper mentions: "We consider the octopus objective [13] which was constructed such that GD takes exponential time to escape saddle points.", which refers to a synthetic objective function rather than a traditional dataset. |
| Dataset Splits | No | No specific dataset splits are mentioned in the paper. The numerical validation uses a synthetic objective function without traditional data partitioning. |
| Hardware Specification | No | The paper does not provide specific details about the hardware used for the experiments. The NeurIPS checklist indicates: "The illustrative experiments in this paper required negligible compute." |
| Software Dependencies | No | The paper does not explicitly list specific software dependencies with version numbers. While source code is available, the paper itself does not detail these dependencies. |
| Experiment Setup | Yes | We select all hyperparameters as in [13, 5], and set the only additional hyperparameter L = 1. We compare against vanilla GD and perturbed vanilla GD [13, Alg 1], and vary the constant L {1, 1.5, 2, 3} and dimension n {5, 10}, thus creating counterparts to [11, Figs 3 and 4]. Algorithm 1 also lists its required parameters: x0 Rn, γ, λ > 0, perturbation radius r > 0, time interval T > 0, tolerance G > 0, with parameters given in (12) and (13). |