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..
Finite-Time Analysis of Stochastic Nonconvex Nonsmooth Optimization on the Riemannian Manifolds
Authors: Emre Sahinoglu, Youbang Sun, Shahin Shahrampour
NeurIPS 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | The numerical results support the theory and demonstrate the practical effectiveness of the algorithms. We provide the following numerical experiments to validate our results. |
| Researcher Affiliation | Academia | Emre Sahinoglu Northeastern University EMAIL Youbang Sun Tsinghua University EMAIL Shahin Shahrampour Northeastern University EMAIL |
| Pseudocode | Yes | Algorithm 1 Riemannian Online to Non Convex (RO2NC) |
| Open Source Code | Yes | The anonymized code for the numerical experiments is available at the following https://github.com/emreesahinoglu/RO2NC-Riemannian Nonsmooth.git |
| Open Datasets | No | We consider the sparse principal component problem defined on the Euclidean unit sphere Sn 1 in Rn. The objective function can be written as minx Sn 1{ x Ax + µ x 1}, where A = E[νν ] and ν N(0, A) is sampled from a multivariate Gaussian distribution. |
| Dataset Splits | No | The paper describes a synthetic dataset generation process for its numerical experiments but does not involve splitting an existing dataset into training, validation, and test sets. It mentions parameters for running epochs and iterations, not data splits: "We run Algorithm 1 using both parallel transport and projection operations for K = 500 epochs, each consisting of T = 200 iterations." |
| Hardware Specification | No | The experiments are toy examples. They can be run on a laptop. |
| Software Dependencies | No | The paper does not explicitly mention specific software dependencies with version numbers. While code is provided, the paper text itself does not list software like Python, PyTorch, etc., along with their versions. |
| Experiment Setup | Yes | For RO2NC, we choose our retraction curves to be Retrx(v) = (x + v)/ x + v , and we use exponential mappings for calculating the gradient estimator in ZO-RO2NC. We run Algorithm 1 using both parallel transport and projection operations for K = 500 epochs, each consisting of T = 200 iterations. Convergence of the algorithms depends on the selection of parameters D and η. For both settings, η is chosen orders of magnitude smaller than D. |