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..
A Nullspace Property for Subspace-Preserving Recovery
Authors: Mustafa D Kaba, Chong You, Daniel P Robinson, Enrique Mallada, Rene Vidal
ICML 2021 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | This paper derives a necessary and sufficient condition for subspace-preserving recovery that is inspired by the classical nullspace property. Based on this novel condition, called here the subspace nullspace property, we derive equivalent characterizations that either admit a clear geometric interpretation that relates data distribution and subspace separation to the recovery success, or can be verified using a finite set of extreme points of a properly defined set. We further exploit these characterizations to derive new sufficient conditions, based on inner-radius and outer-radius measures and dual bounds, that generalize existing conditions and preserve the geometric interpretations. Our primary goal is to present an in-depth theoretical analysis of subspace-preserving recovery through a nullspace-propertylike condition, and not necessarily to construct computationally efficient tools. |
| Researcher Affiliation | Collaboration | 1e Bay Inc., San Jose, CA, USA. 2Dept. of Elect. Eng. & Comp. Sci., University of California at Berkeley, Berkeley, CA, USA. 3Dept. of Ind. & Sys. Eng., Lehigh University, Bethlehem, PA, USA. 4Dept. of Elect. & Comp. Eng., Johns Hopkins University, Baltimore, MD, USA. 5MINDS & Dept. of Biom. Eng., Johns Hopkins University, Baltimore, MD, USA. |
| Pseudocode | No | The paper presents theorems, proofs, definitions, and mathematical formulations, but it does not include pseudocode or clearly labeled algorithm blocks. |
| Open Source Code | No | The paper does not mention or provide any link to open-source code for the methodology described. |
| Open Datasets | No | The paper is theoretical and does not conduct empirical experiments using datasets. It discusses theoretical conditions and properties but does not mention any specific dataset for training or evaluation. |
| Dataset Splits | No | The paper is theoretical and does not conduct empirical experiments, thus it does not mention dataset splits for training, validation, or testing. |
| Hardware Specification | No | The paper is theoretical and focuses on mathematical conditions and characterizations rather than experimental implementation. Therefore, it does not mention any hardware specifications used for experiments. |
| Software Dependencies | No | The paper is theoretical and presents mathematical conditions and proofs. It does not describe any experimental implementation or list software dependencies with version numbers. |
| Experiment Setup | No | The paper is theoretical and focuses on deriving mathematical conditions. It does not describe an experimental setup, hyperparameters, or training configurations. |