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..
Finding k in Latent $k-$ polytope
Authors: Chiranjib Bhattacharyya, Ravindran Kannan, Amit Kumar
ICML 2021 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | The paper introduces the notion of Interpolative Convex Rank(ICR) of a matrix, and shows that k = ICR of a subset smoothed data matrix where k is the number of vertices in Lk P (see details in Theorem 1). The paper introduces new techniques based on the hyperplane separator theorem for proving lower bounds on the ICR of a matrix (see details in Section 3.4). Under standard assumptions, the paper gives a polynomial time algorithm for finding the correct value of the number of vertices of the polytope K (see Theorem 18). |
| Researcher Affiliation | Collaboration | 1Department of Computer Science and Automation, IISc Bangalore, India 2Microsoft Research India Lab., Bangalore, India 3Department of Computer Science and Engineering, IIT Delhi, India. |
| Pseudocode | Yes | Algorithm 1 Algorithm for finding the number of extreme points of K. Algorithm 2 Algorithm for finding the approximations to the vertices of K. |
| Open Source Code | No | The paper does not provide any statement or link regarding the availability of open-source code for the described methodology. |
| Open Datasets | No | The paper is theoretical and does not describe experiments using a dataset, public or otherwise. |
| Dataset Splits | No | The paper is theoretical and does not describe experiments or dataset splits for training, validation, or testing. |
| Hardware Specification | No | The paper is theoretical and does not describe any specific hardware used for experiments. |
| Software Dependencies | No | The paper is theoretical and does not specify software dependencies with version numbers. |
| Experiment Setup | No | The paper is theoretical and does not describe any experimental setup or hyperparameters. |