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 [1].
Convergence of linear programming hierarchies for Gibbs states of spin systems
Authors: Hamza Fawzi, Omar Fawzi
TMLR 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this paper we study certified algorithms to approximate ยต(f) when f is a local function, i.e., depending only on variables in a set B V of small size. ... We study two hierarchies of linear programs giving upper and lower bounds on ยต(f). ... The main result in this section shows that if ยต has spatial mixing, then the linear programming-based upper and lower bounds will converge exponentially fast (in dist(supp(f), ฮc)) to ยต(f). ... We are now ready to state our main convergence theorem. |
| Researcher Affiliation | Academia | Hamza Fawzi1 and Omar Fawzi2 1DAMTP, University of Cambridge, United Kingdom 2Inria, ENS de Lyon, UCBL, LIP, France |
| Pseudocode | No | The paper does not contain any structured pseudocode or algorithm blocks. It describes mathematical methods and theorems. |
| Open Source Code | No | The paper does not provide any statements about releasing code or links to source code repositories for the described methodology. |
| Open Datasets | No | The paper is theoretical and focuses on 'Gibbs states of spin systems' and 'Ising models on a d-dimensional grid' which are mathematical models, not specific datasets used for empirical evaluation. Thus, it does not provide access information for open datasets. |
| Dataset Splits | No | This paper is theoretical and does not describe experiments with datasets, therefore it does not specify dataset splits. |
| Hardware Specification | No | The paper is theoretical and does not describe experimental implementation, hence no specific hardware details are provided. |
| Software Dependencies | No | The paper is theoretical and does not describe experimental implementation, hence no specific software dependencies or version numbers are provided. |
| Experiment Setup | No | This paper is theoretical and focuses on mathematical proofs and convergence rates, not on empirical experimentation. Therefore, it does not contain specific experimental setup details or hyperparameters. |