Convergence of linear programming hierarchies for Gibbs states of spin systems
Authors: Hamza Fawzi, Omar Fawzi
TMLR 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this paper we study certified algorithms to approximate µ(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 µ(f). ... The main result in this section shows that if µ has spatial mixing, then the linear programming-based upper and lower bounds will converge exponentially fast (in dist(supp(f), Λc)) to µ(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. |