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..
Maximizing Influence in an Ising Network: A Mean-Field Optimal Solution
Authors: Christopher Lynn, Daniel D. Lee
NeurIPS 2016 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We apply our algorithm on random and real-world networks, demonstrating, remarkably, that the MF optimal external fields (i.e., the external fields which maximize the MF magnetization) shift from focusing on high-degree individuals at high temperatures to focusing on low-degree individuals at low temperatures. We present numerical experiments to probe the structure and performance of MF optimal external fields. |
| Researcher Affiliation | Academia | Christopher W. Lynn Department of Physics and Astronomy University of Pennsylvania EMAIL Daniel D. Lee Department of Electrical and Systems Engineering University of Pennsylvania EMAIL |
| Pseudocode | Yes | Algorithm 1: An ϵ-approximation to MF-IIM Input: System (N, J, b, β) for which there exists a stable non-negative steady-state, budget H, accuracy parameter ϵ > 0 Output: External field h that approximates a MF optimal external field h t = 0; h(0) FH; α (0, 1 L) ; repeat M MF (b+h(t)) i χMF ij (b + h(t)); h(t + 1) = PFH h(t) + α h M MF (b + h(t)) ; t++; until M MF (b + h ) M MF (b + h(t)) ϵ; h = h(t); |
| Open Source Code | No | The paper does not provide an explicit statement or link to open-source code for the methodology described. |
| Open Datasets | Yes | We consider a real-world collaboration network (Figure 3) composed of 904 individuals, where each edge is unweighted and represents the co-authorship of a paper on the ar Xiv [26]. We note that co-authorship networks are known to capture many of the key structural features of social networks [27]. For b = 0 and H = 40, the center plot in Figure 3 illustrates the sharp shift in the solution to MF-IIM at βc = 0.05 from highto low-degree nodes. Furthermore, the right plot in Figure 3 compares the performance of the MF optimal external field with the node-selection heuristics described above, where we again consider the system at βc as a worst-case scenario, demonstrating that Algorithm 1 is scalable and performs well on real-world networks. [26] J. Leskovec and A. Krevl. SNAP Datasets: Stanford large network dataset collection, June 2014. |
| Dataset Splits | No | The paper describes experiments on various networks (hub-and-spoke, stochastic block, collaboration network) and compares performance, but it does not specify any explicit training, validation, or test dataset splits. |
| Hardware Specification | No | The paper does not provide specific details about the hardware (e.g., CPU/GPU models, memory, or cloud instances) used for running the numerical simulations. |
| Software Dependencies | No | The paper does not specify any software dependencies with version numbers (e.g., programming languages, libraries, or solvers) used for its implementation or experiments. |
| Experiment Setup | Yes | Algorithm 1: An ϵ-approximation to MF-IIM Input: System (N, J, b, β) for which there exists a stable non-negative steady-state, budget H, accuracy parameter ϵ > 0 Output: External field h that approximates a MF optimal external field h t = 0; h(0) FH; α (0, 1 L) ; repeat M MF (b+h(t)) i χMF ij (b + h(t)); h(t + 1) = PFH h(t) + α h M MF (b + h(t)) ; t++; until M MF (b + h ) M MF (b + h(t)) ϵ; h = h(t); The left plot in Figure 1 compares the average degree of the MF and exact optimal external fields over a range of temperatures for an external field budget H = 1, verifying that the solution to MF-IIM shifts from focusing on high-degree nodes at low interaction strengths to low-degree nodes at high interaction strengths. For b = 0 and H = 20, the center plot in Figure 2 demonstrates that the solution to MF-IIM shifts from focusing on Block 1 at low β to focusing on Block 2 at high β and that the shift occurs near βc. For b = 0 and H = 40, the center plot in Figure 3 illustrates the sharp shift in the solution to MF-IIM at βc = 0.05 from highto low-degree nodes. |