Maximizing Influence in an Ising Network: A Mean-Field Optimal Solution
Authors: Christopher Lynn, Daniel D. Lee
NeurIPS 2016 | Conference PDF | Archive PDF | Plain Text | 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 chlynn@sas.upenn.edu Daniel D. Lee Department of Electrical and Systems Engineering University of Pennsylvania ddlee@seas.upenn.edu |
| 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. |