论文标题
平均现场信息Hessian矩阵图
Mean field information Hessian matrices on graphs
论文作者
论文摘要
我们在有限图上得出了平均场信息Hessian矩阵。 “信息”是指概率单纯性的熵功能。 “平均场”是指在图形上支持的概率的非线性权重函数。这两个概念定义了平均场最佳运输类型度量。在这个度量空间中，我们首先在图形上得出了能量的Hessian矩阵，包括线性，相互作用能，熵。我们将其最小的特征值命名为图表上的平均电场RICCI曲率边界。接下来，我们提供了两点空间和图形产品的示例。我们上次介绍了拟议矩阵的几个应用。例如，我们证明Costa的熵功率不平等在两点空间上。
We derive mean-field information Hessian matrices on finite graphs. The "information" refers to entropy functions on the probability simplex. And the "mean-field" means nonlinear weight functions of probabilities supported on graphs. These two concepts define a mean-field optimal transport type metric. In this metric space, we first derive Hessian matrices of energies on graphs, including linear, interaction energies, entropies. We name their smallest eigenvalues as mean-field Ricci curvature bounds on graphs. We next provide examples on two-point spaces and graph products. We last present several applications of the proposed matrices. E.g., we prove discrete Costa's entropy power inequalities on a two-point space.
