In Coevolving Latent Space Networks with Attractors (CLSNA) models, nodes in a latent space represent social actors, and edges indicate their dynamic interactions. Attractors are added at the latent level to capture the notion of attractive and repulsive forces between nodes, borrowing from dynamical systems theory. However, CLSNA reliance on MCMC estimation makes scaling difficult, and the requirement for nodes to be present throughout the study period limit practical applications. We address these issues by (i) introducing a Stochastic gradient descent (SGD) parameter estimation method, (ii) developing a novel approach for uncertainty quantification using SGD, and (iii) extending the model to allow nodes to join and leave over time. Simulation results show that our extensions result in little loss of accuracy compared to MCMC, but can scale to much larger networks. We apply our approach to the longitudinal social networks of members of US Congress on the social media platform X. Accounting for node dynamics overcomes selection bias in the network and uncovers uniquely and increasingly repulsive forces within the Republican Party.

翻译：在含吸引子的共演化潜在空间网络（CLSNA）模型中，潜在空间中的节点代表社会行为者，边表示其动态交互作用。借鉴动力系统理论，在潜在层面引入吸引子以捕捉节点间的吸引力和排斥力概念。然而，CLSNA对MCMC估计的依赖使其难以扩展，且要求节点在整个研究期内持续存在限制了实际应用。我们通过以下方式解决了这些问题：（i）引入随机梯度下降（SGD）参数估计方法，（ii）开发了基于SGD的不确定性量化新方法，（iii）扩展模型以允许节点随时间加入和离开。仿真结果表明，与MCMC相比，本扩展方法的精度损失极小，但可扩展至规模更大的网络。我们将该方法应用于社交媒体平台X上美国国会议员的纵向社交网络。考虑节点动态性克服了网络中的选择偏差，并揭示了共和党内部独特且日益增强的排斥力。