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：在含吸引子共演化潜空间网络（CLSNA）模型中，潜空间中的节点代表社会行动者，边则表征其动态交互。借鉴动力系统理论，我们在潜层引入吸引子机制以捕捉节点间的吸引与排斥力。然而，CLSNA方法依赖MCMC估计导致扩展困难，且要求节点在整个研究时段持续存在限制了实际应用。我们通过以下方式解决这些问题：（i）引入基于随机梯度下降（SGD）的参数估计方法；（ii）开发了一种利用SGD进行不确定性量化的新方法；（iii）拓展模型允许节点随时间加入和退出。仿真结果表明，相较于MCMC方法，我们的扩展方案在保持精度的同时可扩展至更大规模的网络。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。通过考虑节点动态性，我们克服了网络中的选择偏差，并揭示了共和党内部独特且渐强的排斥力。