Our technical contribution is mainly two-fold.

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ELBO can be formulated into maximizing the objective of V AE as in Eq. (4). Based on the condition (i.e.subject to) of the loss function, we enforce z In total 3,780 MOFs were selected for the experiment. QMOF dataset was summarized in Appendix, Table 1. Meshes in MeshSeg dataset can be formed into graphs of triangle grids. The statistics of MeshSeg dataset has been summarized in Appendix, Table 1.

Their generative modeling has great potential in real-world applications such as material design and graphics synthesis. Classical models either rely on domain-specific predefined generation principles (e.g., in crystal net design),

CorrV AE, that recovers semantics and the correlation of properties through disentangled latent vectors.

The Friedkin-Johnsen (FJ) model has been extensively explored and validated, spanning applications in social science, systems and control, game theory, and algorithmic research. In this paper, we introduce an advanced generalization of the FJ model, termed FJ-MM which incorporates both memory effects and multi-hop (higher-order neighbor) influence. This formulation allows agents to naturally incorporate both current and previous opinions at each iteration stage. Our numerical results demonstrate that incorporating memory and multi-hop influence significantly reshapes the opinion landscape; for example, the final opinion profile can exhibit reduced polarization. We analyze the stability and equilibrium properties of the FJ-MM model, showing that these properties can be reduced to those of a comparison model--namely, the standard FJ model with a modified influence matrix. This reduction enables us to leverage established stability results from FJ dynamics. Additionally, we examine the convergence rate of the FJ-MM model and demonstrate that, as can be expected, the time lags introduced by memory and higher-order neighbor influences result in slower convergence.