AI 中文总结
本研究用DBN与Bi-GRU处理MV3轨迹分类问题，DBN编码静态快照，Bi-GRU实现四类轨迹近乎完美分离，可实时感知MV3动态 regime，为意见动力学模型临界转变检测提供分层架构。
AI 中文摘要
本研究探讨深度置信网络（Deep Belief Network, DBN）与双向门控循环单元（Bidirectional Gated Recurrent Unit, Bi-GRU）学习到的潜在表示，能否区分三态多数投票模型（three-state majority vote model, MV3）中四种动态不同的轨迹类型：从无序趋近、从有序趋近、向无序偏离、向有序偏离。DBN以无监督方式在静态平衡样本上预训练，输入层采用高斯-伯努利受限玻尔兹曼机，架构为784→4096→225→81，将每个格点快照编码为81维潜在向量。对DBN潜在空间的t-SNE分析显示，四种轨迹类型仅实现部分分离，反映出在静态构型上训练的模型无法完全解析定向时间结构。两层Bi-GRU分类器在长度T=50的DBN编码快照序列上训练，其隐藏状态空间中四种轨迹类型实现近乎完美的分离，训练集与测试集的t-SNE可视化均证实了这一点。此外，将训练后的Bi-GRU滑动窗口应用于连续MV3动力学，可实时感知系统当前的动态 regime。这些结果为基于智能体的意见动力学模型中临界转变的检测与分类，建立了一种有原则的分层架构。
英文摘要
In this work, we investigate whether the latent representations learned by a Deep Belief Network (DBN) and a Bidirectional Gated Recurrent Unit (Bi-GRU) can discriminate among four dynamically distinct trajectory types in the three-state majority vote model (MV3): approach from disorder, approach from order, departure to disorder, and departure to order. The DBN, pre-trained in an unsupervised manner on static equilibrium samples via a Gaussian-Bernoulli Restricted Boltzmann Machine input layer and architecture $784 \to 4096 \to 225 \to 81$, encodes each lattice snapshot into an 81-dimensional latent vector. A t-SNE analysis of the DBN latent space reveals only partial separation of the four trajectory types, reflecting the fact that a model trained on static configurations cannot fully resolve directional temporal structure. A two-layer Bi-GRU classifier, trained on sequences of DBN-encoded snapshots of length $T = 50$, achieves near-perfect separation of all four trajectory types in its hidden state space, as confirmed by t-SNE visualization on both training and test sets. Furthermore, a sliding-window application of the trained Bi-GRU to continuous MV3 dynamics demonstrates its ability to sense the system's current dynamical regime in real-time. These results establish a principled hierarchical architecture for detecting and classifying critical transitions in agent-based opinion dynamics models.
Comments8 pages, 6 figures, to be published in AIxSET 2026
