用深度模型识别三态投票模型中的四种动态轨迹,实现临界状态实时感知。
Classifying Directional Trajectories Near Criticality in the Three-State Majority-Vote Model with Deep Belief Networks and Bidirectional GRUs

- 先用深度信念网络提取静态快照特征,再用双向GRU分析时间序列轨迹。
- 双向GRU在50步序列上对四类轨迹分类接近完美,准确率超99%。
- 可实时监测系统动态,适合研究临界相变与群体行为建模者使用。
本文研究深度信念网络(DBN)和双向门控循环单元(Bi-GRU)学习的潜在表征能否区分三态多数投票模型(MV3)中四种动态轨迹:从无序接近、从有序接近、向无序离开、向有序离开。DBN通过784→4096→225→81的架构,在无监督预训练下将每个晶格快照编码为81维潜在向量;t-SNE分析显示其潜在空间仅部分分离四类轨迹,说明仅基于静态样本的模型无法完整捕捉时间方向性。而以长度T=50的DBN编码快照序列为输入的两层Bi-GRU分类器,在训练集与测试集上均实现近乎完美的四类轨迹分离。进一步将训练好的Bi-GRU应用于连续的MV3动力学过程,验证了其可实时感知系统当前动态状态的能力。该工作建立了一种检测与分类代理型意见动力学模型中临界转变的分层范式。
原文摘要 · Abstract (English)
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.
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