Classifying Directional Trajectories Near Criticality in the Three-State Majority-Vote Model with Deep Belief Networks and Bidirectional GRUs

2026-08-18

AI Summary

研究使用DBN和Bi-GRU来区分三态多数投票模型中的四种动态轨迹类型，解决了基于静态样本训练的模型无法完全解析时间方向性结构的问题。

Abstract

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.

Problem

• Deep Belief Network
• Bidirectional Gated Recurrent Unit
• three-state majority vote model
• trajectory types

Innovation

• Deep Belief Network
• Bidirectional Gated Recurrent Unit
• three-state majority vote model
• t-SNE visualization
• critical transitions