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arXiv Machine Learning By Mauricio A. Valle, Gonzalo A. Ruz

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

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The study explores whether a Deep Belief Network (DBN) and a Bidirectional Gated Recurrent Unit (Bi‑GRU) can distinguish four 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, trained unsupervised on static equilibrium snapshots, partially separates these trajectories in its 81‑dimensional latent space, while a two‑layer Bi‑GRU trained on sequences of DBN‑encoded snapshots achieves near‑perfect classification, as confirmed by t‑SNE visualizations on both training and test data. A sliding‑window application of the Bi‑GRU to continuous MV3 dynamics further demonstrates real‑time detection of the system’s current dynamical regime.

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