Siamese Network Locates Criticality in 3D Percolation

Label-efficient similarity learning can reduce annotation needs for physics and scientific ML tasks by teaching models to discover order parameters from sparse labels. According to the arXiv paper arXiv:2507.14159 by Shanshan Wang et al., the authors introduce a Siamese Neural Network (SNN) framework to identify phase transitions in three-dimensional site and bond percolation models. The paper reports that using only 22 labeled probability points drawn from non-critical regions, the SNN locates percolation thresholds with percent-level accuracy and yields estimates of the critical exponent nu consistent with literature values, per arXiv. The authors further report that the learned representation correlates with the normalized largest-cluster size S_max/L^3 (correlation r>0.99) and that a model trained on simple cubic lattices generalizes to face-centered cubic lattices without retraining, according to arXiv.