The paper presents a supervised, scale‑shared neural architecture that learns a coarse‑graining rule for two‑dimensional site percolation. By recursively applying this rule, the model generates a latent field from which the crossing probability is predicted and a fine‑graining decoder reconstructs the largest‑cluster mask. Trained only on small lattices, the network extrapolates to larger systems, accurately recovers the spanning cluster, and reproduces finite‑size scaling near the critical point, demonstrating that the latent representation captures critical fluctuations and scale‑dependent flows consistent with renormalization‑group theory.
By Anaclara Alvez, Luca Camagna, Sergio Chibbaro, Cyril Furtlehner, Fran\c{c}ois Landes, Gianluca Manzan, Lorenzo Mensi
The paper models the dynamics of Stochastic Gradient Descent (SGD) as a percolation process, showing that architectural symmetries cause subnetworks to merge in discrete blocks rather than sequentially. These structural transitions produce variance spikes in a macroscopic order parameter, analogous to physical phase transitions. The authors also demonstrate that this trapping mechanism and its scaling cascade apply to Adam and AdamW under a heavy‑tailed noise model.
By Sai Niranjan Ramachandran, Suvrit Sra
arXiv:2507. 14159v2 Announce Type: replace-cross Abstract: Predicting critical phenomena from limited labeled data remains a challenging task in statistical physics.
By Shanshan Wang, Dian Xu, Jianmin Shen, Feng Gao, Wei Li, Weibing Deng
arXiv:2606. 20347v1 Announce Type: new Abstract: Neural networks learn features that reflect the hierarchical, multi-scale structure of natural data.
By Aryeh Brill, Tom Ingebretsen Carlson
arXiv:2607. 10285v1 Announce Type: new Abstract: We study how unsupervised autoencoders trained on microscopic spin configurations from the Ising model learn macroscopic, theory-relevant variables underlying the data-generating process.
By Max Weinmann, Miriam Klopotek
arXiv:2512. 13853v2 Announce Type: replace Abstract: In this work, we investigate the existence and effect of percolation in training deep Neural Networks (NNs) with dropout.
By Finley Devlin, Jaron Sanders