The paper introduces a supervised, scale‑shared neural architecture for two‑dimensional site percolation, implementing a neural renormalization group flow. The model recursively applies a learned coarse‑graining rule across scales, producing a latent field that predicts crossing probability and a fine‑graining decoder that reconstructs the largest‑cluster mask. Trained only on small lattices, it extrapolates to larger systems, accurately recovers the spanning cluster, and yields observables that follow expected finite‑size scaling near the critical point, highlighting the importance of critical fluctuations in the latent representation.
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: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
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:2607. 07127v1 Announce Type: cross Abstract: Lattice field theory is the workhorse of non-perturbative physics, used to simulate phenomena from the strong nuclear force to critical phenomena in materials.
By Tobias G\"obel, Julian R. Ebelt, Zier Mensch, Mathis Gerdes, Miranda C. N. Cheng
arXiv:2608. 01833v1 Announce Type: cross Abstract: Grokking is a striking phenomenon in neural network training, where a model can undergo a prolonged period of pure memorization before abrupt generalization.
By Lai Shun Chan, Xiaotian Zhang, Yue Shang, Ge Zhang, Entao Yang
arXiv:2606. 10324v1 Announce Type: new Abstract: The analogy between deep neural network forward passes and renormalization group (RG) flows has been repeatedly noted in the literature, but existing treatments remain qualitative: depth is described as a coarse-graining scale, attention is likened to a partition function, and representations are said to flow toward fixed points.
By Parviz Haggi-Mani, Irina Rish
arXiv:2607. 04680v1 Announce Type: new Abstract: Grain growth is governed by the reduction in grain boundary energy and exhibits well-established statistical scaling laws.
By Zhihui Tian, Kang Yang, Michael Tonks, Amanda R. Krause, Joel B. Harley
The paper investigates how machine learning models can regress scale‑free processes, such as earthquakes or avalanches, focusing on predicting rare, large events that require extrapolation. It studies two self‑similar systems: a 2‑dimensional fractional Gaussian field and the Abelian sandpile model. Experiments compare existing architectures (U‑net, Riesz network) with new proposals (wavelet‑based Graph Neural Network, Fourier embedding, Fourier‑Mellin Neural Operator) to identify spectral bias and coarse‑graining challenges and suggest inductive biases to address them.
By Anaclara Alvez-Canepa, Cyril Furtlehner, Fran\c{c}ois P. Landes
arXiv:2606. 01302v1 Announce Type: new Abstract: Modern large-scale deep learning exhibits two striking empirical phenomena: behavioural scaling laws (predictable performance gains with increasing scale) and emergent mechanisms (structured internal representations and circuits in deep neural networks).
By Matthew Farrugia-Roberts