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 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.
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: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:2608. 06597v1 Announce Type: cross Abstract: A scientific theory of deep learning, comprising learning dynamics and statistical properties of learned models, is rapidly gaining attention.
By Bj\"orn Ladewig, Ibrahim Talha Ersoy, Karoline Wiesner
arXiv:2606. 31282v1 Announce Type: new Abstract: Modern deep neural networks often contain far more parameters than needed to fit their training data, yet they achieve impressive generalization.
By Ari Pakman, Lior Kreimer, Yakir Berchenko
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:2607. 24818v1 Announce Type: cross Abstract: Accurate prediction of crystal properties remains a key challenge in computational materials science.
By Sanjay Chakraborty
arXiv:2608. 14743v1 Announce Type: new Abstract: The identification and reconstruction of the boundaries separating basins of attraction in multistable, multidimensional dynamical systems presents a fundamental challenge in computational dynamics.
By Ellis R. Crabtree, Dimitris G. Giovanis, Anastasia Georgiou, George Datseris, Ioannis G. Kevrekidis
arXiv:2606. 00776v1 Announce Type: new Abstract: Fast and accurate prediction of crystal properties is a central challenge in new materials design.
By Shrimon Mukherjee, Kishalay Das, Partha Basuchowdhuri, Pawan Goyal, Niloy Ganguly
arXiv:2512. 18454v3 Announce Type: replace Abstract: Predictive machine learning models generally excel on in-distribution data, but their performance degrades on out-of-distribution (OOD) inputs.
By David Graber, Victor Armegioiu, Rebecca Buller, Siddhartha Mishra