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
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
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:2511. 02258v3 Announce Type: replace-cross Abstract: This paper studies the high-dimensional scaling limits of online stochastic gradient descent (SGD).
By Parsa Rangriz
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. 10384v1 Announce Type: cross Abstract: Criticality has been proposed as a key organizing principle in biological neural systems, yet its origin and relevance in artificial neural networks remain unclear.
By Feixiang Ren, Ling Feng
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
arXiv:2401. 04013v2 Announce Type: replace Abstract: Deep learning models, such as wide neural networks, can be conceptualized as nonlinear dynamical physical systems characterized by a multitude of interacting degrees of freedom.
By Ori Shem-Ur, Yaron Oz
arXiv:2511. 07308v3 Announce Type: replace Abstract: Understanding the training dynamics of deep neural networks remains a major open problem, with physics-inspired approaches offering promising insights.
By Ildus Sadrtdinov, Ekaterina Lobacheva, Ivan Klimov, Mikhail Burtsev, Mikhail I. Katsnelson, Dmitry Vetrov
arXiv:2501. 02436v5 Announce Type: replace Abstract: Advancements in artificial intelligence call for a deeper understanding of the fundamental mechanisms underlying deep learning.
By Yuchen Lin, Yong Zhang, Sihan Feng, Hong Zhao
arXiv:2601. 10962v2 Announce Type: replace Abstract: Stochastic gradient descent (SGD) is central to deep learning, yet the dynamical origin of its preference for flatter, more generalizable solutions remains unclear.
By Ning Yang, Yikuan Zhang, Qi Ouyang, Chao Tang, Yuhai Tu
arXiv:2511. 02003v2 Announce Type: replace Abstract: We present the bulk--boundary decomposition as a new framework for understanding the training dynamics of deep neural networks.
By Donghee Lee, Hye-Sung Lee, Jaeok Yi