arXiv:2606. 20347v1 Announce Type: new Abstract: Neural networks learn features that reflect the hierarchical, multi-scale structure of natural data.
Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.
arXiv:2507. 14159v2 Announce Type: replace-cross Abstract: Predicting critical phenomena from limited labeled data remains a challenging task in statistical physics.
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.
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 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.
arXiv:2606. 07686v1 Announce Type: cross Abstract: Physics-Informed Neural Network (PINN) is a way of including knowledge in the form of equations in Machine Learning methods.
arXiv:2609.06093v1 Announce Type: new Abstract: Connectomes, graph-level maps of neurons and their synaptic connections, provide a structural basis for understanding how brain circuits support functi...