arXiv:2606. 20347v1 Announce Type: new Abstract: Neural networks learn features that reflect the hierarchical, multi-scale structure of natural data.
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...
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.
arXiv:2512. 03578v3 Announce Type: replace-cross Abstract: Time series extrinsic regression (TSER) refers to the task of predicting a continuous target variable from an input time series.
arXiv:2606. 30064v1 Announce Type: new Abstract: We introduce a data-driven probabilistic framework for learning systems based on Gibbs measures on hierarchical structures.
We introduce a data-driven probabilistic framework for learning systems based on Gibbs measures on hierarchical structures. Unlike standard empirical risk minimization, where a dataset is used to identify a single optimal parameter, our approach transforms the empirical loss function into an interaction potential defining an energy-based model.
The study explores whether a Deep Belief Network (DBN) and a Bidirectional Gated Recurrent Unit (Bi‑GRU) can distinguish four distinct trajectory types in the three‑state majority‑vote model (MV3): approach from disorder, approach from order, departure to disorder, and departure to order. The DBN, trained unsupervised on static equilibrium snapshots, partially separates these trajectories in its 81‑dimensional latent space, while a two‑layer Bi‑GRU trained on sequences of DBN‑encoded snapshots achieves near‑perfect classification, as confirmed by t‑SNE visualizations on both training and test data. A sliding‑window application of the Bi‑GRU to continuous MV3 dynamics further demonstrates real‑time detection of the system’s current dynamical regime.
The paper introduces Adaptive Derivative-Ordered Random Explanation (ADORE), a unified framework that uses first- and second-order derivatives to capture nonlinear feature interactions and feature-sample dynamics. ADORE combines global feature importance with local sample contributions, quantifying both magnitude and direction of feature impact while identifying critical samples. It achieves computational efficiency via randomized SVD and dynamic sparsity detection, outperforming LIME and SHAP across tabular, text, and image data, and is released as an open-source Python package on GitHub.