Learning and extrapolating scale-invariant processes

arXiv:2601.14810 · cond-mat.dis-nn, cs.LG · Submitted 2026-01-21 · Read on arXiv

cond-mat.dis-nn, cs.LG

Submitted: 2026-01-21

Updated: 2026-09-02

Terminology

• Machine Learning — 10× in this paper
• Graph Neural Network — 7× in this paper
• Wavelet Transform — 7× in this paper · explained in 2 episodes
• AUC — 6× in this paper · explained in 2 episodes
• Abelian Sandpile Model — 6× in this paper
• Generative Model — 4× in this paper · explained in 2 episodes
• Loss Function — 4× in this paper · explained in 2 episodes
• Generative Models — 3× in this paper · explained in 2 episodes
• Accuracy — 2× in this paper · explained in 1 episode
• Generalization — 2× in this paper · explained in 13 episodes
• Latent Representation — 2× in this paper · explained in 2 episodes
• Transformer — 2× in this paper · explained in 2 episodes
• Activation Function — 1× in this paper · explained in 1 episode
• Area Under the Curve (AUC) — 1× in this paper · explained in 1 episode
• Consistency — 1× in this paper · explained in 3 episodes
• Decode — 1× in this paper · explained in 2 episodes
• DeepONet — 1× in this paper · explained in 2 episodes
• Embeddings — 1× in this paper · explained in 2 episodes
• Generative Modeling — 1× in this paper · explained in 3 episodes
• Graph Neural Network (GNN) — 1× in this paper · explained in 2 episodes
• Gravitational Lensing — 1× in this paper · explained in 2 episodes
• Hilbert Space — 1× in this paper · explained in 2 episodes
• Interpretability — 1× in this paper · explained in 15 episodes
• Reconstruction Error — 1× in this paper · explained in 2 episodes
• Regularization — 1× in this paper · explained in 3 episodes
• Scaling Laws — 1× in this paper · explained in 4 episodes
• Trace — 1× in this paper · explained in 2 episodes
• U-net architecture — 1× in this paper · explained in 3 episodes

Sources

• Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges
• Scale-Equivariant Steerable Networks
• Locally Scale-Invariant Convolutional Neural Networks
• A Linear Stochastic Model of Turbulent Cascades and Fractional Fields
• Robustifying Fourier Features Embeddings for Implicit Neural Representations

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