If you can distinguish, you can express: Galois theory, Stone--Weierstrass, machine learning, and linguistics

arXiv:2510.09902 · math.HO, stat.ML · Submitted 2025-10-10 · Read on arXiv

math.HO, stat.ML

Submitted: 2025-10-10

Updated: 2026-09-01

Comments: Revision to draw out the main story more clearly

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Alignment — 8× in this paper · explained in 1 episode
• Point Clouds — 8× in this paper · explained in 2 episodes
• GNNs — 4× in this paper · explained in 2 episodes
• Sample Complexity — 4× in this paper · explained in 15 episodes
• Abstraction — 3× in this paper · explained in 1 episode
• Bispectrum — 3× in this paper · explained in 3 episodes
• Embeddings — 2× in this paper · explained in 2 episodes
• Feature Extraction — 2× in this paper · explained in 2 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Activation Function — 1× in this paper · explained in 1 episode
• Adam — 1× in this paper · explained in 2 episodes
• Alignment Problem — 1× in this paper · explained in 1 episode
• Generalization — 1× in this paper · explained in 13 episodes
• Graph Neural Networks (GNNs) — 1× in this paper · explained in 7 episodes
• Matrix Completion — 1× in this paper · explained in 3 episodes
• Pragmatics — 1× in this paper · explained in 2 episodes
• Regularization — 1× in this paper · explained in 3 episodes

Sources

• The generalized phase retrieval problem over compact groups
• G-Invariant Representations using Coorbits: Bi-Lipschitz Properties
• ShapeNet: An Information-Rich 3D Model Repository
• The separating Noether number of small groups
• Orbit recovery from invariants of low degree in representations of finite groups
• Maximum likelihood for high-noise group orbit estimation and single-particle cryo-EM
• The bispectrum as a source of phase-sensitive invariants for Fourier descriptors: a group-theoretic approach
• On Universality of Deep Equivariant Networks
• On Universality Classes of Equivariant Networks
• Quantitative Approximation Rates for Group Equivariant Learning

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