Function-Counting Theory for Low-Dimensional Data Structures

arXiv:2607.01010 · stat.ML, cs.IT, cs.LG, math.CA, math.CO · Submitted 2026-07-01 · Read on arXiv

Konstantin Häberle, Helmut Bölcskei

stat.ML, cs.IT, cs.LG, math.CA, math.CO

Submitted: 2026-07-01

Comments: 49 pages, 7 figures

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

Terminology

• Generalization — 28× in this paper · explained in 14 episodes
• Sparsity — 19× in this paper · explained in 5 episodes
• Orthogonal Projection — 5× in this paper · explained in 2 episodes
• VC Dimension — 4× in this paper · explained in 2 episodes
• Degeneracies — 2× in this paper · explained in 2 episodes
• Degeneracy — 2× in this paper · explained in 4 episodes
• Intrinsic Dimension — 2× in this paper · explained in 3 episodes
• Core — 1× in this paper · explained in 2 episodes
• Equivariance — 1× in this paper · explained in 3 episodes
• Monotonicity — 1× in this paper · explained in 2 episodes
• Redundancy — 1× in this paper · explained in 2 episodes
• Representation Learning — 1× in this paper · explained in 3 episodes
• Sample Complexity — 1× in this paper · explained in 20 episodes

Sources

• Separation Capacity of Scattering Networks

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