Linear Independence of Polynomial Compositions and Identifiability of Deep Neural Networks

arXiv:2608.27113 · math.AC, cs.LG, math.AG · Submitted 2026-08-27 · Read on arXiv

math.AC, cs.LG, math.AG

Submitted: 2026-08-27

Updated: 2026-08-27

Terminology

• Activation Function — 2× in this paper · explained in 1 episode
• Alignment — 2× in this paper · explained in 1 episode
• Core — 1× in this paper · explained in 2 episodes

Sources

• Linear independence of powers for polynomials
• Activation degree thresholds and expressiveness of polynomial neural networks
• The Symmetries of Three-Layer ReLU Networks
• Most ReLU Networks Admit Identifiable Parameters
• The Alexander-Hirschowitz theorem for neurovarieties
• Identifiable Equivariant Networks are Layerwise Equivariant
• Identifiability of Deep Polynomial Neural Networks

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