Neural Networks With Dense Weights Are Not Universal Approximators

arXiv:2602.07618 · cs.LG, stat.ML · Submitted 2026-02-07 · Read on arXiv

cs.LG, stat.ML

Submitted: 2026-02-07

Updated: 2026-09-24

Code: https://github.com/levi776/Dense-Neural-Networks-are-not-Universal-Approximators

Terminology

• Accuracy — 13× in this paper · explained in 1 episode
• Generalization — 9× in this paper · explained in 13 episodes
• Pruning — 8× in this paper · explained in 4 episodes
• Advances in Neural Information Processing Systems — 7× in this paper
• Adjacency Matrix — 4× in this paper · explained in 1 episode
• Adam — 3× in this paper · explained in 2 episodes
• Activation Function — 2× in this paper · explained in 1 episode
• Embeddings — 2× in this paper · explained in 2 episodes
• Quantization — 2× in this paper · explained in 12 episodes
• Sparsity — 2× in this paper · explained in 4 episodes
• Adaptation — 1× in this paper · explained in 1 episode
• Aggregation — 1× in this paper · explained in 1 episode
• Distillation — 1× in this paper · explained in 2 episodes
• Generalization Bounds — 1× in this paper · explained in 2 episodes
• Regularization — 1× in this paper · explained in 3 episodes
• Representation Learning — 1× in this paper · explained in 2 episodes
• United States National Science Foundation — 1× in this paper
• United States-Israel Binational Science Foundation — 1× in this paper
• VC Dimension — 1× in this paper · explained in 2 episodes

Sources

• Sparse Double Descent: Where Network Pruning Aggravates Overfitting
• Higher-Order Graphon Neural Networks: Approximation and Cut Distance
• Edge Directionality Improves Learning on Heterophilic Graphs

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