Polynomial Bounds for VC Dimension of Sigmoidal and General Pfaffian Neural Networks

By Marek Karpinski, A. Macintyre. 1997

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

1. Gábor Lugosi
2. Stéphane Boucheron
3. Olivier Bousquet
4. Zhen Fang
5. Jiahua Dong
6. Francis R. Bach
7. Yixuan Li
8. Vladimir Koltchinskii

Citations in the corpus

• On the Complexity of Neural Network Classifiers: A Comparison Between Shallow and Deep Architectures (2014, unknown): “Current available results show that the VC-dim is O(p2), for networks with arctan(·) or tanh(·) activation, where p is the number of parameters [45]–[47].”
• Introduction to Statistical Learning Theory (2004, background): “Macintyre [44], Khovanskii [45], Koiran and Sontag [46], Macintyre and Sontag [47], Steele [48], and Wenocur and Dudley [49].”
• Theory of classification : a survey of some recent advances (2005, background): “Macintyre [114], Koiran and Sontag [121], Anthony and Bartlett [9], and Bartlett and Maass [28].”
• Is Out-of-Distribution Detection Learnable? (2022, background): “However, generally, hypothesis spaces generated by feed-forward neural networks with proper activation functions have finite VC dimension [37, 38].”