On the Kolmogorov neural networks

2023/10/31 by Aysu Ismayilova, Vugar Ismailov, Ismayilova, Aysu +1 · 1 voice · 4 citations
#cs.NE #cs.LG #math.FA #stat.ML

paper · pdf · doi:10.48550/arxiv.2311.00049

Abstract

In this paper, we show that the Kolmogorov two hidden layer neural network model with a continuous, discontinuous bounded or unbounded activation function in the second hidden layer can precisely represent continuous, discontinuous bounded and all unbounded multivariate functions, respectively.

Cited by

• A Practitioner's Guide to Kolmogorov-Arnold Networks
• Explicit Construction of Approximate Kolmogorov-Arnold Superpositions with C2-Smoothness
• Kolmogorov–Arnold Networks [wikipedia]
• Kolmogorov–Arnold representation theorem [wikipedia]

Discussions

• Kolmogorov Neural Networks can represent discontinuous functions [hn, 133 points, 31 comments]

Related

• The Kolmogorov-Arnold representation theorem revisited
• The Proof of Kolmogorov-Arnold May Illuminate Neural Network Learning
• A three layer neural network can represent any multivariate function
• The Representation Power of Neural Networks: Breaking the Curse of Dimensionality
• No one-hidden-layer neural network can represent multivariable functions