On the representation of continuous functions of several variables as superpositions of continuous functions of one variable and addition

By R. S. Gatsaeva. 2018

196 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/b4e281bc0b499b844842d798167f9578994700a2

How researchers see this paper

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

In Control and Systems Engineering

1. Angshul Majumdar
2. Matus Telgarsky
3. Janki Mehta

In Mechanics of Materials

1. Angshul Majumdar
2. Matus Telgarsky
3. Janki Mehta

Citations in the corpus

• Benefits of Depth in Neural Networks (2016, methodology): “The author is indebted to Joshua Zahl for help navigating semi-algebraic geometry and for a simplification of the multivariate case in Theorem 1.1, and to Rastislav Telgársky for an introduction to this general topic via Kolmogorov’s Superposition Theorem (Kolmogorov, 1957).”
• RODEO: Robust DE-aliasing autoencOder for real-time medical image reconstruction (2017, background): “It is known that neural networks can act as universal function approximators [2-5]; the first work on this topic was from Kolmogorov [2], later this approximation capacity was proven by Kukrova [3], Hornik [4] and Cybenko [5].”