An Improved Bound on the VC-Dimension of Neural Networks with Polynomial Activation Functions
J. Maurice Rojas, M. Vidyasagar
TL;DR
This paper presents a tighter upper bound on the VC-dimension of neural networks that use polynomial activation functions, leveraging algebraic geometry results to refine capacity estimates.
Contribution
It introduces an improved theoretical upper bound on VC-dimension for polynomial-activation neural networks, based on semi-algebraic set analysis.
Findings
Derived a new upper bound for VC-dimension
Utilized Rojas' result on semi-algebraic sets
Enhanced understanding of neural network capacity
Abstract
In this note, we derive an improved upper bound for the VC-dimension of neural networks with polynomial activation functions. This improved bound is based on a result of Rojas on the number of connected components of a semi-algebraic set.
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Taxonomy
TopicsNeural Networks and Applications · Machine Learning and Algorithms · Fuzzy Logic and Control Systems