On the Vapnik-Chervonenkis dimension of the Ising-perceptron
S. Mertens
TL;DR
This paper numerically calculates the VC dimension of the Ising perceptron with binary patterns for small system sizes, revealing it is larger than N/2 and likely lacks a well-defined limit as N grows.
Contribution
It provides the first numerical estimates of the VC dimension for the Ising perceptron, challenging previous assumptions about its asymptotic behavior.
Findings
VC dimension exceeds N/2 for small N
No clear asymptotic limit observed for large N
Numerical enumeration method applied to system sizes up to N=31
Abstract
The VC dimension of the Ising perceptron with binary patterns is calculated by numerical enumerations for system sizes N <= 31. It is significantly larger than N/2. The data suggest that there is probably no well defined asymptotic behaviour for N to infinity.
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