Participation Ratio
Participation Ratio is a metric for measuring the concentration of a distribution. Within the KAG framework it is used to measure the concentration of the magnitudes of Jacobian minors, but it suffers from a scale dependency defect in which its maximum value varies with network size.
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The existing metric for measuring minor concentration, Participation Ratio (PR), has a fundamental flaw: its maximum value depends on network scale (the number of minors), making it impossible to judge, independent of architecture, whether a given PR value represents high or low concentration.
When α=2, α-RC reduces to an explicit transformation of the Participation Ratio, thereby eliminating scale dependence while retaining PR's interpretability.
The number of minors grows combinatorially with network scale (input dimension and number of hidden units), which is the root of the PR metric's scale dependence.
All Facts (3)
The existing metric for measuring minor concentration, Participation Ratio (PR), has a fundamental flaw: its maximum value depends on network scale (the number of minors), making it impossible to judge, independent of architecture, whether a given PR value represents high or low concentration.
50%UnverifiedWhen α=2, α-RC reduces to an explicit transformation of the Participation Ratio, thereby eliminating scale dependence while retaining PR's interpretability.
50%UnverifiedThe number of minors grows combinatorially with network scale (input dimension and number of hidden units), which is the root of the PR metric's scale dependence.
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