Regularly varying tail
A concept in extreme value theory used to characterize heavy-tailed distributions, in which the tail probability decays as a power law multiplied by a slowly varying function; the tail index t determines the rate of decay, and when t lies in (1,2) the variance is infinite while the mean is finite.
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The paper focuses on the nonlinear SGD setting in which the gradient noise has a regularly varying tail index t ∈ (1,2).
A regularly varying tail index t ∈ (1,2) means infinite variance but finite mean, and the normalized sum converges to a t-stable distribution rather than a normal distribution.
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The paper focuses on the nonlinear SGD setting in which the gradient noise has a regularly varying tail index t ∈ (1,2).
50%UnverifiedA regularly varying tail index t ∈ (1,2) means infinite variance but finite mean, and the normalized sum converges to a t-stable distribution rather than a normal distribution.
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