Unverified50% confidenceFactExact time
In the infinite-variance case t ∈ (1,2), the central fluctuation scale of SGD is of order η^{1/t}, and the limit is a t-stable distribution.
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10/19/2026
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Related Claims
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.77% similarUnverifiedThe Cauchy distribution is a special case of the t-distribution with degrees of freedom ν=1; its expected value and variance do not exist, the sample mean does not converge to a stable value, and the CLT fails in this case.67% similarUnverifiedThe smaller the degrees of freedom of the t-distribution, the heavier the tails; as the degrees of freedom approach infinity, the t-distribution converges to the standard normal distribution.66% similarUnverifiedWhen ρ has covariance Σ, the prior Gibbs distribution corresponding to the conjugate decomposition has covariance Σ^(1/3), causing the prior to also be dispersed when ρ is dispersed, resulting in better alignment between the two and preventing the Lipschitz constant from exploding.65% similarUnverifiedThe paper proves that the SGD iterates converge to a stable OU process at the central fluctuation scale and uses this limit to characterize the tail probabilities.65% similar
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