Markov Chain Decoders Overcome the Heavy-Tail Limitations of Lipschitz Generative Models 文章

arXiv:2605.18931v2 Announce Type: replace-cross Abstract: Heavy-tailed distributions are prevalent in performance evaluation, network traffic, and risk modeling. This behavior poses a fundamental challenge for modern deep generative models. Standard Variational Autoencoders (VAEs) employ Gaussian decoder likelihoods and Lipschitz-constrained neural networks, a combination that is structurally incapable of producing heavy-tailed outputs: the Gaussian tail decays exponentially, and Lipschitz continuity prevents the decoder from amplifying rare events from the latent space input to sufficiently overcome this decay. We provide both a theoretical characterization of this limitation and a controlled empirical demonstration using synthetic Pareto data across a grid of tail indices $\alpha$ $\in$ {2, 3, 5, 30} and dimensions d $\in$ {1, 5, 10}.