Markov chain Phase-Type decoders in VAEs overcome the structural inability of Gaussian-Lipschitz models to produce heavy-tailed outputs, cutting tail KS distance by up to 6x and extreme quantile error by up to 10x on synthetic Pareto data.
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For linear-rate master equations the generating function admits an exact composition-multiplier representation whose Taylor coefficients on any finite window are obtained from a closed lower-triangular ODE of size 2(N+1), independent of the truncation cap N; the same closure is combined with Strang–
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Markov Chain Decoders Overcome the Heavy-Tail Limitations of Lipschitz Generative Models
Markov chain Phase-Type decoders in VAEs overcome the structural inability of Gaussian-Lipschitz models to produce heavy-tailed outputs, cutting tail KS distance by up to 6x and extreme quantile error by up to 10x on synthetic Pareto data.
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Solving linear-rate ODE hierarchies (like master equations) using closures and operator splitting
For linear-rate master equations the generating function admits an exact composition-multiplier representation whose Taylor coefficients on any finite window are obtained from a closed lower-triangular ODE of size 2(N+1), independent of the truncation cap N; the same closure is combined with Strang–