Constructive universal distribution generation through deep ReLU networks

ICML 2020 Dmytro PerekrestenkoStephan MüllerHelmut Bölcskei

We present an explicit deep network construction that transforms uniformly distributed one-dimensional noise into an arbitrarily close approximation of any two-dimensional target distribution of finite differential entropy and Lipschitz-continuous pdf. The key ingredient of our design is a generalization of the "space-filling'' property of sawtooth functions introduced in (Bailey & Telgarsky, 2018)... (read more)

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