On Verifying Entropic Vectors with Distributions Generated by Neural Networks

This paper proposes a novel algorithm to verify entropic vectors with probability mass functions parametrized and generated by neural networks. Given a target vector, we minimize the normalized distance by training a neural network, which reveals the entropic nature of the target, with the underlying distribution obtained accordingly. Empirical results demonstrate improved normalized distances and convergence performances compared with prior works. We also conduct optimizations of Ingleton score and Ingleton violation index, where a new lower bound of Ingleton violation index is obtained. An inner bound of the almost entropic region with four random variables is constructed with the proposed method, presenting the current best inner bound measured by the volume ratio.