Negative Shannon Information Hides Networks

Abstract

Shannon information is defined for characterizing the uncertainty information of classical probabilistic distributions. As an uncertainty measure it is generally believed to be positive. This holds for any information quantity from two random variables because of the polymatroidal axioms. However, it is unknown why there is negative information for more than two random variables on finite dimensional spaces. It is first shown that the negative tripartite Shannon mutual information implies specific Bayesian network representations of its joint distribution. Then it is shown that the negative Shannon information is obtained from general tripartite Bayesian networks with quantum realizations. This provides a device‐independent witness of negative Shannon information. Finally the result is extended for general networks. The present result shows new insights in the network compatibility from non‐Shannon information inequalities.

MAGNNETO: A Graph Neural Network-Based Multi-Agent System for Traffic Engineering

“…For instance, this process can be done periodically (e.g., each 5-10 minutes as in [11]), where the TM is first estimated and then optimized. Some proposals trigger the optimization process when a relevant change is detected in the TM [33], while others use prediction techniques to optimize it in advance [34]. Also, some real-world operators make estimates considering their customers' subscriptions and operate based on a static TM.…”