M\"obius transforms and Shapley values for vector-valued functions on weighted directed acyclic multigraphs

ArXi:2510.05786v3 Announce Type: replace-cross M\"obius inversion and Shapley values are two mathematical tools for characterizing and decomposing higher-order structure in complex systems. The former defines higher-order interactions as discrete derivatives over a partial order; the latter provides a principled way to attribute those interactions back to the `atomic' elements of the system. Both have found wide application, from combinatorics and cooperative game theory to machine learning and explainable AI.