Compositional Boundaries for Density Fusion 文章

arXiv:2606.05871v1 Announce Type: cross Abstract: Distributed uncertainty-management systems often combine local probabilistic models along aggregation trees chosen by communication, privacy, or scheduling constraints. The final density should depend on the weighted sources, not on the particular order in which intermediate nodes combine them. We study this requirement as an algebraic compositionality problem for binary fusion of weighted probability densities. The central question is when a local fusion rule can be executed hierarchically while remaining order-invariant. We establish a compositional boundary for local segment-valued fusion rules. Within the class of continuous binary rules with additive output weights and weight-only coefficients, order-invariant hierarchical execution characterizes normalized weighted linear pooling; norm-induced segment balancing realizes the corresponding coefficient.