Framing Dempster–Shafer evidence combination as convolutional networks for efficient mass function computation

Dempster–Shafer Theory (DST) provides a well-established framework for managing uncertainty and imprecision. However, its practical application is often constrained by the high computational cost of the combination rule when integrating information from multiple sources, and it has seen only limited integration into deep learning models. Although acceleration strategies such as tensor-based parallelization, matrix projection, and quantum implementations have been investigated, the exponential dependence on the number of hypotheses is inherent to the power-set representation, and these methods often require specialized hardware or custom implementations, which limit their practical applicability. This study proposes a new reformulation of the evidence combination rule within the framework of convolutional operators. The proposed formulation recasts the combination process as an iterative, analytically tractable convolutional sequence and formally derives the inductive properties of the corresponding kernels. The reformulation naturally leads to an N -layer convolutional architecture with fixed, predefined kernels, thereby providing a concrete computational form. The proposed computation model can represent various combination rules, such as conjunctive and disjunctive rules, by appropriately adjusting the kernels in the convolutional operator. Furthermore, the proposed model can adapt to downstream tasks by learning a new rule from data, extending its practical scope.