ConcepTensor：A Probabilistic Relational Representation Architecture for DAGs Embedded in High-Dimensional Tensors

Cognitive representation requires encoding entities and their hierarchical relations in a concept system into a queryable and reasoning-ready formal structure. Existing methods follow two paths. Symbolic hierarchical structures are explicit and traceable, but are constrained to a single parent, unable to express an entity belonging to multiple upper concepts. Distributed vector representations are flexible and generalizable, but are not white-box, and their internal representations are not traceable. White-box, general, and scalable properties are difficult to achieve simultaneously: Bayesian networks are the only model that is both white-box and general, but their exact inference complexity grows exponentially with graph size, and the inference process gradually becomes non-hand-verifiable. This paper proposes ConceptTensor, which embeds a multi-parent DAG into a high-dimensional tensor space and computes relations directly via tensor contraction. Entity coordinates are determined by Dirichlet posterior; hierarchy, parent, and child are carried by three tensor axes; relations such as parent, child, common parent, common child, sibling, and multi-hop are all directly given by tensor contraction. The architecture decouples representation from inference, involves no training, and every intermediate value is hand-verifiable. On six query tasks over multi-parent DAGs, it achieves an order-of-magnitude efficiency improvement over Bayesian networks.