AI RESEARCH
Relations Are Channels: Knowledge Graph Embedding via Kraus Decompositions
arXiv CS.AI
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ArXi:2605.10317v1 Announce Type: cross Knowledge graph embedding (KGE) models typically represent each relation as an operator on entity embeddings. In this work, we identify three structural axioms that any principled relation operator must satisfy, linearity, trace preservation, and complete positivity, and show that they characterize a Kraus channel structure via the Kraus representation theorem. The completeness constraint defining this family is equivalent to these axioms, providing a principled foundation rather than an externally imposed condition.