Production AI retrieval systems increasingly require more than vector similarity search. A GigaOm CxO Decision Brief examines how tensors — as multi-dimensional data structures — provide a more expressive framework for combining semantic, lexical, behavioral, and business signals in a unified retrieval and ranking pipeline. Key findings highlight that architectural fragmentation across vector databases, rerankers, and feature stores introduces latency and operational complexity at scale. Tensor-native architectures treat multidimensional data as first-class citizens, supporting emerging retrieval models like multi-vector and late-interaction approaches. The brief argues that retrieval is evolving from a nearest-neighbor problem into a ranking and decision-making problem.