Quantum mechanics-based multitensor AI/ML uniquely able to discover, validate, and interpret predictors from small-cohort noisy high-dimensional multiomic data

Prediction in medicine remains limited. Previously, by using our “comparative spectral decompositions” of two matrices and, separately, two third-order tensors, we demonstrated accurate, precise, actionable, and interpretable tumor whole-genome and, separately, whole-transcriptome predictors—of patients’ survival, treatment responses, and drug targets—in different cancers. Here, we introduce a unified framework that generalizes these exact and structure-preserving algorithms to multiple tensors of any order to model real-world data that measure multiple aspects of interrelated phenomena. We prove properties (e.g., existence and uniqueness) and define metrics (e.g., the “multitensor joint Shannon entropy” and the “multitensor comparative angular distance”) necessary to derive, test, and explain a model. We highlight the novel connection to the quantum mechanical concept of “entanglement” in addition to that of “superposition.” We illustrate the framework in the discovery and validation of two novel predictors in neuroblastoma—each with three entangled representations—in the tumor and blood genomes and tumor transcriptome, where the result of the measurement of any one representation approximately determines the results of the measurements of the other two. Finally, we show that in every representation, the two predictors combined are consistently more accurate than the best standard-of-care biomarker (i.e., the one-gene test for tumor MYCN amplification), and we interpret them in terms of known and new disease mechanisms and drug targets.