Speaker
Description
Quantum-inspired machine learning based on Matrix Product States (MPS) provides scalable models for high-dimensional classification while naturally exposing physically interpretable observables derived from quantum many-body theory. We present a unified analysis of MPS classifiers across biomedical omics, structural neuroimaging, hyperspectral remote sensing, and wildfire susceptibility prediction, focusing on both learning dynamics and model interpretability.
Our primary result is the identification of grokking as a dynamical transition in the tensor-network representation. Across multiple binary and multiclass classification tasks, the onset of generalization is consistently accompanied by abrupt changes in entanglement entropy, local magnetizations, and connected correlations, indicating a reorganization of the learned quantum state. In contrast, persistently overfitted models retain disordered entanglement structures and fail to exhibit this transition. Complementary information-theoretic analyses using transfer entropy and O-information further reveal that successful generalization is associated with redundancy-dominated higher-order interactions, whereas overfitting remains characterized by persistent synergistic information patterns.
Beyond learning dynamics, quantum observables provide a principled framework for interpretability. Correlation networks derived from trained MPS identify robust neuroanatomical hubs in psychiatric disorders and biologically meaningful gene communities in hepatocellular carcinoma, while reduced-density-matrix diagnostics reveal the hierarchy of class distinguishability in multiclass wildfire susceptibility prediction.
These results establish quantum-inspired tensor networks as a unified framework that combines competitive predictive performance with direct access to the internal organization of learned representations, offering new insights into generalization, higher-order feature interactions, and interpretable machine learning across diverse scientific domains.
| Topic | Tensor methods and quantum-inspired machine learning |
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