Quantum Geometry of Data
This approach could advance understanding of cognitive phenomena in quantum cognition, but it appears incremental as it builds on existing quantum machine learning concepts.
The paper tackles the problem of representing data in machine learning by encoding it as quantum geometry, using learned Hermitian matrices to map data points to Hilbert space states, which captures global properties and avoids the curse of dimensionality, as demonstrated on synthetic and real-world examples.
We demonstrate how Quantum Cognition Machine Learning (QCML) encodes data as quantum geometry. In QCML, features of the data are represented by learned Hermitian matrices, and data points are mapped to states in Hilbert space. The quantum geometry description endows the dataset with rich geometric and topological structure - including intrinsic dimension, quantum metric, and Berry curvature - derived directly from the data. QCML captures global properties of data, while avoiding the curse of dimensionality inherent in local methods. We illustrate this on a number of synthetic and real-world examples. Quantum geometric representation of QCML could advance our understanding of cognitive phenomena within the framework of quantum cognition.