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International Journal of Theoretical Physics

A Quantum-inspired Approach to Pattern Recognition and Machine Learning. Part I

María Luisa Dalla Chiara, Roberto Giuntini, Giuseppe Sergioli

Published Feb 21, 2024• 0 citations
Publisher
DOI
10.1007/s10773-024-05566-2

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Quantum-inspired machine learning aims to leverage the principles of quantum mechanics to enhance data analysis and pattern recognition. This paper introduces a novel framework, Quantum-Inspired Machine Learning (QIM), designed to mimic the structure of topological data analysis (TDA), enabling the identification of complex patterns and anomalies. We propose a 'topological density' metric as a core feature extraction method, driving the development of a machine learning model that explores the interconnectedness of data points. The core claim is that this approach offers a fundamentally different perspective on data, leading to the detection of hidden patterns and anomalies previously difficult to identify using traditional machine learning techniques. This research explores the potential of QIM to revolutionize data analysis by introducing a novel approach to feature representation and pattern detection.
The goal of this study is to present a universal large-scale machine learning model based on spectral processing. By machine learning, we mean input-output mapping approximation generated by training sets. We treat tasks such as pattern recognition and classification as special problems in mapping approximation. The structures of the approximators are implemented using Hamiltonian neural network-based biorthogonal and orthogonal transformations. From a mathematical point of view, these structures can be seen as an implementation of non-expansive mappings. An interesting property of approximators is the reconstruction and recognition of incomplete or distorted patterns. The reconstruction property gives rise to a proposition of a superposition processor and reversible computations. Finally, the models of machine learning described here are adequate for processing data with real and complex values by defining Q-inspired neural networks.