Hamiltonian and Q-Inspired Neural Network-Based Machine Learning

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.