Hierarchical Interaction Hyper-Tensors

Key Points

• The research aims to establish the HIHT framework as an extended approach to model multi-mode recursive hierarchical systems.
• Introduced the Hierarchical Interaction Hyper-Tensor framework as a generalization of the Depth-Propagation Tensor model.
• Developed recursive propagation equations and conducted convergence analysis.
• Explored emergent statistical metrics and functional-analytic embeddings.
• Analyzed the irreducibility structure and operator growth bounds within the framework.
• Established compactness in continuous limits and examined structural spectral regimes.
• Provided a rigorous foundation for nonlinear multi-mode spectral theory.
• Demonstrated convergence properties of recursive equations within the HIHT framework.
• Identified the importance of compactness in continuous limits for theoretical applications.
• Showed structural spectral regimes that characterize the behavior of multi-mode systems.