Multifunctional Adaptive Element for Neuromorphic Electronics Based on the Kuznetsov Tensor

This paper presents a concept of a new class of multifunctional adaptive elements for neuromorphic electronics, based on the mathematical framework of the Kuznetsov tensor. The proposed element integrates the functions of information storage, processing, and redistribution, providing high adaptability to changing system conditions while preventing overloads, singular states, and data losses. The Kuznetsov tensor enables modeling of multidimensional metrics of local and global flows of energy and information within neuromorphic networks, ensuring optimization of computational processes at both individual node and network-wide levels.The element demonstrates the potential of a self-regulating redistribution architecture, capable of dynamically adapting to workload variations and changes in connection topology, maintaining system stability and enhancing energy efficiency. This concept can be applied in neuromorphic processors, quantum computing devices, and artificial intelligence systems requiring predictable and reliable operation of complex multidimensional networks.The paper discusses the fundamental operating principles of the element, the mechanisms of interaction with information and energy flows, and integration possibilities within modern computational architectures. The proposed approach opens new avenues for the development of intelligent adaptive devices, capable of managing information and energy dynamics considering singularities and entropy-driven processes, which is of interest for both fundamental and applied research in neuromorphic electronics and information technology.