Some aspects of directly parallel operation of neural networks and their subtle energy

There is a need to develop an instrumental mathematical base for new technologies, in particular for a fundamentally new type of neural network with parallel computing, in particular for creating artificial intelligence, but this is not the main task of a neural network, and not with the usual parallel computing through sequential computing. Nobel laureates in physics 2023 Ferenc Kraus and his colleagues Pierre Agostini and Anna Lhuillier used a short-pulse laser to generate attosecond pulses of light to study the dynamics of electrons in matter. According to our Theory of singularities of the type synthesizing, its action corresponds to singularity ↑I↓h q , which allows one to reach the upper level of subtle energies to manipulate lower levels. In April 2023, we proposed using a short-pulse laser to achieve the desired goals by a directly parallel neural network [1]. We then proposed the fundamental development of this directly parallel neural network. In the articles new mathematical structures and operators are constructed through one action - “containment” [1-13]. Here, the construction of new mathematical structures and operators is carried out with generalization to any actions. The significance of our articles is in the formation of the presumptive mathematical structure of subtle energies, this is being done for the first time in science, and the presumptive classification of the mathematical structures of subtle energies for the first time. The experiments of the 2022 Nobel laureates Asle Ahlen, John Clauser, Anton Zeilinger and the experiments in chemistry Nazhipa Valitov eloquently demonstrate that we are right and that these studies are necessary