A theory capable of guiding the development of future artificial intelligence (AI) systems built on modern digital hybrid high-performance computing platforms has not yet been created. However, the evolution of neuromorphic computing platforms towards transformers of large language model (LLM) with attention mechanisms has undoubtedly become a turning point in the application of computer technologies in almost all areas of knowledge. Nevertheless, due to the inductive-statistical inference methods inherent in LLMs, they demonstrate a stable tendency to so-called hallucinations, which limits their practical application in solving complex technological problems. The report considers the urgent technological problem of increasing the real performance of hybrid supercomputers operating in shared-use center modes. The solution to this problem is achieved not by significantly expanding the used computing processors, but by applying conceptual machine learning methods to manage the available computing resources of the supercomputer. It is shown that when choosing a criterion for optimizing computing processes based on real performance growth, it is necessary to find a constructive solution not only to several technological problems, but also to a number of fundamental problems that still do not have an unambiguous algorithmic description, for example, the fundamental halting problem. In the article, using the example of managing computing processes in a hybrid supercomputer cluster, it is shown that the real performance of supercomputer platforms can be increased by using an exo-intellectual architecture of memory-oriented computing. The proposed architecture expands the capabilities of software technologies, endowing digital computing platforms with the ability to both inductive and conceptual learning, which allows for effective resolution of contradictions arising between logical conclusions based on a variety of deductive knowledge about the physical feasibility of the solutions obtained, and inductive hallucinations of large linguistic models.