Adaptive algorithm for preventing errors in mathematical reasoning in artificial intelligence systems

The paper identifies the features of solving simple arithmetic problems with a logical compo-nent using chatbots with generative artificial intelligence. Copilot is considered as such a chat-bot. It was found that when the query is extended or clarified, the probability of obtaining the correct answer decreases because expanding the query parameters leads to errors in forming the answer. Such a problem really exists and is called the limitations of large language models in mathematical reasoning. The user’s query and the search for information to answer their ques-tion occur non-linearly. Users change and supplement their queries, which only worsens the fi-nal answer of the chatbot. To minimize the occurrence of such errors and inaccuracies, it is pro-posed to use an approach with a non-linear Z-approximation. Given that Z-transformations are based on adaptive algorithms and are able to change the structural features of these algorithms, with each iteration of such an algorithm, there will be an approximation to a certain point con-taining the correct answer and not moving beyond the search area. In this case, the behavior of the user who adds new constraints and refinements to the problem to the chatbot with generative artificial intelligence can be described through the recurrent relations of the generated small-rational approximations. As a result, this allows you to build a direction of movement to the correct answer with a restriction of remarks that are not essential for the essence of understand-ing the problem. The proposed algorithm enables performing such calculations for user actions that are described by basic trigonometric functions. The algorithm has been tested for the func-tions sin x, cos x, tg x, arctg x in the Python programming language using the TensorFlow li-brary. As a result, the algorithm allowed us to obtain the correct solution to the problem, but an increase in the task execution time was recorded when the logical conditions became more complicated.