Аннотация:The gradient descent ideas in the backpropagation error (BPE) form with some additional algorithms development allowed to realize deep learning of neural networks and led to a revolution in machine learning. A huge learning parameters number made it possible to replace discrete concepts with a vector description. There are some other ideas that are no less profound than gradient descent. Such as memory localization, decomposition of complex objects, and transformations linearization. The transition from internal vectors to maps of simple objects is considered as the promising direction for neural network algorithms development that can implement these ideas. It seems possible with states subspaces maps to overcome some of the problems that deep learning cannot cope without new ideas. A general plan for constructing an interacting maps hierarchical structure is considered, which can work in the Systems 1 and 2 modes according to Kahneman. Mathematical ideas for the linear approximation implementation using neural network maps are given. Other aspects of the general plan also have been preliminary worked out, but a significant amount of work remains to be done to improve the algorithms, ensure the stability of their convergence and confirm their performance by modeling. It will take time and funding. Nevertheless, the success in each of other ideas implementation: localization, decomposition, and linearization can lead to progress in the development of AI, comparable to the introduction of the gradient descent idea into the deep neural networks training, which caused a revolution in machine learning.