Neural Network Axiomatic Solver Coaching AGI Method for Solving Scientific and Practical Problems

Modern neural network methods combine work with an axiomatic mathematical description (laws, equations, invariants, logical rules) and the power of neural networks for learning from data, pattern recognition and differentiation through complex spaces. This combination produces systems that can learn from data, observe given laws and, as a result, make predictions, solve problems and even discover new hypotheses. Quality depends on the formulation of axioms and the presence of correct formulations, the complexity of scaling to very large axiomatic bases, trade-offs between the accuracy of fitting to data and compliance with laws, interpretation and verification of results. Modern neural network methods with an axiomatic mathematical description have better generalization and physical interpretability due to compliance with axioms, the ability to work with small data due to built-in laws and the ability to discover new dependencies within the framework of formalized rules. Theoretical principles and formal axioms set requirements for neural networks and their training so that solutions to scientific problems correspond to the laws of nature, invariances, data characteristics and other desired properties. Power: an axiomatic neural network tends to be accurately modeled given its sufficient complexity and large scientific data and knowledge. The author proposes a neural network axiomatic solver coaching AGI method for solving scientific and practical problems according to their formulations and developed systems of axioms.