Abstract

Behind general terms like adversarial attacks and generative adversarial networks, such criteria as AI resilience and AI robustness gained a crucial importance, in trying to make the emergent AI tools reliable, energy-efficient and safe. From mathematical perspective, these problems boil down to finding a mathematically sound quantification of the smallest-sufficient amounts of the perturbations of function arguments that lead to the largest possible perturbations of the approximated function values.

Here, an entropy-optimising perspective on adversarial algorithms from AI is proposed to attack this problem. It is shown that adopting this perspective helps proving computational conditions for the global optimality and uniqueness of adversarial attacks based on cheaply verifiable mathematical criteria. Further, it is shown how this perspective can be used for developing self-attacking learning algorithms, that generate optimal new data points for training, replacing one of the trained agents with this mathematical criterion. On a broad selection of various synthetic and real-life problems from hydrodynamics and biomedicine, it is shown that such self-attacking learning algorithms allow training orders-of-magnitude simpler and cheaper models with superior performance, and can be used to directly train the optimal controls in complex systems, requiring only a small fraction of the training data and outperforming a set of contemporary AI tools as comprehensive as the author was able to find, including boosted random forests, deep neural networks, and foundational models based on transformer architectures, both in terms of complexity (measured as the model descriptor length) and predictive performance.

Keywords

Mathematical Subject Classification

Milestones

Authors