An entropy-optimal path to humble AI (2506.17940v1)

Abstract: Progress of AI has led to a creation of very successful, but by no means humble models and tools, especially regarding (i) the huge and further exploding costs and resources they demand, and (ii) the over-confidence of these tools with the answers they provide. Here we introduce a novel mathematical framework for a non-equilibrium entropy-optimizing reformulation of Boltzmann machines based on the exact law of total probability. It results in the highly-performant, but much cheaper, gradient-descent-free learning framework with mathematically-justified existence and uniqueness criteria, and answer confidence/reliability measures. Comparisons to state-of-the-art AI tools in terms of performance, cost and the model descriptor lengths on a set of synthetic problems with varying complexity reveal that the proposed method results in more performant and slim models, with the descriptor lengths being very close to the intrinsic complexity scaling bounds for the underlying problems. Applying this framework to historical climate data results in models with systematically higher prediction skills for the onsets of La Ni~na and El Ni~no climate phenomena, requiring just few years of climate data for training - a small fraction of what is necessary for contemporary climate prediction tools.