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.

翻译：人工智能的发展催生了极为成功但远非谦逊的模型与工具，尤其体现在两方面：(i) 其所需成本与资源极为庞大且持续激增；(ii) 这些工具对其提供的答案表现出过度自信。本文基于全概率定律，提出一种非平衡熵优化的玻尔兹曼机重构数学框架。该框架产生了一种高性能、低成本的免梯度下降学习范式，具备数学可证明的存在性与唯一性判据，以及答案置信度/可靠性度量方法。在一系列复杂度各异的合成问题上，与前沿人工智能工具在性能、成本及模型描述长度方面的对比表明：所提方法能生成性能更优且更精简的模型，其描述长度非常接近底层问题的本征复杂度缩放边界。将该框架应用于历史气候数据，所得模型对拉尼娜与厄尔尼诺气候现象起始时刻的预测能力呈现系统性提升，且仅需数年气候数据即可完成训练——这仅是当代气候预测工具所需训练数据的极小部分。