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Quantum field-theoretic machine learning

机译：量子场 - 理论机学习

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We derive machine learning algorithms from discretized Euclidean field theories, making inference and learning possible within dynamics described by quantum field theory. Specifically, we demonstrate that the ? 4 scalar field theory satisfies the Hammersley-Clifford theorem, therefore recasting it as a machine learning algorithm within the mathematically rigorous framework of Markov random fields. We illustrate the concepts by minimizing an asymmetric distance between the probability distribution of the ? 4 theory and that of target distributions, by quantifying the overlap of statistical ensembles between probability distributions and through reweighting to complex-valued actions with longer-range interactions. Neural network architectures are additionally derived from the ? 4 theory which can be viewed as generalizations of conventional neural networks and applications are presented. We conclude by discussing how the proposal opens up a new research avenue, that of developing a mathematical and computational framework of machine learning within quantum field theory.
机译：我们从离散的欧几里德场理论中获得机器学习算法，在量子场理论描述的动态内进行推断和学习。具体而言，我们证明了？ 4标量场理论满足Hammersley-Clifford Theorem，因此在马尔可夫随机字段的数学严格框架内重新定位它作为机器学习算法。通过最小化概率分布之间的不对称距离来说明概念吗？ 4理论和目标分布，通过量化概率分布之间的统计集合重叠以及通过更长范围的交互重新重量对复合动作的重叠。神经网络架构另外源自？提供了可以被视为传统神经网络和应用的概括的理论。我们通过讨论该提案如何开辟新的研究大道，在量子场理论中开发机器学习的数学和计算框架的结论。

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