论文标题
P-ADIC统计领域理论和深度信念网络
p-Adic Statistical Field Theory and Deep Belief Networks
论文作者
论文摘要
在这项工作中，我们启动了P-ADIC统计场理论（SFTS）和神经网络（NNS）之间的对应关系的研究。在P-Adic时空上的一般量子场理论中，可以用严格的方式制定。如今，这些理论被视为数学玩具模型，以理解真实理论的问题。在这项工作中，我们表明这些理论与深度信念网络（DBN）密切相关。 Hinton等。通过堆叠几台受限的玻尔兹曼机器（RBMS）来构建DBN。该结构的目的是获得具有层次结构（深度学习体系结构）的网络。 RBM对应于某个自旋玻璃，我们认为DBN应对应于超级自旋玻璃。通过使用P-ADIC数字可以轻松构建此类系统的模型。在我们的方法中，P-ADIC SFT对应于P-ADIC连续DBN，该理论的离散化对应于P-ADIC离散DBN。我们证明这些最后的机器是通用近似器。在P-ADIC框架中，SFTS和NNS之间的对应关系尚未完全开发。我们指出几个开放问题。
In this work we initiate the study of the correspondence between p-adic statistical field theories (SFTs) and neural networks (NNs). In general quantum field theories over a p-adic spacetime can be formulated in a rigorous way. Nowadays these theories are considered just mathematical toy models for understanding the problems of the true theories. In this work we show these theories are deeply connected with the deep belief networks (DBNs). Hinton et al. constructed DBNs by stacking several restricted Boltzmann machines (RBMs). The purpose of this construction is to obtain a network with a hierarchical structure (a deep learning architecture). An RBM corresponds to a certain spin glass, we argue that a DBN should correspond to an ultrametric spin glass. A model of such a system can be easily constructed by using p-adic numbers. In our approach, a p-adic SFT corresponds to a p-adic continuous DBN, and a discretization of this theory corresponds to a p-adic discrete DBN. We show that these last machines are universal approximators. In the p-adic framework, the correspondence between SFTs and NNs is not fully developed. We point out several open problems.
