arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2002.02664cs.LGcond-mat.stat-mechphysics.comp-phstat.ML
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短视的深度学习

Short sighted deep learning

University of the Witwatersrand(威特沃特斯兰德大学)

Ellen de Melllo Koch, Anita de Mello Koch, Nicholas Kastanos, Ling Cheng

摘要:

解释深度学习如何工作的理论还有待发展。以前的工作表明,深度学习执行粗粒化,在精神上类似于重整化群(RG)。这一想法已被探索的设置中的本地(最近邻相互作用)伊辛自旋晶格。我们将讨论扩展到长程自旋晶格的情形。马尔可夫链蒙特卡罗(MCMC)模拟确定的临界温度和缩放尺寸的系统。该模型被用来训练一个单一的RBM(限制玻尔兹曼机)网络,以及堆叠RBM网络。在早期的伊辛模型研究之后,单层RBM网络的训练权重定义了一个格子模型流。与最近邻Ising的结果相反,长程模型的RBM流不收敛到自旋和能量标度维的正确值。此外,可见节点和隐藏节点之间的相关函数表现出堆叠RBM和RG流之间的关键差异。叠层RBM流似乎向低温移动,而RG流向高温移动。这又不同于最近邻Ising得到的结果。

英文摘要:

A theory explaining how deep learning works is yet to be developed. Previous work suggests that deep learning performs a coarse graining, similar in spirit to the renormalization group (RG). This idea has been explored in the setting of a local (nearest neighbor interactions) Ising spin lattice. We extend the discussion to the setting of a long range spin lattice. Markov Chain Monte Carlo (MCMC) simulations determine both the critical temperature and scaling dimensions of the system. The model is used to train both a single RBM (restricted Boltzmann machine) network, as well as a stacked RBM network. Following earlier Ising model studies, the trained weights of a single layer RBM network define a flow of lattice models. In contrast to results for nearest neighbor Ising, the RBM flow for the long ranged model does not converge to the correct values for the spin and energy scaling dimension. Further, correlation functions between visible and hidden nodes exhibit key differences between the stacked RBM and RG flows. The stacked RBM flow appears to move towards low temperatures whereas the RG flow moves towards high temperature. This again differs from results obtained for nearest neighbor Ising.

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