arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2001.00927cond-mat.dis-nncs.LGquant-ph
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自旋玻璃系统的概率密度理论

A Probability Density Theory for Spin-Glass Systems

The RAND Corporation(兰德公司);Google Research(谷歌研究院)

Gavin S. Hartnett, Masoud Mohseni

摘要:

自旋玻璃系统是统计物理和计算机科学中描述多体现象的通用模型。NP难组合优化问题的高质量解可以编码到自旋玻璃系统的低能态中。在一般情况下,评估这些模型的相关物理和计算性能是困难的,由于临界减速附近的相变。理想情况下,人们可以利用深度学习的最新进展来表征这些复杂系统的低能量特性。不幸的是,许多最有前途的机器学习方法只适用于连续变量的分布,因此不能直接应用于离散的自旋玻璃模型。为此,我们发展了一个连续的概率密度理论的自旋玻璃系统的任意尺寸,相互作用和本地的领域。我们展示了我们的配方几何编码的自旋玻璃的关键物理和计算特性的实例方式,而不需要淬火无序平均。我们表明,我们的方法是超越了平均场论,并确定从一个凸的过渡到非凸的能量景观的温度降低过去的临界温度。我们应用我们的形式主义的一些自旋玻璃模型,包括谢灵顿-柯克帕特里克(SK)模型,自旋随机Erdens-Rényi图,和随机限制玻尔兹曼机。

英文摘要:

Spin-glass systems are universal models for representing many-body phenomena in statistical physics and computer science. High quality solutions of NP-hard combinatorial optimization problems can be encoded into low energy states of spin-glass systems. In general, evaluating the relevant physical and computational properties of such models is difficult due to critical slowing down near a phase transition. Ideally, one could use recent advances in deep learning for characterizing the low-energy properties of these complex systems. Unfortunately, many of the most promising machine learning approaches are only valid for distributions over continuous variables and thus cannot be directly applied to discrete spin-glass models. To this end, we develop a continuous probability density theory for spin-glass systems with arbitrary dimensions, interactions, and local fields. We show how our formulation geometrically encodes key physical and computational properties of the spin-glass in an instance-wise fashion without the need for quenched disorder averaging. We show that our approach is beyond the mean-field theory and identify a transition from a convex to non-convex energy landscape as the temperature is lowered past a critical temperature. We apply our formalism to a number of spin-glass models including the Sherrington-Kirkpatrick (SK) model, spins on random Erdős-Rényi graphs, and random restricted Boltzmann machines.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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