北京大学物理学院本科生在量子物理与机器学习研究方面取得进展

无监督生成模型是机器学习和人工智能的重要课题和研究前沿,也被认为是通用人工智能的基础。历史上,物理学为生成型学习提供了很多思想源泉,著名的玻尔兹曼机就来自于统计物理中的伊辛模型和相关的反伊辛问题。最近,北京大学物理学院本科生韩兆宇、王峻及合作者从量子物理的玻恩诠释中获得启发,用量子波函数的概率幅模平方来描述经典数据的概率分布,建立了一个新颖的非监督学习模型——玻恩学习机(BornMachine)。该成果已在线发表于世界知名物理学期刊Physical Review X

生成模型的研究重点是如何从给定的数据集合中学习到数据的联合概率分布,以及从学习到的概率分布中高效地生成新的样本。研究团队提出将数据的联合分布概率编码成量子多体态的概率幅的模平方。他们提出在经典计算机上使用矩阵乘积态(Matrix Product States)来模拟学习的过程。矩阵乘积态的参数即张量网络的张量元,可以通过类似密度矩阵重整化群(Density Matrix Renormalization Group)的算法进行学习,最终形成一个具有泛化能力的生成模型。这个学习算法结合了量子物理与机器学习各自的优点:它不仅可以利用GPU高效地学习到模型参数,还可以利用张量网络的灵活性动态地调节模型表达能力。此外,与传统的基于统计物理的生成模型(例如玻尔兹曼机)相比,玻恩学习机还具备直接生成无关联样本的强大能力,从而可以高效地生成新的数据。

 

作用在一幅MNIST图片上的矩阵乘积态以及它的纠缠谱

基于量子态的概率生成模型融合了量子物理与机器学习的思想,是一个崭新的研究领域。玻恩学习机借助量子态内禀的概率解释及其强大的表达能力,意在为机器学习和人工智能提供更为先进的生成模型和学习算法。此外,这类模型在量子信息处理,量子计算以及多体物理中具有应用潜力。展望将来,最令人兴奋的前景应该会是在一台量子计算机上实现玻恩学习机,从而以全新的方法进行概率型的学习和建模。这项工作用使用张量网络模拟量子计算机的运行,向无监督量子机器学习迈近了一步。

此工作由韩兆宇、王峻,中科院物理研究所副研究员王磊、研究员范桁以及中科院理论物理研究所研究员张潘合作完成。王峻的工作受到国家创新训练项目的支持。

339 thoughts on “北京大学物理学院本科生在量子物理与机器学习研究方面取得进展”

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