论文标题
在几乎连续光谱和对称性破裂中检测信号
Signal detection in nearly continuous spectra and symmetry breaking
论文作者
论文摘要
使用非高斯分布的重新归一化组适当地描述具有大量相互作用自由度的系统的大规模行为。然后，当数据分析中的标准方法分解时，预计物理中使用的重新归一化组技术将对问题有所帮助。目前，具有几乎连续光谱的协方差矩阵的信号检测和识别是数据科学和机器学习中的一个空旷问题。使用Arxiv：2011.02376中引入的字段理论嵌入来重现实验相关性，我们在本文中表明，信号的存在可能以$ \ MathBb {Z} _2 $ - s _-Symmmetry breaking为特征。在我们的研究中，我们使用非扰动重新归一化的形式主义，使用局部电位近似来构建流量的近似解决方案。此外，我们专注于几乎连续的信号构建，这是对Marchenko-Pastur法律的扰动，并具有许多离散的尖峰。
The large scale behavior of systems having a large number of interacting degrees of freedom is suitably described using renormalization group, from non-Gaussian distributions. Renormalization group techniques used in physics are then expected to be helpful for issues when standard methods in data analysis break down. Signal detection and recognition for covariance matrices having nearly continuous spectra is currently an open issue in data science and machine learning. Using the field theoretical embedding introduced in arXiv:2011.02376 to reproduces experimental correlations, we show in this paper that the presence of a signal may be characterized by a phase transition with $\mathbb{Z}_2$-symmetry breaking. For our investigations, we use the nonperturbative renormalization group formalism, using a local potential approximation to construct an approximate solution of the flow. Moreover, we focus on the nearly continuous signal build as a perturbation of the Marchenko-Pastur law with many discrete spikes.
