论文标题
在哈密顿人中添加机器学习：重新归一化的组转换，对称性破坏和恢复
Adding machine learning within Hamiltonians: Renormalization group transformations, symmetry breaking and restoration
论文作者
论文摘要
我们提出了机器学习功能的物理解释，通过将这些功能纳入汉密尔顿人来控制统计系统的性质的可能性。特别是，我们将设计用于相分类的神经网络的预测函数作为偶联变量，耦合到系统的哈密顿量内的外部场。结果表明，与导致显式对称性破坏的常规顺序参数的磁场相比，该场可以通过破坏或恢复对称性来诱导秩序的阶段过渡。然后，通过提出哈密顿 - 敏捷的重新持续方法来研究临界行为，并根据来自神经网络的数量形成重新归一化组映射。提供了与操作员相关的关键点和关键指数的准确估计。我们通过讨论该方法如何为桥接机器学习和物理学提供重要一步的结论。
We present a physical interpretation of machine learning functions, opening up the possibility to control properties of statistical systems via the inclusion of these functions in Hamiltonians. In particular, we include the predictive function of a neural network, designed for phase classification, as a conjugate variable coupled to an external field within the Hamiltonian of a system. Results in the two-dimensional Ising model evidence that the field can induce an order-disorder phase transition by breaking or restoring the symmetry, in contrast with the field of the conventional order parameter which causes explicit symmetry breaking. The critical behavior is then studied by proposing a Hamiltonian-agnostic reweighting approach and forming a renormalization group mapping on quantities derived from the neural network. Accurate estimates of the critical point and of the critical exponents related to the operators that govern the divergence of the correlation length are provided. We conclude by discussing how the method provides an essential step toward bridging machine learning and physics.
