论文标题
无量纲的机器学习：施加确切单位
Dimensionless machine learning: Imposing exact units equivariance
论文作者
论文摘要
单位模棱两可（或单位协方差）是从测量量相关性之间的关系之间的关系必须遵守自洽的维度尺度的要求。在这里，我们以（非紧密的）小组动作来表达这种对称性，并采用了尺寸分析和Equivariant机器学习中的思想，以提供准确的单位 - 等价机器的机器学习的方法：对于任何给定的学习任务，我们首先使用尺寸分析中的经典结果来构建其输入的无尺寸无尺寸版本，然后在尺寸分析中表现出来，然后在无上限空间中执行本质。我们的方法可用于在广泛的机器学习方法上施加单位等效性，这些机器学习方法与旋转和其他组一样。我们讨论了在符号回归和仿真之类的上下文中可以获得的样本中和样本外预测准确性的提高，而对称性很重要。我们用涉及物理和生态学动态系统的简单数值示例来说明我们的方法。
Units equivariance (or units covariance) is the exact symmetry that follows from the requirement that relationships among measured quantities of physics relevance must obey self-consistent dimensional scalings. Here, we express this symmetry in terms of a (non-compact) group action, and we employ dimensional analysis and ideas from equivariant machine learning to provide a methodology for exactly units-equivariant machine learning: For any given learning task, we first construct a dimensionless version of its inputs using classic results from dimensional analysis, and then perform inference in the dimensionless space. Our approach can be used to impose units equivariance across a broad range of machine learning methods which are equivariant to rotations and other groups. We discuss the in-sample and out-of-sample prediction accuracy gains one can obtain in contexts like symbolic regression and emulation, where symmetry is important. We illustrate our approach with simple numerical examples involving dynamical systems in physics and ecology.
