论文标题
基本域预测的小组不变的机器学习
Group invariant machine learning by fundamental domain projections
论文作者
论文摘要
从几何拓扑的角度来看，我们解决了有监督的小组不变和模棱两可的机器学习的精心研究的问题。我们使用预处理步骤提出了一种新颖的方法，该方法涉及将输入数据投射到参数对称群体轨道的几何空间中。然后，这些新数据可以成为任意机器学习模型（神经网络，随机森林，支持矢量机等）的输入。 我们给出了一种算法来计算有效实施的几何投影，我们就在某些示例机器学习问题上说明了我们的方法（包括预测旋转矩阵的霍奇数量的良好问题），在每种情况下都发现了与文献相对于其他人的准确性相对于其他情况的提高。几何拓扑观点还使我们能够对所谓的固有方法进行统一的描述，以构成文献中许多其他方法。
We approach the well-studied problem of supervised group invariant and equivariant machine learning from the point of view of geometric topology. We propose a novel approach using a pre-processing step, which involves projecting the input data into a geometric space which parametrises the orbits of the symmetry group. This new data can then be the input for an arbitrary machine learning model (neural network, random forest, support-vector machine etc). We give an algorithm to compute the geometric projection, which is efficient to implement, and we illustrate our approach on some example machine learning problems (including the well-studied problem of predicting Hodge numbers of CICY matrices), in each case finding an improvement in accuracy versus others in the literature. The geometric topology viewpoint also allows us to give a unified description of so-called intrinsic approaches to group equivariant machine learning, which encompasses many other approaches in the literature.
