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.
翻译:我们从几何地貌学的角度来研究受监督的群落变异和等同机器学习的问题。 我们建议采用一种新颖的方法,采用预处理步骤,将输入数据投射到几何空间,这相当于对称组的轨道。 然后,这种新数据可以成为任意机学模型(神经网络、随机森林、支持-摄像机等)的输入。 我们用算法来计算几何投影,这是有效的执行,我们用算法来说明我们对某些机器学习的典型问题(包括精心研究的预测CICY矩阵的Hodge数字的问题)的处理方法,在每种情况下都发现精确性相对于其他文献的准确性都有改进。 几何地表学观点还使我们能够统一描述所谓的集体变异机器学习的内在方法,其中包括文献中的许多其他方法。