The Splendors and Miseries of Heavisidisation
V.Dolotin and A.Morozov
机器学习(ML)适用于科学问题,即那些有明确答案的人,只有当这个答案可以带到一种特殊形式G:X⟶Z与G(x⃗)表示为迭代的Heaviside函数的组合时。 目前,如果存在这种表示,那么这些表示存在哪些障碍,如果不存在,那么将已知的公式转换为这种形式的方法就远非显而易见。 这引起了一个以这样的术语重新制定普通科学的计划 - 这听起来像是建设性数学方法的有力增强,只是这次它涉及所有自然科学。 我们描述了这条漫长的道路上的第一步。
Machine Learning (ML) is applicable to scientific problems, i.e. to those which have a well defined answer, only if this answer can be brought to a peculiar form G: X⟶ Z with G(x⃗) expressed as a combination of iterated Heaviside functions. At present it is far from obvious, if and when such representations exist, what are the obstacles and, if they are absent, what are the ways to convert the known formulas into this form. This gives rise to a program of reformulation of ordinary science in suc...