When considering a real log canonical threshold (RLCT) that gives a Bayesian generalization error, in general, papers replace a mean error function with a relatively simple polynomial whose RLCT corresponds to that of the mean error function, and obtain its RLCT by resolving its singularities through an algebraic operation called blow-up. Though it is known that the singularities of any polynomial can be resolved by a finite number of blow-up iterations, it is not clarified whether or not it is possible to resolve singularities of a specific polynomial by applying a specific blow-up algorithm. Therefore this paper considers the blow-up algorithm for the polynomials called sum-of-products (sop) polynomials and its RLCT.

翻译：当考虑给出贝叶斯广义误差率的真实对数典型阈值时，一般情况下，论文将一个均误差函数替换为一个相对简单的多项式，其RLCT对应于均误差函数的RLCT，并通过一种称为炸裂的代数操作来解决其奇点，从而获得其RLCT。虽然已知任何多项式的奇点都可以通过有限次的炸裂迭代来解决，但尚不清楚是否可以通过应用特定的炸裂算法来解决特定多项式的奇点。因此，本文考虑了用于多项式的炸裂算法，即积和式（SOP）多项式和其RLCT。