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：在考虑给出贝叶斯泛化误差的实对数规范阈值（RLCT）时，通常论文会用一个相对简单的多项式替换均值误差函数，该多项式的RLCT与均值误差函数的RLCT相对应，并通过称为爆破的代数操作来解析其奇点以获得RLCT。尽管已知任何多项式的奇点都可以通过有限次迭代爆破来解析，但对于特定多项式是否可以通过应用特定爆破算法来解析其奇点，尚不清楚。因此，本文研究了称为乘积和（sop）多项式的爆破算法及其RLCT。