  We study the parameter dependence of numerical results obtained by the tensor
renormalization group. We often observe an irregular behavior as the parameters
are varied with the method, which makes it difficult to perform the numerical
derivatives in terms of the parameter. With the use of two-dimensional Ising
model we explicitly show that the sharp cutoff used in the truncated singular
value decomposition causes this unwanted behavior when the level crossing
happens between singular values below and above the truncation order as the
parameters are varied. We also test a smooth cutoff, instead of the sharp one,
as a truncation scheme and discuss its effects.
