In school we round numbers like 0.5, 1123.5 towards the bigger number. It’s a “round half up” method.

That introduces an undesired bias some cases. For example if we have a large data set, and we aggregate some column containing a lot of .5 fractions. In order to adjust for it in many cases a rounding of 0.5 towards nearest even number is applied. It’s “Rounding half to even” or “banker’s rounding”.

This method is used in IEEE Standard for Floating-Point Arithmetic (IEEE 754). Python, numpy and pytorch use it as well.

Truncation like int(0.5) and int(1.5) just keeps the integer part.

Example

>>> import torch
>>> import math
>>> import numpy as np

Defining an array with a lot of .5-s:

>>> a = [x / 2. for x in range(10)]
>>> a
[0.0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5]

Truncation just keeps the integer part:

>>> list(map(int, a))
[0, 0, 1, 1, 2, 2, 3, 3, 4, 4]

Rounding introduces more even numbers:

>>> list(map(round, a))
[0, 0, 1, 2, 2, 2, 3, 4, 4, 4]

Truncation in pytorch:

>>> torch.tensor(a, dtype=torch.int)
tensor([0, 0, 1, 1, 2, 2, 3, 3, 4, 4], dtype=torch.int32)

>>> torch.tensor(a, dtype=torch.float64).type(torch.int64)
tensor([0, 0, 1, 1, 2, 2, 3, 3, 4, 4])

Rounding in pytorch:

>>> torch.tensor(a, dtype=torch.float64).round()
tensor([0., 0., 1., 2., 2., 2., 3., 4., 4., 4.], dtype=torch.float64)

Truncation and rounding in numpy works the same way:

>>> np.array(a, dtype=np.int)
array([0, 0, 1, 1, 2, 2, 3, 3, 4, 4])

>>> np.round(a)
array([0., 0., 1., 2., 2., 2., 3., 4., 4., 4.])