What is difference between tf.truncated_normal and tf.random_normal?

tf.truncated_normal() selects random numbers from a normal distribution whose mean is close to 0 and values are close to 0. For example, from -0.1 to 0.1. It's called truncated because your cutting off the tails from a normal distribution.

tf.random_normal() selects random numbers from a normal distribution whose mean is close to 0, but values can be a bit further apart. For example, from -2 to 2.

In machine learning, in practice, you usually want your weights to be close to 0.

The documentation says it all: For truncated normal distribution:

The values are drawn from a normal distribution with specified mean and standard deviation, discarding and re-drawing any samples that are more than two standard deviations from the mean.

Most probably it is easy to understand the difference by plotting the graph for yourself (%magic is because I use jupyter notebook):

import tensorflow as tf
import matplotlib.pyplot as plt

%matplotlib inline  

n = 500000
A = tf.truncated_normal((n,))
B = tf.random_normal((n,))
with tf.Session() as sess:
    a, b = sess.run([A, B])

And now

plt.hist(a, 100, (-4.2, 4.2));
plt.hist(b, 100, (-4.2, 4.2));

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The point for using truncated normal is to overcome saturation of tome functions like sigmoid (where if the value is too big/small, the neuron stops learning).