keras 层的归一化输出

Question

I want to create a Keras model with Tensorflow background that returns a vector with norm 1. For this purpose, the model ends with the next layer:

main_network = Lambda(lambda t: K.l2_normalize(t, axis=1))(x)

I have also created a test in which I only create the model and, without training, I make a random prediction to check that the output has norm 1. But the test fails:

AssertionError: 0.37070954 != 1 within 0.1 delta

So the Lambda layer is not working correctly since it is not normalizing the output. I tried different values for the axis parameter and with all possible values, the test fails. But am I missing?

Answer 1

Ok, I fixed the problem. For same reason, K.l2_normalize does not work with very small numbers, so I simply changed the line by this one:

main_network = Lambda(lambda t: K.l2_normalize(1000*t, axis=1))(x)

And the now the test works right!!

Answer 2

L2 normalize formula is:

       x
---------------
sqrt(sum(x**2))

For example, for an input [3, 1, 4, 3, 1] is [3/6, 1/6, 4/6, 3/6, 1/6] = 12/6 which indicates the output of L2-normalize is not necessary to be one . If you need something that normalizes the output to the sum of 1, you probably need Softmax :

Here is an example that you can check the output of the softmax is one:

import tensorflow as tf
from tensorflow.python.keras import backend as K
from tensorflow.python.keras.layers import Lambda

x = tf.keras.layers.Input(tensor=tf.constant([[1, 2, 3, 4, 5]], dtype=tf.float32))
n_layer = Lambda(lambda t: K.softmax(t, axis=-1))(x)

with tf.Session() as sess:
    sess.run(tf.global_variables_initializer())
    print(n_layer.eval())