What is logits softmax and softmax cross entropy with logits in Python

Question

I was going through the tensorflow API docs here. In the tensorflow documentation, they used a keyword called logits. What is it? In a lot of methods in the API docs it is written like

tf.nn.softmax(logits, name=None)

If what is written is those logits are only Tensors, why keeping a different name like logits?

Another thing is that there are two methods I could not differentiate. They were

tf.nn.softmax(logits, name=None)
tf.nn.softmax_cross_entropy_with_logits(logits, labels, name=None)

What are the differences between them? The docs are not clear to me. I know what tf.nn.softmaxdoes. But not the other. An example will be really helpful.

Answer 1

Suppose you have two tensors, where y_hat contains computed scores for each class (for example, from y = W*x +b) and y_true contains one-hot encoded true labels.

y_hat  = ... # Predicted label, e.g. y = tf.matmul(X, W) + b
y_true = ... # True label, one-hot encoded

If you interpret the scores in y_hat as unnormalized log probabilities, then they are logits.

Additionally, the total cross-entropy loss computed in this manner:

y_hat_softmax = tf.nn.softmax(y_hat)
total_loss = tf.reduce_mean(-tf.reduce_sum(y_true * tf.log(y_hat_softmax), [1]))

is essentially equivalent to the total cross-entropy loss computed with the function softmax_cross_entropy_with_logits():

total_loss = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(y_hat, y_true))