## What\'s the Difference Between Softmax and softmax_cross_entropy_with_logits in TensorFlow?

Logits in Tensorflow and the Distinction Between Softmax and softmax_cross_entropy_with_logits

In TensorFlow, the term "logits" refers to unscaled outputs of preceding layers, representing linear relative scale. They are commonly used in machine learning models to represent the pre-probabilistic activations before applying a softmax function.

Difference Between Softmax and softmax_cross_entropy_with_logits

Softmax (tf.nn.softmax) applies the softmax function to input tensors, converting log-probabilities (logits) into probabilities between 0 and 1. The output maintains the same shape as the input.

softmax_cross_entropy_with_logits (tf.nn.softmax_cross_entropy_with_logits) combines the softmax step and the calculation of cross-entropy loss in one operation. It provides a more mathematically sound approach for optimizing cross-entropy loss with softmax layers. The output shape of this function is smaller than the input, creating a summary metric that sums across the elements.

Example

Consider the following example:

<code class="python">import tensorflow as tf

# Create logits
logits = tf.constant([[0.1, 0.3, 0.5, 0.9]])

# Apply softmax
softmax_output = tf.nn.softmax(logits)

# Compute cross-entropy loss and softmax
loss = tf.nn.softmax_cross_entropy_with_logits(logits, tf.one_hot([0], 4))

print(softmax_output)  # [[ 0.16838508  0.205666    0.25120102  0.37474789]]
print(loss)  # [[0.69043917]]</code>

The softmax_output represents the probabilities for each class, while the loss value represents the cross-entropy loss between the logits and the provided labels.

When to Use softmax_cross_entropy_with_logits

It is recommended to use tf.nn.softmax_cross_entropy_with_logits for optimization scenarios where the output of your model is softmaxed. This function ensures numerical stability and eliminates the need for manual adjustments.

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