## How do Logits, Softmax, and Softmax Cross-Entropy Work Together in Machine Learning?

Understanding Logits, Softmax, and Softmax Cross-Entropy

In machine learning, particularly with deep neural networks, it's crucial to understand the concept of logits, softmax, and softmax cross-entropy.

Logits

Logits refer to the raw, unscaled output of a neural network layer before undergoing the softmax transformation. They are often represented as a vector of real-valued numbers and are not constrained to being between 0 and 1.

Softmax

Softmax is a mathematical function that transforms logits into probabilities. It applies an exponential function to each element of a logit vector and then normalizes the result so that the sum of probabilities equals 1. This results in a probability distribution over multiple classes.

Softmax Cross-Entropy

Softmax cross-entropy is a loss function commonly used in classification tasks. It combines the softmax transformation with the calculation of cross-entropy loss. Cross-entropy measures the distance between the predicted probability distribution (produced by softmax) and the true ground-truth label.

Difference Between tf.nn.softmax and tf.nn.softmax_cross_entropy_with_logits

Both tf.nn.softmax and tf.nn.softmax_cross_entropy_with_logits operate on logits. However, they serve different purposes:

• tf.nn.softmax: Outputs a probability distribution over the classes, which is useful for multi-class classification.
• tf.nn.softmax_cross_entropy_with_logits: Combines softmax with the cross-entropy loss, resulting in a single scalar loss value that represents the distance between the predicted and true probabilities.

Example

Consider a deep neural network with a task of classifying images into two classes: cat and dog. The last layer of the network might output a vector of two logits [0.5, 0.8].

• tf.nn.softmax: The output of tf.nn.softmax on these logits would be [0.3553, 0.6447], an array of probabilities where the second element (0.6447) represents the probability of being a dog.
• tf.nn.softmax_cross_entropy_with_logits: Assume the label for this image is [0, 1], indicating that it's a dog. The output of tf.nn.softmax_cross_entropy_with_logits would be a scalar loss value representing the cross-entropy between the predicted probabilities [0.3553, 0.6447] and the true label [0, 1].

In conclusion, logits provide the raw output of a neural network, softmax transforms them into probabilities, and softmax cross-entropy combines these probabilities with the true label to compute a loss value for optimization. Understanding these concepts is essential for designing effective machine learning models.

The above is the detailed content of ## How do Logits, Softmax, and Softmax Cross-Entropy Work Together in Machine Learning?. For more information, please follow other related articles on the PHP Chinese website!