Deep Dive into Softmax and Cross Entropy | PyTorch Explained

In this article, we will take a closer look at two key concepts in machine learning: Softmax and Cross Entropy. These concepts are commonly used in classification tasks, and are essential for understanding how neural networks work.

Softmax Function

The Softmax function is a mathematical function that converts a vector of numbers into a probability distribution. It is commonly used in the output layer of neural networks for multi-class classification tasks. The Softmax function takes an input vector of arbitrary real numbers and transforms it into a vector of probabilities that sum to 1.

The formula for the Softmax function is as follows:

softmax(x_i) = e^x_i / ∑_j e^x_j

Cross Entropy Loss

Cross Entropy is a loss function used in classification tasks to measure the difference between predicted probabilities and actual labels. It is commonly used in conjunction with the Softmax function in neural networks. The Cross Entropy loss function penalizes the model more severely for making larger errors, which helps to improve the accuracy of the model.

The formula for the Cross Entropy loss function is as follows:

CE(y, &hat;y) = -∑_i y_i log(&hat;y_i)

PyTorch Implementation

In PyTorch, both Softmax and Cross Entropy functions are readily available for use in neural network models. The PyTorch library provides simple and efficient implementations of these functions, making it easy for developers to incorporate them into their projects.

Here is an example code snippet showing how to use Softmax and Cross Entropy functions in PyTorch:

    import torch
    import torch.nn as nn
    
    # Define a sample input tensor
    input_tensor = torch.randn(3, 5)
    
    # Apply Softmax function
    softmax = nn.Softmax(dim=1)
    output_softmax = softmax(input_tensor)
    
    # Define sample target labels
    target = torch.LongTensor([0, 2, 1])
    
    # Calculate Cross Entropy loss
    loss = nn.CrossEntropyLoss()
    output_loss = loss(output_softmax, target)
  

By using these built-in functions in PyTorch, developers can easily implement and train neural networks for classification tasks with high accuracy and efficiency.