Understanding Softmax Function in Neural Networks

This article will cover the essence of Softmax in terms of its principle and applications, helping you understand the Softmax function in one go.

Softmax Activation Function

1. Essence of Softmax Essence

Softmax is generally used as the last layer in a neural network for output in multi-class problems. Its essence is an activation function that normalizes a value vector into a probability distribution vector, with the sum of probabilities equal to 1.

Softmax Activation Function

Classification Problem: Classifying input data into predefined categories based on their features.

In the field of machine learning, classification problems are generally considered supervised learning. The goal of classification is to determine which known sample class a new sample belongs to based on certain features of known samples.

Classification problems can be divided into binary classification and multi-class classification based on the number of categories.

• Binary Classification: Indicates there are two categories in the classification task. In binary classification, we typically use common algorithms such as logistic regression, support vector machines, etc.

• Multi-class Classification: Indicates there are multiple categories in the classification task. In multi-class classification, we can use common algorithms such as decision trees, random forests, etc.

Binary and Multi-class Classification

Understanding Classification Problems in Detail:Neural Network Algorithms – Understanding Regression and Classification

Activation Function: A function added to artificial neural networks to help the network learn complex patterns in data.

Activation Function

In neurons, the input goes through a series of weighted sums and is then subjected to another function, which is the activation function here. Similar to the model based on neurons in the human brain, the activation function ultimately determines whether to transmit signals and what content to send to the next neuron.

Activation functions introduce non-linear elements into neural networks, enabling the network to approximate complex non-linear functions and thus solve a wider range of problems.

Activation Function

From Binary to Multi-class: Activation function evolves from Sigmoid to Softmax.

For binary classification problems, Sigmoid is a commonly used activation function that maps any real number to the interval (0, 1), where values can naturally be interpreted as probabilities.

Sigmoid Function

For multi-class problems, Softmax is a very important tool. It can convert a vector into a set of probability values, with the sum of these probabilities equal to 1.

Softmax Function

Common activation functions include Sigmoid, Tanh, Relu, and Softmax.

Learn More About Activation Functions:Understand AI – Four Common Activation Functions: Sigmoid, Tanh, ReLU, and Softmax

2. Principle of Softmax Principle

Principle of Neural Networks: Calculate predicted values through forward propagation, measure the gap between predicted values and true values through loss functions, compute gradients and update parameters through backpropagation, and introduce non-linear factors through activation functions.

• Forward Propagation: Data flows from the input layer through the hidden layers to the output layer, with each layer performing linear transformations through weights and biases, and obtaining non-linear outputs through activation functions.

• Activation Function: Introduces non-linearity to neural networks, enhancing the model’s expressive power.

• Loss Function: Measures the gap between predicted values and true values, such as mean squared error for regression and cross-entropy for classification.

• Backpropagation: Calculates the gradients of parameters layer by layer from the output layer to the input layer based on the gradient information of the loss function, updating parameters to minimize the loss function value.

• Gradient Descent: An optimization algorithm that updates network parameters based on calculated gradients at a certain learning rate, gradually approaching the optimal solution.

Learn More About Loss Functions:Neural Network Algorithms – Understanding Loss Functions

Learn More About Backpropagation:Neural Network Algorithms – Understanding Backpropagation

Learn More About Gradient Descent:Neural Network Algorithms – Understanding Gradient Descent

Mathematical Principle of Softmax: For a given real-valued vector, it first calculates the exponent (e to the power) of each element, then the ratio of each element’s exponent to the total exponent of all elements forms the output of the softmax function. This computation not only keeps the output values between 0 and 1 but also ensures that the sum of all output values equals 1.

Mathematical Principle of Softmax

3. Applications of Softmax

CNN Architecture: Composed of convolutional layers, pooling layers, and fully connected layers. The convolutional layer extracts local features of the image through convolution kernels, the pooling layer reduces data dimensions through downsampling, and the fully connected layer outputs the final result.

CNN Architecture

Learn More About CNN:Neural Network Algorithms – Understanding CNN (Convolutional Neural Network)

CNN’s Softmax Layer: A common classification layer, usually placed as the last layer in convolutional neural networks, used to convert the feature maps output by the convolutional neural network into a probability distribution.

CNN’s Softmax Layer

Transformer Architecture: Achieves efficient encoding of input sequences and generation of output sequences through components like input embeddings, positional encoding, multi-head attention, residual connections, layer normalization, masked multi-head attention, and feed-forward networks.

Transformer Architecture

Learn More About Transformer: Neural Network Algorithms – Understanding Transformer

Softmax in Transformers: Used to convert raw attention scores into probability distributions for input tokens. This distribution assigns higher attention weights to more relevant tokens and lower weights to less relevant tokens. Transformers use Softmax to weigh the importance of different input tokens when generating output through the attention mechanism.

Transformer’s Softmax Layer