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### Types of Activation Functions in Neural Networks

Activation functions play a crucial role in neural networks, determining the output of each neuron in the network. They introduce non-linearity to the model, allowing it to learn complex patterns and make accurate predictions. In this article, we will explore several types of activation functions commonly used in neural networks:

### Sigmoid / Logistic Activation Function

The sigmoid function, also known as the logistic function, is one of the most popular activation functions. It maps any real-valued number to a value between 0 and 1. This makes it suitable for binary classification problems, where the output needs to be probabilistic. The sigmoid function is defined as:

- Range: (0, 1)

- Smooth and differentiable

- Output is easily interpretable as a probability

### Tanh Function (Hyperbolic Tangent)

The hyperbolic tangent (tanh) function is similar to the sigmoid function, but it maps each input to a value between -1 and 1. This allows it to capture both positive and negative values, making it more suitable for classification problems with outputs ranging from -1 to 1. The tanh function is defined as:

- Range: (-1, 1)

- Symmetric around the origin

- Output is sensitive to small changes in input

### ReLU Function

The Rectified Linear Unit (ReLU) function is a commonly used activation function in deep learning models. Unlike the sigmoid and tanh functions, ReLU is a non-linear function that introduces sparsity in the network. It maps negative values to zero, while positive values remain unchanged. The ReLU function is defined as:

- Range: [0, +∞)

- Simple and computationally efficient

- Does not suffer from the vanishing gradient problem

### Leaky ReLU Function

The Leaky ReLU function is a modification of the ReLU function that addresses the “dying ReLU” problem, where neurons become non-responsive during training. It adds a small slope to negative inputs, allowing for the passage of small negative values. The Leaky ReLU function is defined as:

- Range: (-∞, +∞)

- Allows for learning even when neurons are inactive

- Can be more robust to noise in the input

### Softmax Function

The softmax function is commonly used as the activation function in the output layer of classification models. It converts a vector of real numbers into a probability distribution over multiple classes, ensuring that the sum of all probabilities is equal to 1. The softmax function is defined as:

- Range: (0, 1)

- Outputs can be interpreted as class probabilities

- Used for multi-class classification

### Identity Function

The identity function, also known as the linear function, is a simple activation function that outputs the same value as the input. It is commonly used in regression problems, where the network needs to predict continuous values. The identity function is defined as:

- Range: (-∞, +∞)

- No non-linearity introduced

- Output is a linear combination of the input

### Conclusion

In summary, activation functions are a critical component of neural networks, allowing for non-linearity and complex pattern recognition. The choice of activation function depends on the nature of the problem and the desired properties of the network. Whether it is the sigmoid, tanh, ReLU, Leaky ReLU, softmax, or identity function, each activation function has its own characteristics and suitability for different tasks. Understanding these functions is essential for designing efficient and accurate neural network models.