An activation function in a neural network is a mathematical function that introduces non-linearity into the output of a neuron. In other words, it takes the weighted sum of the inputs to the neuron and adds a bias term, then applies a non-linear function to produce the output of the neuron.
The choice of activation function can greatly impact the performance of a neural network. There are several popular activation functions, including:
- Sigmoid function: A smooth, S-shaped curve that maps any input to a value between 0 and 1. It was one of the first activation functions used in neural networks, but is less commonly used today due to its vanishing gradient problem.
- ReLU (Rectified Linear Unit) function: A simple, piecewise linear function that returns 0 for any negative input, and the input value itself for any positive input. It is the most commonly used activation function today due to its simplicity and effectiveness.
- Tanh (hyperbolic tangent) function: A smooth, S-shaped curve similar to the sigmoid function, but maps inputs to a value between -1 and 1. It can be useful in some applications where inputs can have negative values.
- Softmax function: An activation function typically used in the output layer of a neural network for multi-class classification problems. It maps the output of the network to a probability distribution over the possible classes.
There are many other activation functions, and researchers are constantly exploring new ones to improve neural network performance in different applications.
Activation functions are used in neural networks for several reasons:
- Introducing non-linearity: Without activation functions, neural networks would simply be a series of linear transformations. However, many real-world problems are inherently non-linear, and thus require non-linear transformations to be effectively modeled. Activation functions introduce non-linearity into the output of each neuron, allowing neural networks to model more complex relationships between inputs and outputs.
- Stabilizing gradients: When training a neural network using backpropagation, the gradients can become unstable and either vanish or explode. Activation functions can help to stabilize the gradients and make training more efficient.
- Providing output range: Activation functions can restrict the output of a neuron to a certain range, such as between 0 and 1 for the sigmoid function or between -1 and 1 for the tanh function. This can be useful for certain types of problems, such as binary classification or regression with outputs bounded by certain limits.
- Non-monotonic functions: Certain activation functions are non-monotonic, which means that they introduce local maxima and minima in the output of the neuron. This can help to prevent the network from getting stuck in local optima during training and improve its ability to find the global optimum.
Overall, activation functions play a critical role in the effectiveness and efficiency of neural networks, and the choice of activation function can greatly impact the performance of the network on a given task.