Sigmoid Activations
What are Sigmoid Activations?
Sigmoid Activation is a type of mathematical function used in artificial neural networks (ANNs). It is represented by the mathematical expression f(x) = 1/(1+e-x), where x stands for input and e stands for the Euler's number. Sigmoid functions have an S-shaped curve and are widely used in ANN to transform input data into output values with nonlinear behavior.
How does Sigmoid Activation work?
When the input value is very small or negative, the output value of the sigmoid function is around zero. As the input value increases, the output value grows and approaches one. Sigmoid activation is known for nonlinear behavior and is often used in ANN as a threshold function to determine the firing rate of neurons. ANNs use this threshold function to simulate the behavior of biological neurons in a neural network.
Drawbacks of Sigmoid Activation
Several factors limit the usefulness of sigmoid activations in ANNs. One of these is that they cause vanishing gradients, which can occur when the activation function saturates at the extreme ends of the curve. This means that the gradient of the function during training becomes too small, hindering the optimization process. Similarly, this leads to slower convergence, which can result in longer training times. As a result, researchers have been looking for alternative activation functions that can mitigate these problems.
Alternatives to Sigmoid Activation
There are several alternative activation functions that have been found to be better suited to ANNs. One of the most popular is the Rectified Linear Unit (ReLU) activation function, which is defined as f(x) = max(0, x). It overcomes the problem of vanishing gradients because it does not saturate at the extreme ends of the curve.
Another alternative is the Leaky Rectified Linear Unit (Leaky ReLU) which addresses some of the shortcomings of ReLU. It introduces a small, positive slope for x < 0, which avoids the "dying ReLU" problem that occurs when the gradient of the function is zero for negative input values. There are many more activation functions that have been proposed, each with its own advantages and disadvantages.
Sigmoid activation functions are widely used in ANNs due to their mathematical simplicity and ability to capture nonlinear behavior. However, their drawbacks, which include slow convergence and saturation, have led to the development of alternative activation functions. ReLU has become one of the most popular alternatives due to its simple design and fast training times. Despite these shortcomings, sigmoid functions remain useful in certain types of ANNs and continue to find their place in machine learning applications.
