# Activation Function Essay

## Activation Function

#### Definition of activation function

An activation function in computational networks as a node that defines an output depending on its set of inputs. Generally, an activation function is said to be one of the most essential parameters in neural networks. When selecting specific nodes of an activation function it is necessary to be careful. It is also important to ensure proper training is done with a neural network because this determines how an activation function works with the network.

#### The roles and types of activation function

However in biological neural networks it is an abstract representation of the actual potential of the firing in a cell. The activation function in this case can be binary in the sense that it is not firing any cell.

There are several types of activation functions and they each play a unique role:

• Identity function. This is usually used with input unit. In some instances the net input can be multiplied with a constant in order to form a linear function. It is illustrated using the equation below:

g(x) = x

• Binary step function. This is usually used with single layer networks and is sometimes referred to as the Heaviside function or Threshold function. The output of this function is limited to two values, 1 or 0. If x is greater or equal to theta (θ) then the output value will be one. However, where x is less than theta then the output value will be equal to 0. It is illustrated using the equation below:

g(x) = 1 if x ≥ θ

g(x) = 0 if x < θ

• Sigmoid function. This function is best used with the neural networks especially when they are trained using backward propagation method. It is mainly preferred because it can dramatically reduce the burden of computing during training and is also very easy to identify. This function is used with the outputs which lie between 0 and 1. It is illustrated using the equation below:
• Binary sigmoid function. This function bears similar characteristics with those of the sigmoid function. However, these functions are usually used with the outputs whose values lie between -1 and 1. They can be illustrated using the following equation:

#### Choosing activation functions

Generally, sigmoid functions are more popular than any other types of activation functions. Where there is need to
introduce the element of non-linearity into a network, activation functions are used together with hidden units. Even though linear functions are important, the non-linearity or capability to characterize a non-linear function is the element that makes multilayer networks more powerful in training. Non-linear functions can therefore facilitate training over any network.

Nevertheless, it is important to consider the methods used in the training. For instance, in back propagation method, the non-linear function must be differentiable.  It might also be necessary to bind the values. Activation functions should also be chosen carefully so as to suit the distribution of target values especially when used with output units. When used with sigmoid functions, the outputs should be scaled so that they are in the same range as the output of the activation function.

Where a target value has no bounded range, then it is better to use the unbounded activation functions. In most cases, the identity function is preferred under such circumstances. An exponential output activation function is also used in instances where the target values are positive yet have no known upper limit.

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