why we cannot use the RELU activation function in the output layer?

The Rectified Linear Unit (ReLU) activation function has become one of the most widely used activation functions in deep learning, especially in the hidden layers. However, it is not suitable for use in the output layer. Here, we will discuss why this is the case.

First, it is important to understand the purpose of activation functions. They are used to introduce non-linearity into the model and make it capable of representing complex relationships between the inputs and outputs. In the hidden layers, ReLU is effective in converting linear combinations of inputs into non-linear outputs, which can help to capture more complex relationships.

However, in the output layer, we need to ensure that the predicted values are in a specific range. For example, in a binary classification problem, the output should be either 0 or 1. In a regression problem, the predicted value may need to be within a certain range, such as between 0 and 1. In these cases, using a ReLU activation function in the output layer would not be suitable as it would only produce positive values.

Additionally, ReLU is not a smooth function, which means that small changes in input can lead to large changes in output. This property is undesirable in the output layer as it can lead to unstable predictions. For example, in a regression problem, small changes in the input features should lead to small changes in the predicted output value. However, this is not the case when using ReLU as the activation function in the output layer.

In conclusion, ReLU is a powerful activation function for hidden layers but is not suitable for the output layer. This is because it only produces positive values and is not a smooth function, which can lead to unstable predictions. When choosing an activation function for the output layer, it is important to consider the range of the predicted values and the desired properties of the function. Some commonly used activation functions for the output layer include the sigmoid, softmax, and linear functions.