The ReLU activation function is a non-linear function that is commonly used in deep learning models, including convolutional neural networks (CNNs) like ResNet50. The ReLU function is defined as follows:

ReLU(x) = max(0, x)

In other words, the ReLU function takes an input x and returns the maximum of 0 and x. This means that if the input x is negative, the output is 0, but if the input x is positive, the output is just x.

One of the key benefits of the ReLU function is that it helps to prevent the "vanishing gradient" problem in deep learning models. This problem occurs when the gradients (which represent how much the weights in the model need to be adjusted) become very small as they are propagated backwards through the layers of the model during training. When this happens, the model can't learn as effectively, and it may take a long time (or never) to converge to a good solution.

The ReLU function helps to prevent the vanishing gradient problem by ensuring that the gradients are always non-zero for positive inputs. This means that the weights in the model can be adjusted more effectively during training, and the model can learn more quickly and effectively.

Here's an example to help illustrate this. Let's say we have a deep learning model with many layers, and we're using a sigmoid activation function (which is a common non-linear function used in deep learning) in each layer. The sigmoid function is defined as follows:

sigmoid(x) = 1 / (1 + exp(-x))

Now let's say we're training this model on some data, and we're backpropagating the gradients through the layers. As we do this, we notice that the gradients are getting smaller and smaller as they move backwards through the layers. This is because the derivative of the sigmoid function becomes very small as the input gets very large or very small.

If we were to switch to using the ReLU activation function instead, the gradients would not become small as easily, because the derivative of the ReLU function (rate of change of the sigmoid function at a given point) is either 0 or 1 (depending on whether the input is positive or negative). This means that the model can learn more effectively, and we may be able to train it more quickly and get better results.

I hope this helps to illustrate the importance of the ReLU activation function in deep learning models!