How is the loss function used in backpropagation?

How is the loss function used in backpropagation?

We adjust these random weights using the backpropagation. While performing the back-propagation we need to compute how good our predictions are. To do this, we use the concept of Loss/Cost function. The Loss function is the difference between our predicted and actual values.

How is the derivative treated as a constant in backpropagation?

While finding the partial derivative, the remaining terms are treated as constants. If you consider the curve in the above figure as our loss function with respect a feature, then we can say that the derivative is the slope of our loss function and represents the instantaneous rate of change of y with respect to x.

What does the third term mean in backpropagation?

Our third term encompasses the inputs that we used to pass into our sigmoid activation function. Recall that during forward propagation, the outputs of the hidden layer are multiplied by the weights. These linear combinations are then passed into the activation function and the final output layer.

How does gradient descent work in backpropagation?

This gives us the direction of the change of our function. Below is an equation that shows how to update weights using the Gradient Descent.

Why is the gradient of the error function used in backpropagation?

The reason for this assumption is that the backpropagation algorithm calculates the gradient of the error function for a single training example, which needs to be generalized to the overall error function. The second assumption is that it can be written as a function of the outputs from the neural network. .

When to use the update rule in backpropagation?

Hold that thought, and now let’s use the same update rule used in backpropagation to update x: According to the backpropagation update rule we’d want to move x to the right if x is negative (i.e. x + α ), and we’d like to move x to the left if x is positive (i.e. x — α ).

How is the derivative of the cost function evaluated in backpropagation?

Essentially, backpropagation evaluates the expression for the derivative of the cost function as a product of derivatives between each layer from left to right – “backwards” – with the gradient of the weights between each layer being a simple modification of the partial products (the “backwards propagated error”).