What do you need to know about backpropagation?

What do you need to know about backpropagation?

Recall from our video that covered the intuition for backpropagation, that, for stochastic gradient descent to update the weights of the network, it first needs to calculate the gradient of the loss with respect to these weights. And calculating this gradient, is exactly what we’ll be focusing on in this video.

How does gradient descent work in backpropagation?

Gradient descent operates in a similar way when trying to find the minimum of a function: It starts at a random location in parameter space and then iteratively reduces the error J until it reaches a local minimum. At each step of the iteration, it determines the direction of steepest descent and takes a step along that direction.

How to sum gradients over all consumers in backpropagation?

And then we sum those gradients over all consumers. As a prerequisite to implementing backpropagation, we need to specify a function for each operation that computes the gradients with respect to the inputs of that operation, given the gradients with respect to the output.

How is the gradient of the loss function calculated?

In this episode, we’re finally going to see how backpropagation calculates the gradient of the loss function with respect to the weights in a neural network. So let’s get to it. We’re now on episode number four in our journey through understanding backpropagation.

Why is the gradient always negative in backpropagation?

So, always the negative of the Gradient shows the directions along which the weights should be moved in order to optimize the loss function. So, this way the gradient guides the model whether to increase or decrease weights in order to optimize the loss function.

How do you calculate the gradient in backprop?

Calculating this gradient is exactly what we’ll be focusing on in this episode. We’re first going to start out by checking out the equation that backprop uses to differentiate the loss with respect to weights in the network.

Where does the name backpropagation come from in math?

The “backwards” part of the name stems from the fact that calculation of the gradient proceeds backwards through the network, with the gradient of the final layer of weights being calculated first and the gradient of the first layer of weights being calculated last.

How does backpropagation work in a neural network?

Given the first result, we go back and adjust the weights and biases, so that we optimize the cost function — called a backwards pass. We essentially try to adjust the whole neural network, so that the output value is optimized. In a sense, this is how we tell the algorithm that it performed poorly or good.

How is total net input calculated in backpropagation?

We figure out the total net input to each hidden layer neuron, squash the total net input using an activation function (here we use the logistic function ), then repeat the process with the output layer neurons. Total net input is also referred to as just net input by some sources.

How to calculate the partial derivative in backpropagation?

We calculate the partial derivative of the total net input to with respect to the same as we did for the output neuron: Finally, we’ve updated all of our weights! When we fed forward the 0.05 and 0.1 inputs originally, the error on the network was 0.298371109. After this first round of backpropagation, the total error is now down to 0.291027924.