How to calculate new weights for neurons - what is the general equation for it?
closed as too broad by Stephen Rauch, Mephy, oW_, BrunoGL, tuomastik Aug 11 at 5:29
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I can point you to a good resource http://blog.kaggle.com/2017/12/06/introduction-to-neural-networks-2/
I'm assuming you already understand forward propagation.(Initialize the weights randomly, calculate the net input and use an activation function over the net input to get the output and then forward the output to another layer and repeat the process).
The intuition behind back propagation is to gradually update weights that is optimizing your loss function. When you have an output, you run it through a Loss function L and find the loss. Then let's say your optimization function is Gradient Descent, you determine how much the current loss will change with respect to a small change in each of the weights. You calculate the gradient of L(partially differentiate L) with respect to every weight in the network. Then you take a small step(learning rate) in the negative direction of you gradient. And Repeat this process until you've optimized your loss function.
So the equation you're asking for really depends on which optimizing algorithm you're using to optimize your weights. Follow the link and it'll walk you through each step of the back propagation using Gradient Descent.