# How can I implement back-propagation for medium-sized neural networks?

I've been wanting to make my own Neural Network in Python, in order to better understand how it works. I've been following this series of videos as a sort of guide, but it seems the backpropagation will get much more difficult when you use a larger network, which I plan to do. He doesn't really explain how to scale it to larger ones.

Currently, my network feeds forward, but I don't have much of an idea of where to start with backpropagation. My code is posted below, to show you where I'm currently at (I'm not asking for coding help, just for some pointers to good sources, and I figure knowing where I'm currently at might help):

import numpy

class NN:
prediction = []
def __init__(self,input_length):
self.layers = []
self.input_length = input_length
self.layers.append(layer)
if len(self.layers) >1:
self.layers[len(self.layers)-1].setWeights(len(self.layers[len(self.layers)-2].neurons))
else:
self.layers.setWeights(self.input_length)
def feedForward(self, inputs):
_inputs = inputs
for i in range(len(self.layers)):
self.layers[i].process(_inputs)
_inputs = self.layers[i].output
self.prediction = _inputs

def calculateErr(self, target):
out = []
for i in range(0,len(self.prediction)):
out.append(  (self.prediction[i] - target[i]) ** 2  )
return out

class Layer:

neurons = []
weights = []
biases = []
output = []

def __init__(self,length,function):
for i in range(0,length):
self.neurons.append(Neuron(function))
self.biases.append(numpy.random.randn())

def setWeights(self, inlength):
for i in range(0,inlength):
self.weights.append([])
for j in range(0, inlength):
self.weights[i].append(numpy.random.randn())

def process(self,inputs):
for i in range(0, len(self.neurons)):
self.output.append(self.neurons[i].run(inputs,self.weights[i], self.biases[i]))

class Neuron:
output = 0
def __init__(self, function):
self.function = function
def run(self, inputs, weights, bias):
self.output = self.function(inputs,weights,bias)
return self.output

def sigmoid(n):
return 1/(1+numpy.exp(n))

def inputlayer_func(inputs,weights,bias):
return inputs

def l2_func(inputs,weights,bias):
out = 0

for i in range(0,len(inputs)):
out += weights[i] * inputs[i]
out += bias

return sigmoid(out)

NNet = NN(2)

l2 = Layer(1,l2_func)

NNet.feedForward([2.0,1.0])
print(NNet.prediction)


So, is there any resource that explains how to implement the back-propagation algorithm step-by-step?