# Backpropagation Intuition

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Backpropagation Intuition
• Make a better intuition about backpropagation
• Technically a little more complicated

• As from example, there's two unit + 1 unit biased unit from forward propagation
• So here's in the example we first take x(1) take it to the neural networks down to the output.
• z(3)1 is the sigmoid function in layer 3 by take summation of (matrix_weight(2)10 x 1(bias_unit) + matrix_weight(2)11 x activation_unit(2)1).
• eventually a(4)1 is the prediction
• Backpropagation is doing the reverse of the forward. The process is really similar

• The formula of cost function
• if multiclass, then the formula will be added with summation of K unit classification.
• Because we are doing example of 1 output unit, and 1 example, we are also ignoring the regularization term
• For the purpose of the intuition, log will be ignored. We just want to know how close our network in predicting the output

• delta can be thought as an error for every activation value
• delta is actually the partial derivative of z, that if we change z, change the cost function, and eventually changing the actual cost
• The first step is intuitive, first final error  = the final actual ouput - the final predicted output
• Then keep going backwards from last layer to first hidden layer
• By going reverse (from right to left) we are acquiring the delta (error value) by calculating [the previous error_value * matrix_weight]
• Layer indexed from 1, the input layer

• Why? We don't know the value of d(4)1
• Next, give a little better intuition about backpropagation
• Very effective algorithm eventhough a little harder to visualize