- 
    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