# Neural Networks 2

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## Model Representation II : article

Forward propagation: Vectorized implementation

• ``````   (j)                             (j)
a   = g( ... ) 裡面的式子拿出來當 z
k                               k
``````

### Neural Network learning its own features

#### Forward propagation

• 記得每一個 layer 要加上一個 bias unit
• 大神為了 運算/講解 方便，可把 input layer 的 x 看成 a^(1)
• `````` (2)       (2)     (2)   (2)
a    = g( Z   );  a   , Z    ---> 為 three dimensional vector
``````
• `````` 加上:

(2)        (2)
a   = 1 ; a    --->  為 four dimensional vector
0
``````

### Summary

• vactor representation of x and z^j

``````      | x0 |           | z1^(j) |
| x1 |           | z2^(j) |
x = | .  |   z^(j) = |   .    |
| .  |           |   .    |
| xn |           | zn^(j) |
``````
• Setting x = a ^ (1)

``````  (j)   (j−1)    (j−1)
z   = Θ      * a
``````
• we can get a vector of our activation node for layer j:

``````  (j)      (j)
a   = g( z   )
``````
• z Vector

``````  (j+1)   (j)   (j)
z     = Θ   * a
``````
• result

``````          (j+1)     (j+1)
hΘ(x) = a     = g(z     )
``````

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