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Week 4

Artificial Neural Network

Backpropagation

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Artificial Neural Network

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Outline

  • Konsep Turunan Fungsi
  • Forward pass
  • Backward pass

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Turunan Fungsi

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Turunan Fungsi

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Turunan Fungsi

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Turunan Fungsi

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Contoh: Fungsi Sigmoid

Fungsi Sigmoid

https://machinelearningmastery.com/a-gentle-introduction-to-sigmoid-function/

  • Sigmoid selalu naik (monoton increasing)
  • Turunan sigmoid selalu positif (tidak mungkin sigmoid memiliki turunan negatif)

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Turunan Fungsi Sigmoid

  • Jika input x besar positif, maka:
    • output mendekati 1
    • nilai turunan kecil (fungsi mendatar), artinya perubahan sedikit nilai x tidak mempengaruhi nilai outputnya.
  • Jika input x besar negatif, maka:
    • output mendekati 0
    • nilai turunan kecil (fungsi mendatar), artinya perubahan sedikit nilai x tidak mempengaruhi nilai outputnya.
  • Jika x = 0, maka:
    • output 0.5
    • turunan paling besar, yaitu 0.25 (kurva paling curam di Tengah), artinya perubahan kecil pada x → perubahan besar pada output.

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Outline

  • Konsep Turunan Fungsi
  • Forward pass
  • Backward pass

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Forward Pass vs. Backward Pass

  • Forward Pass (Propagasi Maju)
    • Tujuan: Menghitung output jaringan dan nilai cost/error dari suatu input.
    • Alur: Data mengalir dari input → hidden layers → output, layer demi layer, searah ke depan.
  • Backward Pass (Propagasi Balik)
    • Tujuan: Menghitung gradien cost terhadap setiap bobot dan bias, agar bisa diperbaiki lewat gradient descent.
    • Alur: Error mengalir dari output → hidden layers → input, layer demi layer, mundur ke belakang.

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Forward Phase

 

 

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Forward Phase

Persamaan tersebut dapat dituliskan dalam matrix-based expression:

 

 

Pertanyaan: Berapa dimensi setiap matriks pada persamaan di atas?

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Cost Function

Quadratic Cost Function

 

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Cost Function

 

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Cost Function

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Outline

  • Konsep Turunan Fungsi
  • Forward pass
  • Backward pass

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Backpropagation

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Semakin dalam layernya, semakin banyak suku yang harus dikalikan.

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Backpropagation

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Backpropagation

Backpropagation memiliki 4 persamaan fundamental (BP1-BP4)

Kode

Persamaan

Fungsi

BP1

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Hitung error di layer output

BP2

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Geser error ke layer sebelumnya

BP3

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Gradien untuk bias

BP4

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Gradien untuk bobot

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Backpropagation- BP1

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Backpropagation- BP1

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Backpropagation – BP1

BP1: An equation for the error in the output layer

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Backpropagation – BP1

BP1: An equation for the error in the output layer

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Write the equation in matrix-based form

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Backpropagation – BP1

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Backpropagation – BP1

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Backpropagation – BP2

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Backpropagation – BP3

BP3: An equation for the rate of change of the cost with respect to any bias in the network

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Backpropagation – BP4

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Backpropagation – BP4

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Backpropagation

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Gradient Descent

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Backpropagation Algorithm

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Backpropagation Algorithm (cont.)

 

 

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Sigmoid in Backpropagation

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Latihan

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Referensi

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