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Understanding Back-propagation Network Structure for Better Learning

Learn the differences between Perceptron and back-propagation networks, explore the network structure, the learning rules involved, the importance of hidden layers, and an example scenario with Jets or Sharks. Discover the benefits and drawbacks of neural networks in real-world applications.

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Understanding Back-propagation Network Structure for Better Learning

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  1. Back-propagation Chih-yun Lin 1/3/2020

  2. Agenda • Perceptron vs. back-propagation network • Network structure • Learning rule • Why a hidden layer? • An example: Jets or Sharks • Conclusions

  3. Network Structure –Perceptron O Output Unit Wj IjInput Units

  4. Network Structure –Back-propagation Network Oi Output Unit Wj,i ajHidden Units Wk,j Ik Input Units

  5. Learning Rule • Measure error • Reduce that error • By appropriately adjusting each of the weights in the network

  6. Learning Rule –Perceptron • Err = T–O • O is the predicted output • T is the correct output • WjWj+ α * Ij* Err • Ij is the activation of a unit j in the input layer • α is a constant called the learning rate

  7. Learning Rule –Back-propagation Network • Erri = Ti–Oi • Wj,iWj,i+ α * aj * Δi • Δi = Erri * g’(ini) • g’ is the derivative of the activation function g • ajis the activation of the hidden unit • Wk,jWk,j+ α * Ik * Δj • Δj = g’(inj) * ΣiWj,i* Δi

  8. Learning Rule –Back-propagation Network • E = 1/2Σi(Ti–Oi)2 • = - Ik * Δj

  9. Why a hidden layer? • (1 w1) + (1 w2) < ==> w1 + w2 < • (1 w1) + (0 w2) > ==> w1 > • (0 w1) + (1 w2) > ==> w2 > • (0 w1) + (0 w2) < ==> 0 <

  10. Why a hidden layer? (cont.) • (1 w1) + (1 w2) + (1 w3) < ==> w1 + w2 + w3 < • (1 w1) + (0 w2) + (0 w3) > ==> w1 > • (0 w1) + (1 w2) + (0 w3) > ==> w2 > • (0 w1) + (0 w2) + (0 w3) < ==> 0 <

  11. An example: Jets or Sharks

  12. Conclusion • Expressiveness: • Well-suited for continuous inputs,unlike most decision tree systems • Computational efficiency: • Time to error convergence is highly variable • Generalization: • Have reasonable success in a number of real-world problems

  13. Conclusions (cont.) • Sensitivity to noise: • Very tolerant of noise in the input data • Transparency: • Neural networks are essentially black boxes • Prior knowledge: • Hard to used one’s knowledge to “prime” a network to learn better

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