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Understanding Neural Networks: Depth and Computational Graphs

This lecture covers the depth of understanding in neural networks, including computational graphs and backpropagation. Learn how to calculate derivatives and perform standard operations.

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Understanding Neural Networks: Depth and Computational Graphs

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Presentation Transcript

  1. Objectives for Lecture 8: Neural Networks Depth of understanding • After the lecture you are able to…

  2. Repetition

  3. Repetition

  4. Last Week: Today:

  5. Computational Graph Options: 1. Analytical 2. Differencequotient 3. Computationalgraph

  6. Computational GraphSimple example Letscalculatesome derivatives!

  7. Computational GraphSimple example Letscalculatesome derivatives!

  8. Computational GraphSimple example Letscalculatesome derivatives!

  9. Computational GraphSimple example Letscalculatesome derivatives!

  10. Computational GraphSimple example Letscalculatesome derivatives!

  11. Computational GraphSimple example Letscalculatesome derivatives!

  12. Computational GraphSimple example Letscalculatesome derivatives!

  13. Computational GraphSimple example Letscalculatesome derivatives!

  14. Computational GraphSimple example Gradient „flows“ Upstream Gradient Downstream Gradient Letscalculatesome derivatives!

  15. Computational GraphSimple example Letscalculatesome derivatives!

  16. Computational GraphSimple example Letscalculatesome derivatives!

  17. Computational GraphStandard operations Multiplication Addition: Downstream gradient remainsthe same Downstream gradient switchestootherfactor

  18. Computational GraphSimple example, withnumbers

  19. Computational GraphSimple example, withnumbers

  20. Computational GraphSimple example, withnumbers

  21. Computational GraphSimple example, withnumbers

  22. Computational GraphSimple example, withnumbers

  23. Computational GraphSimple example, withnumbers

  24. Computational GraphAbstract function

  25. Computational GraphAbstract function Forward path

  26. Computational GraphAbstract function Savinglocalgradientsduringforwardpath Forward path

  27. Computational GraphAbstract function Alreadycalculatedduringforwardpath Backwardpath

  28. ComputationalGraphAbstract function Alreadycalculatedduringforwardpath Backwardpath

  29. ComputationalGraphAbstract function

  30. Computational Graph ComplexExample

  31. ComputationalGraphComplexExample

  32. ComputationalGraphComplexExample

  33. ComputationalGraphComplexExample

  34. Computational Graph Neuron

  35. Computational GraphNeuron

  36. Computational GraphNeuron

  37. Computational GraphNeuron Local derivative

  38. Computational GraphNeuron

  39. BackpropagationNeuralChain Forward path Input Neuron Layer 1 Layer 2 Loss Function

  40. BackpropagationNeural Chain Forward path Input Neuron Layer 1 Layer 2 Loss Function

  41. BackpropagationNeuralChain Forward path Input Neuron Layer 1 Layer 2 Loss Function Backwardpath

  42. BackpropagationNeuralChain

  43. BackpropagationNeuralChain Forward path Input Neuron Layer 1 Layer 2 Loss Function Backwardpath

  44. BackpropagationNeuralChain

  45. BackpropagationNeuralChain Forward path Input Neuron Layer 1 Layer 2 Loss Function Backwardpath

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