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Deep learning

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DrBaljitSinghKhehra

The document discusses deep learning and convolutional neural networks. It provides details on concepts like convolution, activation maps, pooling, and the general architecture of CNNs. CNNs are made up of repeating sequences of convolutional layers and pooling layers, followed by fully connected layers at the end. Convolutional layers apply filters to input images or feature maps from previous layers to extract features. Pooling layers reduce the spatial size to make representations more manageable.

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Deep Learning Dr. Baljit Singh Khehra Professor CSE Department Baba Banda Singh Bahadur Engineering College Fatehgarh Sahib-140407, Punjab, India
Convolution      M1 N1 N1 f * g (x, y) f * g (x)    0     f (,)g(x , y  )  0 0  f (,)g(x , y  )dd f ()g(x )  f ()g(x )d 2D(continuous, discrete) : 1D(continuous, discrete) : Input Kernel Output is sometimes called Feature map
Convolution
32 3 32x32x3 image width height 32 depth Digital Color Image
32x32x3 image 5x5x3 filter 32 Convolve the filter with the image i.e. “slide over the image spatially, computing dot products” 32 3 Convolutions: More detail
32 3 Convolution Layer 32x32x3 image 5x5x3 filter 32 1 number: the result of taking a dot product between the filter and a small 5x5x3 chunk of the image (i.e. 5*5*3 =75-dimensional dot product + bias) Convolutions: More detail
32 3 activation mapConvolution Layer 32x32x3 image 5x5x3 filter 32 1 28 28 convolve (slide) over all spatial locations Convolutions: More detail
32 3 6 28 For example, if we had 6 5x5 filters, we’ll get 6 separate activation maps: activation maps 32 28 Convolution Layer We stack these up to get a “new image” of size28x28x6!
Size of Image after Convolution  Input Image of Size M×N denoted as  If Number of Filter: NF applied on input image, then Activation Maps will be NF  Size of each filter is m×n  Filters are denoted as  Let stride be s and padding be p  Then, size of each activation map ),(),(),( :),( yxByxGyxR yxf fff ),(,..........),,(),,( 21 yxgyxgyxg NF ),(),(),( ..................................... ),(),(),( ),(),(),( 222 111 kjhkjhkjh kjhkjhkjh kjhkjhkjh b NF g NF r NF bgr bgr                 1 2 1 2 s npN s mpM
Example  Input Image of Size M×N=32×32 denoted as  If Number of Filter: NF=6 applied on input image, then Activation Maps will be NF=6  Size of each filter is m×n=5×5  Filters are denoted as  Let stride be s=1 and padding be p=0  Then, size of each activation map will be 28×28 ),(),(),( :),( yxByxGyxR yxf fff ),(,..........),,(),,( 621 yxgyxgyxg ),(),(),( ..................................... ),(),(),( ),(),(),( 666 222 111 kjhkjhkjh kjhkjhkjh kjhkjhkjh bgr bgr bgr             1 1 50*232 1 1 50*232
Input Image: 32x32x3 10 5x5 filters with stride (s)= 1, pad (p)=2 Output volume size: ? Another Example
Input volume: 32x32x3 10 5x5 filters with stride 1, pad 2 Output volume size: [(32+2*2-5)/1+1]×[(32+2*2-5)/1+1] = 32×32 spatially, so 32x32x10 Output
• 7 • 7x7 input (spatially) assume 3x3 filter • 7 A closer look at spatial dimensions: Convolutions: More detail
• 7 • 7x7 input (spatially) assume 3x3 filter • 7 A closer look at spatial dimensions: Convolutions: More detail
• 7 • 7x7 input (spatially) assume 3x3 filter • 7 A closer look at spatial dimensions: Convolutions: More detail
• 7 • 7x7 input (spatially) assume 3x3 filter • 7 A closer look at spatial dimensions: Convolutions: More detail
7 • • 7x7 input (spatially) assume 3x3 filter 7 A closer look at spatial dimensions: Convolutions: More detail [(7+2*0-3)/1+1]×[(7+2*0-3)/1+1] = 5×5 Output
7x7 input (spatially) assume 3x3 filter applied with stride 2 7 7 A closer look at spatial dimensions: Convolutions: More detail
7x7 input (spatially) assume 3x3 filter applied with stride 2 7 7 A closer look at spatial dimensions: Convolutions: More detail
7x7 input (spatially) assume 3x3 filter applied with stride 2 => 3x3 output! 7 7 A closer look at spatial dimensions: Convolutions: More detail [(7+2*0-3)/2+1]×[(7+2*0-3)/2+1] = 3×3 Output
7x7 input (spatially) assume 3x3 filter applied with stride 3? 7 7 A closer look at spatial dimensions: Convolutions: More detail [(7+2*0-3)/3+1]×[(7+2*0-3)/3+1] = [4/3+1]×[4/3+1] =2.33×2.33
7x7 input (spatially) assume 3x3 filter applied with stride 3? 7 7 A closer look at spatial dimensions: doesn’t fit! cannot apply 3x3 filter on 7x7 input with stride 3. Convolutions: More detail
In practice: Common to zero pad the border 0 0 0 0 0 0 0 0 0 0 e.g. input 7x7 3x3 filter, applied with stride 1 pad with 1 pixel border => what is theoutput? Convolutions: More detail [(7+2*1-3)/1+1]×[(7+2*1-3)/1+1] = 7×7 Output
In practice: Common to zero pad the border e.g. input 7x7 3x3 filter, applied with stride 2 pad with 1 pixel border => what is theoutput? 0 0 0 0 0 0 0 0 0 0 Convolutions: More detail [(7+2*1-3)/2+1]×[(7+2*1-3)/2+1] = 4×4 Output
In practice: Common to zero pad the border 0 0 0 0 0 0 0 0 0 0 Convolutions: More detail e.g. input 7x7 3x3 filter, applied with stride 3 pad with 1 pixel border => what is theoutput? [(7+2*1-3)/3+1]×[(7+2*1-3)/3+1] = 3×3 Output
Preview: ConvNet is a sequence of Convolution Layers, interspersedwith activation functions 32 32 3 28 28 6 CONV, ReLU e.g. 6 5x5x3 filters Convolutions: More detail
RELU Activation Function       0 00 )( zifz zif zR
Preview: ConvNet is a sequence of Convolutional Layers, interspersed with activation functions 32 32 3 CONV, ReLU e.g. 6 5x5x3 filters 28 28 6 CONV, ReLU e.g. 10 5x5x6 filters POOL Andrej Karpathy …. 10 24 24 Convolutions: More detail
Pooling layer  makes the representations smaller and more manageable  operates over each activation map independently:
1 1 2 4 5 6 7 8 3 2 1 0 1 2 3 4 Single depth slice x y max pool with 2x2 filters and stride 2 6 8 3 4 MAX POOLING
[(CONVRELU)*NPOOL]*MFC N: up to 5 M is Large FC: Contains neurons that connect to the entire input volume, as in ordinary Neural Networks General Architecture of CNNs
Example to recognize Car from Car, truck, airplane, ship and horse
Deep learning

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Deep learning

  • 1. Deep Learning Dr. Baljit Singh Khehra Professor CSE Department Baba Banda Singh Bahadur Engineering College Fatehgarh Sahib-140407, Punjab, India
  • 2. Convolution      M1 N1 N1 f * g (x, y) f * g (x)    0     f (,)g(x , y  )  0 0  f (,)g(x , y  )dd f ()g(x )  f ()g(x )d 2D(continuous, discrete) : 1D(continuous, discrete) : Input Kernel Output is sometimes called Feature map
  • 5. 32x32x3 image 5x5x3 filter 32 Convolve the filter with the image i.e. “slide over the image spatially, computing dot products” 32 3 Convolutions: More detail
  • 6. 32 3 Convolution Layer 32x32x3 image 5x5x3 filter 32 1 number: the result of taking a dot product between the filter and a small 5x5x3 chunk of the image (i.e. 5*5*3 =75-dimensional dot product + bias) Convolutions: More detail
  • 7. 32 3 activation mapConvolution Layer 32x32x3 image 5x5x3 filter 32 1 28 28 convolve (slide) over all spatial locations Convolutions: More detail
  • 8. 32 3 6 28 For example, if we had 6 5x5 filters, we’ll get 6 separate activation maps: activation maps 32 28 Convolution Layer We stack these up to get a “new image” of size28x28x6!
  • 9. Size of Image after Convolution  Input Image of Size M×N denoted as  If Number of Filter: NF applied on input image, then Activation Maps will be NF  Size of each filter is m×n  Filters are denoted as  Let stride be s and padding be p  Then, size of each activation map ),(),(),( :),( yxByxGyxR yxf fff ),(,..........),,(),,( 21 yxgyxgyxg NF ),(),(),( ..................................... ),(),(),( ),(),(),( 222 111 kjhkjhkjh kjhkjhkjh kjhkjhkjh b NF g NF r NF bgr bgr                 1 2 1 2 s npN s mpM
  • 10. Example  Input Image of Size M×N=32×32 denoted as  If Number of Filter: NF=6 applied on input image, then Activation Maps will be NF=6  Size of each filter is m×n=5×5  Filters are denoted as  Let stride be s=1 and padding be p=0  Then, size of each activation map will be 28×28 ),(),(),( :),( yxByxGyxR yxf fff ),(,..........),,(),,( 621 yxgyxgyxg ),(),(),( ..................................... ),(),(),( ),(),(),( 666 222 111 kjhkjhkjh kjhkjhkjh kjhkjhkjh bgr bgr bgr             1 1 50*232 1 1 50*232
  • 11. Input Image: 32x32x3 10 5x5 filters with stride (s)= 1, pad (p)=2 Output volume size: ? Another Example
  • 12. Input volume: 32x32x3 10 5x5 filters with stride 1, pad 2 Output volume size: [(32+2*2-5)/1+1]×[(32+2*2-5)/1+1] = 32×32 spatially, so 32x32x10 Output
  • 13. • 7 • 7x7 input (spatially) assume 3x3 filter • 7 A closer look at spatial dimensions: Convolutions: More detail
  • 14. • 7 • 7x7 input (spatially) assume 3x3 filter • 7 A closer look at spatial dimensions: Convolutions: More detail
  • 15. • 7 • 7x7 input (spatially) assume 3x3 filter • 7 A closer look at spatial dimensions: Convolutions: More detail
  • 16. • 7 • 7x7 input (spatially) assume 3x3 filter • 7 A closer look at spatial dimensions: Convolutions: More detail
  • 17. 7 • • 7x7 input (spatially) assume 3x3 filter 7 A closer look at spatial dimensions: Convolutions: More detail [(7+2*0-3)/1+1]×[(7+2*0-3)/1+1] = 5×5 Output
  • 18. 7x7 input (spatially) assume 3x3 filter applied with stride 2 7 7 A closer look at spatial dimensions: Convolutions: More detail
  • 19. 7x7 input (spatially) assume 3x3 filter applied with stride 2 7 7 A closer look at spatial dimensions: Convolutions: More detail
  • 20. 7x7 input (spatially) assume 3x3 filter applied with stride 2 => 3x3 output! 7 7 A closer look at spatial dimensions: Convolutions: More detail [(7+2*0-3)/2+1]×[(7+2*0-3)/2+1] = 3×3 Output
  • 21. 7x7 input (spatially) assume 3x3 filter applied with stride 3? 7 7 A closer look at spatial dimensions: Convolutions: More detail [(7+2*0-3)/3+1]×[(7+2*0-3)/3+1] = [4/3+1]×[4/3+1] =2.33×2.33
  • 22. 7x7 input (spatially) assume 3x3 filter applied with stride 3? 7 7 A closer look at spatial dimensions: doesn’t fit! cannot apply 3x3 filter on 7x7 input with stride 3. Convolutions: More detail
  • 23. In practice: Common to zero pad the border 0 0 0 0 0 0 0 0 0 0 e.g. input 7x7 3x3 filter, applied with stride 1 pad with 1 pixel border => what is theoutput? Convolutions: More detail [(7+2*1-3)/1+1]×[(7+2*1-3)/1+1] = 7×7 Output
  • 24. In practice: Common to zero pad the border e.g. input 7x7 3x3 filter, applied with stride 2 pad with 1 pixel border => what is theoutput? 0 0 0 0 0 0 0 0 0 0 Convolutions: More detail [(7+2*1-3)/2+1]×[(7+2*1-3)/2+1] = 4×4 Output
  • 25. In practice: Common to zero pad the border 0 0 0 0 0 0 0 0 0 0 Convolutions: More detail e.g. input 7x7 3x3 filter, applied with stride 3 pad with 1 pixel border => what is theoutput? [(7+2*1-3)/3+1]×[(7+2*1-3)/3+1] = 3×3 Output
  • 26. Preview: ConvNet is a sequence of Convolution Layers, interspersedwith activation functions 32 32 3 28 28 6 CONV, ReLU e.g. 6 5x5x3 filters Convolutions: More detail
  • 28. Preview: ConvNet is a sequence of Convolutional Layers, interspersed with activation functions 32 32 3 CONV, ReLU e.g. 6 5x5x3 filters 28 28 6 CONV, ReLU e.g. 10 5x5x6 filters POOL Andrej Karpathy …. 10 24 24 Convolutions: More detail
  • 29. Pooling layer  makes the representations smaller and more manageable  operates over each activation map independently:
  • 30. 1 1 2 4 5 6 7 8 3 2 1 0 1 2 3 4 Single depth slice x y max pool with 2x2 filters and stride 2 6 8 3 4 MAX POOLING
  • 31. [(CONVRELU)*NPOOL]*MFC N: up to 5 M is Large FC: Contains neurons that connect to the entire input volume, as in ordinary Neural Networks General Architecture of CNNs
  • 32. Example to recognize Car from Car, truck, airplane, ship and horse