stem/AI/Neural Networks/CNN/GAN/DC-GAN.md

Deep Convolutional GAN !

• Generator
  • FCN
  • Decoder
  • Generate image from code
    • Low-dimensional
      • ~100-D
  • Reshape to tensor
    • Upconv to image
  • Train using Gaussian random noise for code
• Discriminator
  • Contractive
  • Cross-entropy Deep Learning#Loss Function
  • Conv and leaky Activation Functions#ReLu layers only
  • Normalised output via Activation Functions#Sigmoid

Deep Learning#Loss Function

D(S,L)=-\sum_iL_ilog(S_i)

• S
  • (0.1, 0.9)^T
  • Score generated by discriminator
• L
  • (1, 0)^T
  • One-hot label vector
  • Step 1
    • Depends on choice of real/fake
  • Step 2
    • One-hot fake vector
• \sum_i
  • Sum over all images in mini-batch

Noise	Image
z	x

• Generator wants
  • D(G(z))=1
  • Wants to fool discriminator
• Discriminator wants
  • D(G(z))=0
  • Wants to correctly catch generator
• Real data wants
  • D(x)=1

J^{(D)}=-\frac 1 2 \mathbb E_{x\sim p_{data}}\log D(x)-\frac 1 2 \mathbb E_z\log (1-D(G(z)))

J^{(G)}=-J^{(D)}

• First term for real images
• Second term for fake images

Mode Collapse

• Generator gives easy solution
• Learns one image for most noise that will fool discriminator
• Mitigate by minibatch discriminator
  • Match G(z) distribution to x

What is Learnt?

• Encoding texture/patch detail from training set
  • Similar to FCN
  • Reproducing texture at high level
  • Cues triggered by code vector
    • Input random noise
• Iteratively improves visual feasibility
  • Different to FCN
• Discriminator is a task specific classifier
• Difficult to train over diverse footage
  • Mixing concepts doesn't work
  • Single category/class