69 lines
1.6 KiB
Markdown
69 lines
1.6 KiB
Markdown
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Deep Convolutional GAN
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![[dc-gan.png]]
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- Generator
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- FCN
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- Decoder
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- Generate image from code
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- Low-dimensional
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- ~100-D
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- Reshape to tensor
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- Upconv to image
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- Train using Gaussian random noise for code
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- Discriminator
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- Contractive
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- Cross-entropy loss
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- Conv and leaky [[Activation Functions#ReLu|ReLu]] layers only
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- Normalised output via sigmoid
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## Loss
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$$D(S,L)=-\sum_iL_ilog(S_i)$$
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- $S$
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- $(0.1, 0.9)^T$
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- Score generated by discriminator
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- $L$
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- $(1, 0)^T$
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- One-hot label vector
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- Step 1
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- Depends on choice of real/fake
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- Step 2
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- One-hot fake vector
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- $\sum_i$
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- Sum over all images in mini-batch
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| Noise | Image |
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| ----- | ----- |
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| $z$ | $x$ |
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- Generator wants
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- $D(G(z))=1$
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- Wants to fool discriminator
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- Discriminator wants
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- $D(G(z))=0$
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- Wants to correctly catch generator
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- Real data wants
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- $D(x)=1$
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$$J^{(D)}=-\frac 1 2 \mathbb E_{x\sim p_{data}}\log D(x)-\frac 1 2 \mathbb E_z\log (1-D(G(z)))$$
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$$J^{(G)}=-J^{(D)}$$
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- First term for real images
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- Second term for fake images
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# Mode Collapse
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- Generator gives easy solution
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- Learns one image for most noise that will fool discriminator
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- Mitigate by minibatch discriminator
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- Match G(z) distribution to x
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# What is Learnt?
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- Encoding texture/patch detail from training set
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- Similar to FCN
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- Reproducing texture at high level
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- Cues triggered by code vector
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- Input random noise
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- Iteratively improves visual feasibility
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- Different to FCN
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- Discriminator is a task specific classifier
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- Difficult to train over diverse footage
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- Mixing concepts doesn't work
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- Single category/class
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