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[DL輪読会]Weakly-Supervised Disentanglement Without Compromises

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DEEP LEARNING JP
[DL Papers]
http://deeplearning.jp/

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z = [z1, . . . , zd]T
̂z = [ ̂z1, . . . , ̂zd]T
̂z
f π i zi = fi( ̂zπ(i))
z

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P(z) f
p(z) = p( f(z)) z, f(z)
i, j
∂fi(u)
∂uj
for a . e . u ∈ supp(z)
P( f(z)) p( f(z)) p(z)
β
q(z) =
∫
q(z|x)pdata(x)dx
...

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[DL輪読会]Weakly-Supervised Disentanglement Without Compromises

  1. 1. DEEP LEARNING JP [DL Papers] http://deeplearning.jp/
  2. 2. z = [z1, . . . , zd]T ̂z = [ ̂z1, . . . , ̂zd]T ̂z f π i zi = fi( ̂zπ(i)) z
  3. 3. P(z) f p(z) = p( f(z)) z, f(z) i, j ∂fi(u) ∂uj for a . e . u ∈ supp(z) P( f(z)) p( f(z)) p(z) β q(z) = ∫ q(z|x)pdata(x)dx q(z) p(z) p( f(z)) p(z)
  4. 4. β
  5. 5. β
  6. 6. (x1, x2) (x1, x2) k ≥ 1
  7. 7. (x1, x2) (x1, x2) k ≥ 1
  8. 8. p(z) = Πd i=1p(zi), p(˜z) = Πd i=1p(˜zi) S ∼ p(S), x1 = g⋆ (z), x2 = g⋆ (f(z, ˜z, S)) f i ∉ S ˜zi
  9. 9. (x1, x2) (x1, x2) k ≥ 1
  10. 10. (x1, x2) ∼ p(x1, x2) = ∫ ∫ ∫ p(x1, x2, z, ˜z, S)dzd˜zdS |S| = k S, S′ ∼ p(S) P(S ∩ S′ = {i}) > 0,∀i ∈ [d] p( ̂zi) q(x1 | ̂z) p( ̂S) q( ̂z) = ∫ q( ̂z|x1)p(x1)dx
  11. 11. S x1, x2 zi∈S zi∉S ̂zi∈T ̂zi∉T (x1, x2) ∼ p(x1, x2 |S) S
  12. 12. p (zi |x1) = p (zi |x2) ∀i ∈ S p (zi |x1) ≠ p (zi |x2) ∀i ∈ ¯S k S k k S
  13. 13. max ϕ,θ 𝔼(x1,x2) 𝔼˜qϕ( ̂z|x1) log (pθ (x1 | ̂z)) +𝔼˜qϕ( ̂z|x2) log (pθ (x2 | ̂z)) −βDKL (˜qϕ ( ̂z||x1)|p( ̂z)) −βDKL (˜qϕ ( ̂z||x2)|p( ̂z)) ˜qϕ ( ̂zi |x1) = a (qϕ ( ̂zi |x1), qϕ ( ̂zi |x2)) ∀i ∈ ̂S ˜qϕ ( ̂zi |x1) = qϕ ( ̂zi |x1) (x1, x2) i ∈ ̂S qϕ ( ̂zi |x1), qϕ ( ̂zi |x2) a δi = DKL (qϕ ( ̂zi |x1) ∥qϕ ( ̂zi |x2))
  14. 14. (x1, x2) (x1, x2) k ≥ 1
  15. 15. β β
  16. 16. β
  17. 17. k (x1, x2) (x1, x2)

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