by xi chen, yan duan, rein houthooft, john schulman, ilya … · 2018-03-21 · supervised learning...
TRANSCRIPT
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by Xi Chen, Yan Duan, Rein Houthooft, John Schulman, Ilya Sutskever, Pieter Abbeel
UC Berkeley, Department of Electrical Engineering and Computer Sciences
OpenAI
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Unsupervised learning of disentangled representation
Usually, learned representation is entangled
(encoded in complicated manner)
When representation is disentangled,
it would be easier to apply to tasks
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Disentangling information
man with glasses man without glasses woman
{ { {
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Supervised Learning Unsupervised Learning
“to learn is
to recognize”
“to learn is to
replicate”
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max log𝐷(𝑥) + log(1 − 𝐷(𝐺(𝑧))max log𝐷(𝐺(𝑧)
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where
𝐷 𝑥 =)𝑃𝑑𝑎𝑡𝑎(𝑥
)𝑃𝑑𝑎𝑡𝑎(𝑥) + 𝑃𝐺(𝑥
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Mutual information between latent code c and
generator distribution G(z, c) should be high
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measures the “amount of information” learned from knowledge
of random variable Y about the other random variable X
is the reduction of
uncertainty in X
when Y is observed
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Given 𝑥 𝑃𝐺 𝑥𝑃𝐺 с|𝑥 should have
small entropyProblem!
𝐼(𝑐; 𝐺(𝑧, 𝑐) )is hard to minimize
directly because of access
to the posterior 𝑃(𝑐|𝑥).
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𝐼 𝑐; 𝐺 𝑧, 𝑐 = 𝐻 𝑐 − 𝐻 𝑐 𝐺 𝑧, 𝑐
= 𝜠𝑥𝐺 𝑧,𝑐 𝜠𝑐′𝑃 𝑐|𝑥 log 𝑃 𝑐′ 𝑥 + 𝐻(𝑐)
= 𝜠𝑥𝐺 𝑧,𝑐 [𝐷𝐾𝐿(𝑃( |𝑥))||𝑄 𝑥 ) + 𝜠𝑐′𝑃 𝑐|𝑥 log 𝑄 𝑐′ 𝑥 ] + 𝐻(𝑐)≥ 0
≥ 𝜠𝑥𝐺 𝑧,𝑐 [𝜠𝑐′𝑃 𝑐|𝑥 log𝑄 𝑐′ 𝑥 ] + 𝐻(𝑐)Treat as a
constant
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Remind the lemma: 𝛦𝑥𝑋,𝑦𝑌|𝑥 𝑓 𝑥, 𝑦 = 𝛦𝑥𝑋,𝑦𝑌|𝑥,𝑥′𝑋|𝑦 𝑓(𝑥′, 𝑦)
𝐿𝐼 𝐺, 𝑄 = 𝛦𝑐𝑃(𝑐),𝑥𝐺(𝑧;𝑐) log𝑄(𝑐|𝑥) + 𝐻(𝑐)
= 𝛦𝑥𝐺(𝑧;𝑐) 𝛦𝑐′𝑃(𝑐|𝑥)[log𝑄 𝑐′ 𝑥 ] + 𝐻(𝑐)
≤ 𝐼 𝑐; 𝐺 𝑧, 𝑐
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In particular, 𝐿𝐼 can be maximized w.r.t. 𝑄 directly and w.r.t. 𝐺 via the
reparametrization trick.
for discrete latent codes, the bound becomes tight and
the maximal mutual information is achieved.
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Manipulating latent codes on MNIST
(a) Digit type (b) No clear meaning
(c) Rotation (d) Width
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(a) Pose (angle) (b) Elevation
(c) Lighting (d) Width
Manipulating latent codes on 3D Faces
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Manipulating latent codes on 3D Chairs
(a) Rotation (b) Width
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Manipulating latent codes on SVHN
(a) Continuous code (b) Discrete code
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