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Motivation Inferring from Images Latent Variables : Dataset MNIST Goh images ; hand of digits written - Goal two variables Infer labels 1. Digit , Style { 9 } y e 0 - , . . , variables 2 RD 7 €

Deep Generative Models Andisi equally " probable ) Neural Network Ideal Use to define : a model generative a Generative Model ,q } label { Digit o f , ... 1 ) Discrete ( yn ~ ,0 0.1 . ... , 1 ) Normal ×neRP ( Zn a o ~ , , Bernoulli ( y×( yn ,7n :& ) ) xn ~ boh P=76P D= 2-50 N= Distribution Joint f p N 4,7 ;D ) M Style ;D ) PC plxn.yn.tn Image = x. pixels ) ( € Rb n= , { , } × × ,X× = , , ...

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Variation al Autoencoders Learn Objective model generative deep and : a a by inference corresponding Medel optimizing ' .n=0a¢( E Tomko # www.nlbspgfxiy?niI*

A Intermezzo encoders Wto :

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Mapping Decoder from to code image 7 × : Multi Perception layer . Oh " ) . tin = 6( Whzn b + ÷ ' ) 6 ( In b + When = ,¢)=§l,§.!×n,p Loss Binary - entropy Cross : L( log In to ,p { + ( l , p ) Xn - ,p ) ) this Minimize log ( c- In

Learned Auto Latent Codes encoder

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Variutional Auto Learned Latent Codes encoder

Variation Auto Auto encoder encoder vs

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Variation al Autoencoders Learn Objective model generative deep and : a a by inference corresponding Medel optimizing ' .n=0a¢( E Tomko # www.nlbspgfxiy?niI*

Practical / Tensor Py Torch Implementations flow :

( 7 style & digit ) Continuous ,7n ) ( Xn both pp nlxnl 9$17 : encodes , ft style ) Continuous Discrete ynifnl pfxn encodes qfbn lxn ) : ,7n + , ,

Disentangled Representations Hao Learn Interpretable Sarthaht Features Bab ah + : Xn 7in 1 , 7h , 2 . ) . 1 : n ,7