LEARNING GENERATIVE MODELS ACROSS INCOMPARABLE SPACES Cha harlot - - PowerPoint PPT Presentation

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Charlotte Bunne Poster #173 173

LEARNING GENERATIVE MODELS ACROSS INCOMPARABLE SPACES

Cha harlot

• tte Bunne

unne, David Alvarez-Melis, Andreas Krause, Stefanie Jegelka

Pos

• ster #173

173

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Charlotte Bunne Poster #173 173

Generative Modeling

generative network

noise

… …

Px

data

=

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Charlotte Bunne Poster #173 173

Beyond Identical Generation ...

generative network

noise

… …

Px

data

?

… enf nfor

• rce style.

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Charlotte Bunne Poster #173 173

Beyond Identical Generation ...

generative network

noise

… …

Px

data … learn n acros

• ss di

different nt di dimens nsions

• ns.

?

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Charlotte Bunne Poster #173 173

Beyond Identical Generation ...

generative network

noise

… …

Px

data … trans nslate be between n repr present ntation.

• n.

x y

graph ?

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Charlotte Bunne Poster #173 173 x z y

Beyond Identical Generation ...

generative network

noise

… …

Px

data … learn n mani nifol

• lds

ds.

x y

?

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Charlotte Bunne Poster #173 173

?

generative network

noise

… …

Px

data … learn n mani nifol

• lds

ds.

E x z y e x y

Challenges

.

1

.

2

. .

3 How to compare samples from incomparable spaces? What should be preserved? What can we modify? How to stabilize learning despite additional freedom?

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Charlotte Bunne Poster #173 173

Optimal Transpor

• rt Distances

L(yi, xl) L(yj, xk)

... distance between distributions: mini nimal cos

• st of transporting mass between them.

noise

… …

yh xl xm yi yj xk

generative network

Px

... find an opt

• ptimal trans

nspor port pl plan n T.

Learning Generative Models

… classical Wasserstein distances assume that spaces are com

• mpa

parabl ble!

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Gromov-Wasserstein Discrepancy

yh xl noise

… …

Dkl Dij xm xk Dhi yi L(Dhi, Dlm) L(Dij, Dkl) intra-space distances yj

Px

intra-space distances

• ptimal

transport plan

generative network

GW(D, ¯ D) := min

T

• ijkl

L(Dik, ¯ Djl)TijTkl

Definition

• n:

Defining a Distance Across Different Spaces

Dlm

tot

• tal discrepancy
• f
• f pairwise distances

acros

• ss dom
• mains

.

1

) := {

{

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Charlotte Bunne Poster #173 173

Gromov-Wasserstein Generative Model

g!(z) = y generator data

noise

… …

. . . . . .

… …

D D GW f⍵() adversary

(GW GAN)

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Charlotte Bunne Poster #173 173

… …

GW GAN

Flexibility of the Model

… recovers geometrical properties of the target distribution, … but global aspects are undetermined

sha hape pe the he ge gene nerated d di distribut bution

• n

via de design gn cons

• nstraint

nts

style adversary

.

2

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Charlotte Bunne Poster #173 173

gθ(Z)

samples in ge generator

• r space

generated samples in fe feature space data samples in fe feature space

fω(X)

fω(gθ(Z))

… …

GW GAN

Flexibility of the Model

… recovers geometrical properties of the target distribution, … but global aspects are undetermined … adversary can arbitrarily … distort the space

regul gularize adv dversary by by enf nfor

• rcing

ng it to

• de

define ne uni unitary trans nsfor

• rmations
• ns

sha hape pe the he ge gene nerated d di distribut bution

• n

via de design gn cons

• nstraint

nts

style adversary

. .

3

.

2

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Charlotte Bunne Poster #173 173

Gromov-Wasserstein Generative Model

By utilizing the Grom

• mov
• v-Wa

Wasser erstei tein discrepancy we disentangle data and generator space.

`

This enables us to learn ge generative mod

• dels acros
• ss different data types and space

dimension

• ns and sh

shape the generated distributions with design constraints.

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• ster #173

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More details, tonight at