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

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LEARNING GENERATIVE MODELS ACROSS INCOMPARABLE SPACES Cha harlot otte Bunne unne , David Alvarez-Melis, Andreas Krause, Stefanie Jegelka Pos oster #173 173 Poster #173 173 & Charlotte Bunne Generative Modeling generative = network

  1. LEARNING GENERATIVE MODELS ACROSS INCOMPARABLE SPACES Cha harlot otte Bunne unne , David Alvarez-Melis, Andreas Krause, Stefanie Jegelka Pos oster #173 173 Poster #173 173 & Charlotte Bunne

  2. Generative Modeling generative = network data noise P x … … Poster #173 173 & Charlotte Bunne

  3. Beyond Identical Generation ... generative ? network data noise P x … … … enf nfor orce style. Poster #173 173 & Charlotte Bunne

  4. Beyond Identical Generation ... generative ? network data noise P x … … … learn n acros oss di different nt di dimens nsions ons. Poster #173 173 & Charlotte Bunne

  5. Beyond Identical Generation ... generative graph ? network data noise P x y … … x … trans nslate be between n repr present ntation. on. Poster #173 173 & Charlotte Bunne

  6. Beyond Identical Generation ... generative ? network data z noise P x y … … y x x … learn n mani nifol olds ds. Poster #173 173 & Charlotte Bunne

  7. . Challenges generative network ? E data e z noise P x y … … y x x How to compare samples from incomparable spaces? 1 . . . … learn n mani nifol olds ds. What should be preserved? What can we modify? 2 How to stabilize learning despite additional freedom? 3 Poster #173 173 & Charlotte Bunne

  8. Learning Generative Models Optimal Transpor ort Distances L ( y i , x l ) generative y i network y j x l y h x m noise P x … … x k L ( y j , x k ) ... distance between distributions : mini nimal cos ost of transporting mass between them. n T . ... find an opt optimal trans nspor port pl plan … classical Wasserstein distances assume that spaces are com ompa parabl ble ! Poster #173 173 & Charlotte Bunne

  9. . <latexit sha1_base64="5dO7VeWeQwCDzXJsk/Ifg7of+5Q=">AB6XicbVDLSgNBEOyNrxhfUY9eBoPgKezGgB4DgniMYh6QLGF2MpsMmZ1dZnqFsAT8AC8eFPHqH3nzb5w8DpY0FBUdPdFSRSGHTdbye3tr6xuZXfLuzs7u0fFA+PmiZONeMNFstYtwNquBSKN1Cg5O1EcxoFkreC0fXUbz1ybUSsHnCcD+iAyVCwSha6b6b9Yolt+zOQFaJtyAlWKDeK351+zFLI6QSWpMx3MT9DOqUTDJ4VuanhC2YgOeMdSRSNu/Gx26YScWaVPwljbUkhm6u+JjEbGjKPAdkYUh2bZm4r/eZ0Uwys/EypJkSs2XxSmkmBMpm+TvtCcoRxbQpkW9lbChlRThjacg3BW35lTQrZe+iXLmrlmo3T/M48nACp3AOHlxCDW6hDg1gEMIzvMKbM3JenHfnY96acxYRHsMfOJ8/xAaN7Q=</latexit> <latexit sha1_base64="5dO7VeWeQwCDzXJsk/Ifg7of+5Q=">AB6XicbVDLSgNBEOyNrxhfUY9eBoPgKezGgB4DgniMYh6QLGF2MpsMmZ1dZnqFsAT8AC8eFPHqH3nzb5w8DpY0FBUdPdFSRSGHTdbye3tr6xuZXfLuzs7u0fFA+PmiZONeMNFstYtwNquBSKN1Cg5O1EcxoFkreC0fXUbz1ybUSsHnCcD+iAyVCwSha6b6b9Yolt+zOQFaJtyAlWKDeK351+zFLI6QSWpMx3MT9DOqUTDJ4VuanhC2YgOeMdSRSNu/Gx26YScWaVPwljbUkhm6u+JjEbGjKPAdkYUh2bZm4r/eZ0Uwys/EypJkSs2XxSmkmBMpm+TvtCcoRxbQpkW9lbChlRThjacg3BW35lTQrZe+iXLmrlmo3T/M48nACp3AOHlxCDW6hDg1gEMIzvMKbM3JenHfnY96acxYRHsMfOJ8/xAaN7Q=</latexit> Defining a Distance Across Different Spaces 1 Gromov-Wasserstein Discrepancy intra-space distances L ( D hi , D lm ) generative y i D lm network D hi y j D kl x l y h x m D ij noise P x … … x k L ( D ij , D kl ) ) := { tot otal discrepancy { GW ( D, ¯ L ( D ik , ¯ � D ) := min D jl ) T ij T kl of pairwise distances of Definition on : T acros oss dom omains ijkl optimal intra-space transport plan distances Poster #173 173 & Charlotte Bunne

  10. Gromov-Wasserstein Generative Model (GW GAN) D noise GW … . … … … . . D generator adversary . . . g ! ( z ) = y data f ⍵ ( � ) Poster #173 173 & Charlotte Bunne

  11. Flexibility of the Model . 2 … recovers geometrical properties of the target distribution, … but global aspects are undetermined style adversary sha hape pe the he ge gene nerated d di distribut bution on via de design gn cons onstraint nts GW GAN … … Poster #173 173 & Charlotte Bunne

  12. Flexibility of the Model . 2 … recovers geometrical properties of the target distribution, … but global aspects are undetermined style . . adversary sha hape pe the he ge gene nerated d di distribut bution on via de design gn cons onstraint nts 3 GW GAN … … … adversary can arbitrarily samples in generated samples in data samples in generator ge or space feature space fe fe feature space … distort the space f ω ( g θ ( Z )) f ω ( X ) g θ ( Z ) regul gularize adv dversary by by enf nfor orcing ng it to o de define ne unitary trans uni nsfor ormations ons Poster #173 173 & Charlotte Bunne

  13. Gromov-Wasserstein Generative Model By utilizing the Grom omov ov-Wa Wasser erstei tein discrepancy we disentangle data and ` generator space. This enables us to learn ge generative mod odels acros oss different data types and space ` dimension ons and sh shape the generated distributions with design constraints. Pos oster #173 173 More details, tonight at Poster #173 173 & Charlotte Bunne

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