title: Idempotent Generative Network
summary: We propose a new approach for generative modeling based on training a neural
  network to be idempotent. An idempotent operator is one that can be applied
  sequentially without changing the result beyond the initial application, namely
  f(f(z))=f(z). The proposed model f is trained to map a source distribution
  (e.g, Gaussian noise) to a target distribution (e.g. realistic images) using
  the following objectives: (1) Instances from the target distribution should map
  to themselves, namely f(x)=x. We define the target manifold as the set of all
  instances that f maps to themselves. (2) Instances that form the source
  distribution should map onto the defined target manifold. This is achieved by
  optimizing the idempotence term, f(f(z))=f(z) which encourages the range of
  f(z) to be on the target manifold. Under ideal assumptions such a process
  provably converges to the target distribution. This strategy results in a model
  capable of generating an output in one step, maintaining a consistent latent
  space, while also allowing sequential applications for refinement.
  Additionally, we find that by processing inputs from both target and source
  distributions, the model adeptly projects corrupted or modified data back to
  the target manifold. This work is a first step towards a ``global projector''
  that enables projecting any input into a target data distribution.
paper_authors._id: 6545179d3be12fed568b3d50
paper_authors.name: Assaf Shocher
paper_authors.status: claimed_verified
paper_authors.statusLastChangedAt: 2023-11-04T10:17:32.968Z
paper_authors._id: 6545241378875dadbfeb79b9
paper_authors.avatarUrl: /avatars/17bfb7a8959ad8a78f14d79e53b6423e.svg
paper_authors.fullname: Assaf Shocher
paper_authors.type: user
paper_authors.user: Assafshocher
paper_authors._id: 6545179d3be12fed568b3d51
paper_authors.name: Amil Dravid
paper_authors.status: admin_assigned
paper_authors.statusLastChangedAt: 2023-11-03T16:07:09.482Z
paper_authors._id: 6352e240a0da8800db964820
paper_authors.avatarUrl: /avatars/4a70851376faac02a6d4e70da55fc510.svg
paper_authors.fullname: Amil Dravid
paper_authors.type: user
paper_authors.user: avd4292
paper_authors._id: 6545179d3be12fed568b3d52
paper_authors.name: Yossi Gandelsman
paper_authors.status: admin_assigned
paper_authors.statusLastChangedAt: 2023-11-03T16:07:18.146Z
paper_authors._id: 62f6942205ca68c0e0ff7b97
paper_authors.avatarUrl: /avatars/b0600de531b4c88f4aa7c30c5ceb06e1.svg
paper_authors.fullname: Yossi Gandelsman
paper_authors.type: user
paper_authors.user: yossig
paper_authors._id: 6545179d3be12fed568b3d53
paper_authors.name: Inbar Mosseri
paper_authors._id: 6545179d3be12fed568b3d54
paper_authors.name: Michael Rubinstein
paper_authors._id: 6545179d3be12fed568b3d55
paper_authors.name: Alexei A. Efros
paper_title: Idempotent Generative Network
paper_summary: We propose a new approach for generative modeling based on training a neural
  network to be idempotent. An idempotent operator is one that can be applied
  sequentially without changing the result beyond the initial application, namely
  f(f(z))=f(z). The proposed model f is trained to map a source distribution
  (e.g, Gaussian noise) to a target distribution (e.g. realistic images) using
  the following objectives: (1) Instances from the target distribution should map
  to themselves, namely f(x)=x. We define the target manifold as the set of all
  instances that f maps to themselves. (2) Instances that form the source
  distribution should map onto the defined target manifold. This is achieved by
  optimizing the idempotence term, f(f(z))=f(z) which encourages the range of
  f(z) to be on the target manifold. Under ideal assumptions such a process
  provably converges to the target distribution. This strategy results in a model
  capable of generating an output in one step, maintaining a consistent latent
  space, while also allowing sequential applications for refinement.
  Additionally, we find that by processing inputs from both target and source
  distributions, the model adeptly projects corrupted or modified data back to
  the target manifold. This work is a first step towards a ``global projector''
  that enables projecting any input into a target data distribution.
paper_ai_summary: A new generative modeling approach uses an idempotent neural network to project data from a source distribution to a target distribution while maintaining consistency and allowing for refinement.
paper_ai_keywords: idempotent neural network generative modeling target manifold source distribution idempotence term