Implicit Generation and Generalization with Energy Based Models - - PowerPoint PPT Presentation

▶
implicit generation and generalization with energy based
SMART_READER_LITE
LIVE PREVIEW

Implicit Generation and Generalization with Energy Based Models - - PowerPoint PPT Presentation

Oct 07, 2023 308 likes •698 views

Implicit Generation and Generalization with Energy Based Models Yilun Du and Igor Mordatch Energy-Based Model E( x ) Distribution defined by energy function Train to maximize data likelihood gradient: Generate model samples

slide-1
SLIDE 1

Implicit Generation and Generalization with Energy Based Models

Yilun Du and Igor Mordatch

slide-2
SLIDE 2
  • Distribution defined by energy function
  • Train to maximize data likelihood
  • Generate model samples implicitly via Langevin Dynamics

Energy-Based Model

  • gradient:

see [LeCun et al, 2006] for review

E(x)

slide-3
SLIDE 3
  • Distribution defined by energy function
  • Train to maximize data likelihood
  • Generate model samples implicitly via Langevin Dynamics

Energy-Based Model

  • gradient:

E(x)

x+

data

slide-4
SLIDE 4
  • Distribution defined by energy function
  • Train to maximize data likelihood
  • Generate model samples implicitly via Langevin Dynamics

Energy-Based Model

  • gradient:

E(x)

x- x+

data hallucination

See [Turner, 2006] for derivation

slide-5
SLIDE 5
  • Distribution defined by energy function
  • Train to maximize data likelihood
  • Generate model samples implicitly via stochastic optimization

Energy-Based Model

  • gradient:

E(x)

x- x0 Langevin Dynamics [Welling and Teh, 2011]

slide-6
SLIDE 6

Why Energy-Based Generative Models?

1 Implicit Generation

  • Flexibility
  • One Object to Learn
  • Compositionalitly
  • Generic Initialization and Computation Time

2 Intriguing Properties

  • Robustness
  • Online Learning
slide-7
SLIDE 7

Why Do EBMs Work Now?

More compute and modern deep learning practices Faster Sampling

  • Continuous gradient based sampling using Langevin Dynamics
  • Replay buffer of past samples (similar to persistent CD)

Stability improvements

  • Constrain Lipschitz constant of energy function (spectral norm)
  • Smoother activations (swish)
  • And others ...
slide-8
SLIDE 8
slide-9
SLIDE 9
slide-10
SLIDE 10

Comparison to Other Generative Models

  • gradient:
slide-11
SLIDE 11

ImageNet 128x128

slide-12
SLIDE 12

Cross Class Mapping

slide-13
SLIDE 13

Cross Class Mapping

slide-14
SLIDE 14

Surprising Benefits of Energy-Based Models

  • Robustness
  • Continual Learning
  • Compositionality
  • Trajectory Modeling
slide-15
SLIDE 15

Surprising Benefits of Energy-Based Models

  • Robustness
  • Continual Learning
  • Compositionality
  • Trajectory Modeling
slide-16
SLIDE 16

Out-of-Distribution Relative Likelihoods

Also observed by [Hendrycks et al 2018] and [Nalisnick et al 2019]

slide-17
SLIDE 17

Out-of-Distribution Relative Likelihoods

Also observed by [Hendrycks et al 2018] and [Nalisnick et al 2019]

slide-18
SLIDE 18

Out-of-Distribution Relative Likelihoods

Also observed by [Hendrycks et al 2018] and [Nalisnick et al 2019]

slide-19
SLIDE 19

Out-of-Distribution Generalization

  • Following [Hendrycks and Gimpel, 2016]
slide-20
SLIDE 20

Robust Classification

slide-21
SLIDE 21

Robust Classification

(recent follow-up submission at ICLR 2020 improves baseline EBM performance)

slide-22
SLIDE 22

Surprising Benefits of Energy-Based Models

  • Robustness
  • Continual Learning
  • Compositionality
  • Trajectory Modeling
slide-23
SLIDE 23

Continual Learning: Split MNIST

Evaluation by [Hsu at al, 2019]

slide-24
SLIDE 24

Evaluation by [Hsu at al, 2019]

Continual Learning: Split MNIST

slide-25
SLIDE 25

Evaluation by [Hsu at al, 2019] EBM: 64.99 ± 4.27

Continual Learning: Split MNIST

(10 seeds)

slide-26
SLIDE 26

Evaluation by [Hsu at al, 2019] EBM: 64.99 ± 4.27 VAE: 40.04 ± 1.31 Would any generative model work instead? Doesn’t look like it:

Continual Learning: Split MNIST

slide-27
SLIDE 27

Surprising Benefits of Energy-Based Models

  • Robustness
  • Continual Learning
  • Compositionality
  • Trajectory Modeling
slide-28
SLIDE 28

Compositionality via Sum of EBMs

[Hinton, 1999] Specify a concept by successively adding constraints [Mnih and Hinton, 2005]

slide-29
SLIDE 29

Compositionality via Sum of Energies

Specify a concept by successively adding constraints

Compositional Visual Generation with EBMs [Du, Li, Mordatch, 2019]

slide-30
SLIDE 30

Compositionality via Sum of Energies

Specify a concept by successively adding constraints

Compositional Visual Generation with EBMs [Du, Li, Mordatch, 2019]

slide-31
SLIDE 31

Compositionality via Sum of Energies

Specify a concept by successively adding constraints

Compositional Visual Generation with EBMs [Du, Li, Mordatch, 2019]

slide-32
SLIDE 32

Compositionality via Sum of Energies

Specify a concept by successively adding constraints

Compositional Visual Generation with EBMs [Du, Li, Mordatch, 2019]

slide-33
SLIDE 33

Compositionality via Sum of Energies

Specify a concept by successively adding constraints

Compositional Visual Generation with EBMs [Du, Li, Mordatch, 2019]

slide-34
SLIDE 34

Surprising Benefits of Energy-Based Models

  • Robustness
  • Continual Learning
  • Compositionality
  • Trajectory Modeling
slide-35
SLIDE 35
  • Train energy to model pairwise state transitions st, st+1
  • Trajectory probability:

s1 sT

  • E(st, st+1)

EBMs for Trajectory Modeling and Control

st st+1

[Du, Lin, Mordatch, 2019]

slide-36
SLIDE 36

EBMs for Trajectory Modeling and Control

  • Train energy to model pairwise state transitions st, st+1
  • Generate trajectories that achieve specific tasks:

s1

EBM Task R(st)

sT

st

(similar to direct trajectory optimization)

[Du, Lin, Mordatch, 2019]

slide-37
SLIDE 37

EBMs for Control

slide-38
SLIDE 38

Source Code

  • Images
  • https://github.com/openai/ebm_code_release
  • Trajectories
  • https://github.com/yilundu/model_based_planning_ebm
  • Compositionality
  • https://drive.google.com/file/d/

138w7Oj8rQl_e40_RfZJq2WKWb41NgKn3

  • Interactive Notebook
  • https://drive.google.com/file/d/

1fCFRw_YtqQPSNoqznIh2b1L2baFgLz4W/view