* Maximum likelihood learning of modern ConvNet-parametrized

* Maximum likelihood learning of

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(mode traversing HMC chains)

(learned V1 cells)

(learned grid cells |

(Initializer is like a policy model, whose solution is refined by a value model)

(Predicting trajectory)

(Change of pose in physical space = rotation of vector in neural space)

(Synthesized images)

(Left: latent space EBM stands on generator. Right: Short-run MCMC in latent space)

The latent space EBM stands on a top-down generation network. It is like a value network or cost function defined in latent space.

The scalar-valued energy function is an objective function, a cost function, an evaluator or a critic. It is about constraints, regularities, rules, perceptual organizations, and Gestalt laws. The energy-based model is descriptive instead of generative, which is the reason we used to call it the descriptive model. It only describes what it wants without bothering with how to get it. Compared to generator model (whose output is high dimensional instead of scalar), the energy-based model is like setting up an equation, whereas the generator model is like generating the solution directly. It is much easier to set up the equation than giving the answer, i.e., it is easier to specify a scalar-valued energy function than a vector-valued generation function, the latter is like a policy network.

The energy-based model in latent space is simple and yet expressive, capturing rules or regularities implicitly but effectively. The latent space seems the right home for energy-based model.

Short-run MCMC in latent space for prior and posterior sampling is efficient and mixes well. One can amortize MCMC with learned network (see our recent work on semi-supervised learning), but in this initial paper we prefer to keep it pure and simple, without mixing in tricks from VAE and GAN.

(Left: latent EBM captures chemical rules implicitly in latent space. Right: generated molecules)

(the symbolic one-hot y is coupled with dense vector z to form an associative memory, and z is the information bottleneck between x and y)

(VAE as alternating projection)

(The model generates both displacement field and appearance)

(neural-symbolic learning)

(Three densities in joint space: pi: latent EBM, p: generator, q: inference)

(reconstruction by short-run MCMC, yes it can reconstruct observed images)

(learned grid cells)

(videos generated by the learned model)

(videos generated by the learned model)

(faces generated and interpolated by the learned model)

(pi is EBM, p is generator, q is inference)

(videos generated by the learned model)

(face rotation by the learned model)

(learning directly from occluded images. Row 1: original images, not available to model; Row 2: training images. Row 3: learning and reconstruction. )

(left: observed; right: synthesized.)

(Langevin dynamics for sampling ConvNet-EBM)

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