This paper proposes a 3D shape descriptor network, which is a deep convolutional energy-based model, for modeling volumetric shape patterns. The maximum likelihood training of the model follows an "analysis by synthesis" scheme and can be interpreted as a mode seeking and mode shifting process. The model can synthesize 3D shape patterns by sampling from the probability distribution via MCMC such as Langevin dynamics. The model can be used to train a 3D generator network via MCMC teaching. The conditional version of the 3D shape descriptor net can be used for 3D object recovery and 3D object super-resolution. Experiments demonstrate that the proposed model can generate realistic 3D shape patterns and can be useful for 3D shape analysis.
Building on the early work of @cite_33 , recently @cite_8 @cite_5 have developed an introspective learning method to learn the energy-based model, where the energy function is discriminatively learned.
@cite_5 @cite_33 @cite_8
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Training energy-based probabilistic models is confronted with apparently intractable sums, whose Monte Carlo estimation requires sampling from the estimated probability distribution in the inner loop of training. This can be approximately achieved by Markov chain Monte Carlo methods, but may still face a formidable obstacle that is the difficulty of mixing between modes with sharp concentrations of probability. Whereas an MCMC process is usually derived from a given energy function based on mathematical considerations and requires an arbitrarily long time to obtain good and varied samples, we propose to train a deep directed generative model (not a Markov chain) so that its sampling distribution approximately matches the energy function that is being trained. Inspired by generative adversarial networks, the proposed framework involves training of two models that represent dual views of the estimated probability distribution: the energy function (mapping an input configuration to a scalar energy value) and the generator (mapping a noise vector to a generated configuration), both represented by deep neural networks. We propose a method for learning expressive energy-based policies for continuous states and actions, which has been feasible only in tabular domains before. We apply our method to learning maximum entropy policies, resulting into a new algorithm, called soft Q-learning, that expresses the optimal policy via a Boltzmann distribution. We use the recently proposed amortized Stein variational gradient descent to learn a stochastic sampling network that approximates samples from this distribution. The benefits of the proposed algorithm include improved exploration and compositionality that allows transferring skills between tasks, which we confirm in simulated experiments with swimming and walking robots. We also draw a connection to actor-critic methods, which can be viewed performing approximate inference on the corresponding energy-based model. We propose a method for learning expressive energy-based policies for continuous states and actions, which has been feasible only in tabular domains before. We apply our method to learning maximum entropy policies, resulting into a new algorithm, called soft Q-learning, that expresses the optimal policy via a Boltzmann distribution. We use the recently proposed amortized Stein variational gradient descent to learn a stochastic sampling network that approximates samples from this distribution. The benefits of the proposed algorithm include improved exploration and compositionality that allows transferring skills between tasks, which we confirm in simulated experiments with swimming and walking robots. We also draw a connection to actor-critic methods, which can be viewed performing approximate inference on the corresponding energy-based model. Energy-Based Models (EBMs) capture dependencies between variables by associating a scalar energy to each configuration of the variab les. Inference consists in clamping the value of observed variables and finding config urations of the remaining variables that minimize the energy. Learning consists in finding an energy function in which observed configurations of the variables a re given lower energies than unobserved ones. The EBM approach provides a common theoretical framework for many learning models, including traditional discr iminative and generative approaches, as well as graph-transformer networks, co nditional random fields, maximum margin Markov networks, and several manifold learning methods. Probabilistic models must be properly normalized, which sometimes requires evaluating intractable integrals over the space of all poss ible variable configurations. Since EBMs have no requirement for proper normalization, this problem is naturally circumvented. EBMs can be viewed as a form of non-probabilistic factor graphs, and they provide considerably more flexibility in th e design of architectures and training criteria than probabilistic approaches .