Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher.
Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?
Some links on this page may take you to nonfederal websites. Their policies may differ from this site.

The problem of continuous inverse optimal control (over finite time horizon) is to learn the unknown cost function over the sequence of continuous control variables from expert demonstrations. In this article, we study this fundamental problem in the framework of energybased model, where the observed expert trajectories are assumed to be random samples from a probability density function defined as the exponential of the negative cost function up to a normalizing constant. The parameters of the cost function are learned by maximum likelihood via an “analysis by synthesis” scheme, which iterates (1) synthesis step: sample the synthesized trajectories from the current probability density using the Langevin dynamics via backpropagation through time, and (2) analysis step: update the model parameters based on the statistical difference between the synthesized trajectories and the observed trajectories. Given the fact that an efficient optimization algorithm is usually available for an optimal control problem, we also consider a convenient approximation of the above learning method, where we replace the sampling in the synthesis step by optimization. Moreover, to make the sampling or optimization more efficient, we propose to train the energybased model simultaneously with a topdown trajectory generator via cooperative learning, where the trajectory generator is used to fast initialize the synthesis step of the energybased model. We demonstrate the proposed methods on autonomous driving tasks, and show that they can learn suitable cost functions for optimal control.more » « less

This paper proposes a representational model for image pairs such as consecutive video frames that are related by local pixel displacements, in the hope that the model may shed light on motion perception in primary visual cortex (V1). The model couples the following two components: (1) the vector representations of local contents of images and (2) the matrix representations of local pixel displacements caused by the relative motions between the agent and the objects in the 3D scene. When the image frame undergoes changes due to local pixel displacements, the vectors are multiplied by the matrices that represent the local displacements. Thus the vector representation is equivariant as it varies according to the local displacements. Our experiments show that our model can learn Gaborlike filter pairs of quadrature phases. The profiles of the learned filters match those of simple cells in Macaque V1. Moreover, we demonstrate that the model can learn to infer local motions in either a supervised or unsupervised manner. With such a simple model, we achieve competitive results on optical flow estimation.more » « less

Video sequences contain rich dynamic patterns, such as dynamic texture patterns that exhibit stationarity in the temporal domain, and action patterns that are nonstationary in either spatial or temporal domain. We show that an energybased spatialtemporal generative ConvNet can be used to model and synthesize dynamic patterns. The model defines a probability distribution on the video sequence, and the log probability is defined by a spatialtemporal ConvNet that consists of multiple layers of spatialtemporal filters to capture spatialtemporal patterns of different scales. The model can be learned from the training video sequences by an “analysis by synthesis” learning algorithm that iterates the following two steps. Step 1 synthesizes video sequences from the currently learned model. Step 2 then updates the model parameters based on the difference between the synthesized video sequences and the observed training sequences. We show that the learning algorithm can synthesize realistic dynamic patterns. We also show that it is possible to learn the model from incomplete training sequences with either occluded pixels or missing frames, so that model learning and pattern completion can be accomplished simultaneously.more » « less

This paper studies the unsupervised crossdomain translation problem by proposing a generative framework, in which the probability distribution of each domain is represented by a generative cooperative network that consists of an energy based model and a latent variable model. The use of generative cooperative network enables maximum likelihood learning of the domain model by MCMC teaching, where the energybased model seeks to fit the data distribution of domain and distills its knowledge to the latent variable model via MCMC. Specifically, in the MCMC teaching process, the latent variable model parameterized by an encoderdecoder maps examples from the source domain to the target domain, while the energybased model further refines the mapped results by Langevin revision such that the revised results match to the examples in the target domain in terms of the statistical properties, which are defined by the learned energy function. For the purpose of building up a correspondence between two unpaired domains, the proposed framework simultaneously learns a pair of cooperative networks with cycle consistency, accounting for a twoway translation between two domains, by alternating MCMC teaching. Experiments show that the proposed framework is useful for unsupervised imagetoimage translation and unpaired image sequence translation.more » « less

We propose a generative model of unordered point sets, such as point clouds, in the form of an energybased model, where the energy function is parameterized by an input permutation invariant bottomup neural network. The energy function learns a coordinate encoding of each point and then aggregates all individual point features into an energy for the whole point cloud. We call our model the Generative PointNet because it can be derived from the discriminative PointNet. Our model can be trained by MCMC based maximum likelihood learning (as well as its variants), without the help of any assisting networks like those in GANs and VAEs. Unlike most point cloud generators that rely on handcrafted distance metrics, our model does not require any handcrafted distance metric for the point cloud generation, because it synthesizes point clouds by matching observed examples in terms of statistical properties defined by the energy function. Furthermore, we can learn a short run MCMC toward the energybased model as a flowlike generator for point cloud reconstruction and interpolation. The learned point cloud representation can be useful for point cloud classification. Experiments demonstrate the advantages of the proposed generative model of point clouds.more » « less

Understanding how grid cells perform path integration calculations remains a fundamental problem. In this paper, we conduct theoretical analysis of a general representation model of path integration by grid cells, where the 2D selfposition is encoded as a higher dimensional vector, and the 2D selfmotion is represented by a general transformation of the vector. We identify two conditions on the transformation. One is a group representation condition that is necessary for path integration. The other is an isotropic scaling condition that ensures locally conformal embedding, so that the error in the vector representation translates conformally to the error in the 2D selfposition. Then we investigate the simplest transformation, i.e., the linear transformation, uncover its explicit algebraic and geometric structure as matrix Lie group of rotation, and explore the connection between the isotropic scaling condition and a special class of hexagon grid patterns. Finally, with our optimizationbased approach, we manage to learn hexagon grid patterns that share similar properties of the grid cells in the rodent brain. The learned model is capable of accurate long distance path integration. Code is available at https://github.com/ruiqigao/gridcellpath.more » « less