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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 themore »Free, publiclyaccessible full text available January 1, 2023

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 localmore »Free, publiclyaccessible full text available January 1, 2023

Free, publiclyaccessible full text available April 1, 2023

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 thatmore »

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 thosemore »

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 domainmore »

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 themore »