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  1. Free, publicly-accessible full text available May 1, 2023
  2. Free, publicly-accessible full text available January 1, 2023
  3. Latent space Energy-Based Models (EBMs), also known as energy-based priors, have drawn growing interests in generative modeling. Fueled by its flexibility in the formulation and strong modeling power of the latent space, recent works built upon it have made interesting attempts aiming at the interpretability of text modeling. However, latent space EBMs also inherit some flaws from EBMs in data space; the degenerate MCMC sampling quality in practice can lead to poor generation quality and instability in training, especially on data with complex latent structures. Inspired by the recent efforts that leverage diffusion recovery likelihood learning as a cure for the sampling issue, we introduce a novel symbiosis between the diffusion models and latent space EBMs in a variational learning framework, coined as the latent diffusion energy-based model. We develop a geometric clustering-based regularization jointly with the information bottleneck to further improve the quality of the learned latent space. Experiments on several challenging tasks demonstrate the superior performance of our model on interpretable text modeling over strong counterparts.
    Free, publicly-accessible full text available January 1, 2023
  4. A flag is a nested sequence of vector spaces. The type of the flag is determined by the sequence of dimensions of the vector spaces making up the flag. A flag manifold is a manifold whose points parameterize all flags of a particular type in a fixed vector space. This paper provides the mathematical framework necessary for implementing self-organizing mappings on flag manifolds. Flags arise implicitly in many data analysis techniques for instance in wavelet, Fourier, and singular value decompositions. The proposed geometric framework in this paper enables the computation of distances between flags, the computation of geodesics between flags, and the ability to move one flag a prescribed distance in the direction of another flag. Using these operations as building blocks, we implement the SOM algorithm on a flag manifold. The basic algorithm is applied to the problem of parameterizing a set of flags of a fixed type.