TASK DEFINITION: In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.
PROBLEM: Temporal logics are useful for describing dynamic system behavior, and have been successfully used as a language for goal definitions during task planning. Prior works on inferring temporal logic specifications have focused on "summarizing" the input dataset -- i.e., finding specifications that are satisfied by all plan traces belonging to the given set. In this paper, we examine the problem of inferring specifications that describe temporal differences between two sets of plan traces. We formalize the concept of providing such contrastive explanations, then present a Bayesian probabilistic model for inferring contrastive explanations as linear temporal logic specifications. We demonstrate the efficacy, scalability, and robustness of our model for inferring correct specifications across various benchmark planning domains and for a simulated air combat mission.

SOLUTION: We present a Bayesian inference model to infer contrastive explanations (as LTL specifications) describing how two sets of plan traces differ.

PROBLEM: We introduce geomstats, a Python package for Riemannian modelization and optimization over manifolds such as hyperspheres, hyperbolic spaces, SPD matrices or Lie groups of transformations. Our contribution is threefold. First, geomstats allows the flexible modeling of many a machine learning problem through an efficient and extensively unit-tested implementations of these manifolds, as well as the set of useful Riemannian metrics, exponential and logarithm maps that we provide. Moreover, the wide choice of loss functions and our implementation of the corresponding gradients allow fast and easy optimization over manifolds. Finally, geomstats is the only package to provide a unified framework for Riemannian geometry, as the operations implemented in geomstats are available with different computing backends (numpy,tensorflow and keras), as well as with a GPU-enabled mode–-thus considerably facilitating the application of Riemannian geometry in machine learning. In this paper, we present geomstats through a review of the utility and advantages of manifolds in machine learning, using the concrete examples that they span to show the efficiency and practicality of their implementation using our package

SOLUTION: We introduce geomstats, an efficient Python package for Riemannian modelization and optimization over manifolds compatible with both numpy and tensorflow .

PROBLEM: Generating complex discrete distributions remains as one of the challenging problems in machine learning. Existing techniques for generating complex distributions with high degrees of freedom depend on standard generative models like Generative Adversarial Networks (GAN), Wasserstein GAN, and associated variations. Such models are based on an optimization involving the distance between two continuous distributions. We introduce a Discrete Wasserstein GAN (DWGAN) model which is based on a dual formulation of the Wasserstein distance between two discrete distributions. We derive a novel training algorithm and corresponding network architecture based on the formulation. Experimental results are provided for both synthetic discrete data, and real discretized data from MNIST handwritten digits.

SOLUTION:
We propose a Discrete Wasserstein GAN (DWGAN) model which is based on a dual formulation of the Wasserstein distance between two discrete distributions.