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.

Input: Consider Input: We present a simple neural model that given a formula and a property tries to answer the question whether the formula has the given property, for example whether a propositional formula is always true. The structure of the formula is captured by a feedforward neural network recursively built for the given formula in a top-down manner. The results of this network are then processed by two recurrent neural networks. One of the interesting aspects of our model is how propositional atoms are treated. For example, the model is insensitive to their names, it only matters whether they are the same or distinct.

Output: A top-down approach how to recursively represent propositional formulae by neural networks is presented.

Input: Consider Input: Determining the optimal order in which data examples are presented to Deep Neural Networks during training is a non-trivial problem. However, choosing a non-trivial scheduling method may drastically improve convergence. In this paper, we propose a Self-Paced Learning (SPL)-fused Deep Metric Learning (DML) framework, which we call Learning Embeddings for Adaptive Pace (LEAP). Our method parameterizes mini-batches dynamically based on the extit{easiness} and extit{true diverseness} of the sample within a salient feature representation space. In LEAP, we train an extit{embedding} Convolutional Neural Network (CNN) to learn an expressive representation space by adaptive density discrimination using the Magnet Loss. The extit{student} CNN classifier dynamically selects samples to form a mini-batch based on the extit{easiness} from cross-entropy losses and extit{true diverseness} of examples from the representation space sculpted by the extit{embedding} CNN. We evaluate LEAP using deep CNN architectures for the task of supervised image classification on MNIST, FashionMNIST, CIFAR-10, CIFAR-100, and SVHN. We show that the LEAP framework converges faster with respect to the number of mini-batch updates required to achieve a comparable or better test performance on each of the datasets.

Output: LEAP combines the strength of adaptive sampling with that of mini-batch online learning and adaptive representation learning to formulate a representative self-paced strategy in an end-to-end DNN training protocol.

Input: Consider Input: We propose to tackle a time series regression problem by computing temporal evolution of a probability density function to provide a probabilistic forecast. A Recurrent Neural Network (RNN) based model is employed to learn a nonlinear operator for temporal evolution of a probability density function. We use a softmax layer for a numerical discretization of a smooth probability density functions, which transforms a function approximation problem to a classification task. Explicit and implicit regularization strategies are introduced to impose a smoothness condition on the estimated probability distribution. A Monte Carlo procedure to compute the temporal evolution of the distribution for a multiple-step forecast is presented. The evaluation of the proposed algorithm on three synthetic and two real data sets shows advantage over the compared baselines.
Output: Proposed RNN-based algorithm to estimate predictive distribution in one- and multi-step forecasts in time series prediction problems