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: Despite the fact that generative models are extremely successful in practice, the theory underlying this phenomenon is only starting to catch up with practice. In this work we address the question of the universality of generative models: is it true that neural networks can approximate any data manifold arbitrarily well? We provide a positive answer to this question and show that under mild assumptions on the activation function one can always find a feedforward neural network that maps the latent space onto a set located within the specified Hausdorff distance from the desired data manifold. We also prove similar theorems for the case of multiclass generative models and cycle generative models, trained to map samples from one manifold to another and vice versa.

Output: We shot that a wide class of manifolds can be generated by ReLU and sigmoid networks with arbitrary precision.


Input: Consider Input: Deep networks often perform well on the data distribution on which they are trained, yet give incorrect (and often very confident) answers when evaluated on points from off of the training distribution. This is exemplified by the adversarial examples phenomenon but can also be seen in terms of model generalization and domain shift.   Ideally, a model would assign lower confidence to points unlike those from the training distribution.   We propose a regularizer which addresses this issue by training with interpolated hidden states and encouraging the classifier to be less confident at these points.   Because the hidden states are learned, this has an important effect of encouraging the hidden states for a class to be concentrated in such a way so that interpolations within the same class or between two different classes do not intersect with the real data points from other classes.   This has a major advantage in that it avoids the underfitting which can result from interpolating in the input space.   We prove that the exact condition for this problem of underfitting to be avoided by Manifold Mixup is that the dimensionality of the hidden states exceeds the number of classes, which is often the case in practice.   Additionally, this concentration can be seen as making the features in earlier layers more discriminative.   We show that despite requiring no significant additional computation, Manifold Mixup achieves large improvements over strong baselines in supervised learning, robustness to single-step adversarial attacks, semi-supervised learning, and Negative Log-Likelihood on held out samples.

Output: A method for learning better representations, that acts as a regularizer and despite its no significant additional computation cost , achieves improvements over strong baselines on Supervised and Semi-supervised Learning tasks.


Input: Consider Input: In this paper, we address the challenge of limited labeled data and class imbalance problem for machine learning-based rumor detection on social media. We present an offline data augmentation method based on semantic relatedness for rumor detection. To this end, unlabeled social media data is exploited to augment limited labeled data. A context-aware neural language model and a large credibility-focused Twitter corpus are employed to learn effective representations of rumor tweets for semantic relatedness measurement. A language model fine-tuned with the a large domain-specific corpus shows a dramatic improvement on training data augmentation for rumor detection over pretrained language models. We conduct experiments on six different real-world events based on five publicly available data sets and one augmented data set. Our experiments show that the proposed method allows us to generate a larger training data with reasonable quality via weak supervision. We present preliminary results achieved using a state-of-the-art neural network model with augmented data for rumor detection.


Output: We propose a methodology of augmenting publicly available data for rumor studies based on samantic relatedness between limited labeled and unlabeled data.