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: State of the art computer vision models have been shown to be vulnerable to small adversarial perturbations of the input. In other words, most images in the data distribution are both correctly classified by the model and are very close to a visually similar misclassified image. Despite substantial research interest, the cause of the phenomenon is still poorly understood and remains unsolved. We hypothesize that this counter intuitive behavior is a naturally occurring result of the high dimensional geometry of the data manifold. As a first step towards exploring this hypothesis, we study a simple synthetic dataset of classifying between two concentric high dimensional spheres. For this dataset we show a fundamental tradeoff between the amount of test error and the average distance to nearest error. In particular, we prove that any model which misclassifies a small constant fraction of a sphere will be vulnerable to adversarial perturbations of size $O(1/\sqrt{d})$. Surprisingly, when we train several different architectures on this dataset, all of their error sets naturally approach this theoretical bound. As a result of the theory, the vulnerability of neural networks to small adversarial perturbations is a logical consequence of the amount of test error observed. We hope that our theoretical analysis of this very simple case will point the way forward to explore how the geometry of complex real-world data sets leads to adversarial examples.

Output: We hypothesize that the vulnerability of image models to small adversarial perturbation is a naturally occurring result of the high dimensional geometry of the data manifold. We explore and theoretically prove this hypothesis for a simple synthetic dataset.

Input: Consider Input: Predictive models that generalize well under distributional shift are often desirable and sometimes crucial to machine learning applications. One example is the estimation of treatment effects from observational data, where a subtask is to predict the effect of a treatment on subjects that are systematically different from those who received the treatment in the data. A related kind of distributional shift appears in unsupervised domain adaptation, where we are tasked with generalizing to a distribution of inputs that is different from the one in which we observe labels. We pose both of these problems as prediction under a shift in design. Popular methods for overcoming distributional shift are often heuristic or rely on assumptions that are rarely true in practice, such as having a well-specified model or knowing the policy that gave rise to the observed data. Other methods are hindered by their need for a pre-specified metric for comparing observations, or by poor asymptotic properties. In this work, we devise a bound on the generalization error under design shift, based on integral probability metrics and sample re-weighting. We combine this idea with representation learning, generalizing and tightening existing results in this space. Finally, we propose an algorithmic framework inspired by our bound and verify is effectiveness in causal effect estimation.

Output: A theory and algorithmic framework for prediction under distributional shift, including causal effect estimation and domain adaptation

Input: Consider Input: Most deep latent factor models choose simple priors for simplicity, tractability
or not knowing what prior to use. Recent studies show that the choice of
the prior may have a profound effect on the expressiveness of the model,
especially when its generative network has limited capacity. In this paper, we propose to learn a proper prior from data for adversarial autoencoders
(AAEs). We introduce the notion of code generators to transform manually selected
simple priors into ones that can better characterize the data distribution. Experimental results show that the proposed model can generate better image quality and learn better disentangled representations than
AAEs in both supervised and unsupervised settings. Lastly, we present its
ability to do cross-domain translation in a text-to-image synthesis task.
Output: Learning Priors for Adversarial Autoencoders