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.

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.
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.

Capturing high-level structure in audio waveforms is challenging because a single second of audio spans tens of thousands of timesteps. While long-range dependencies are difficult to model directly in the time domain, we show that they can be more tractably modelled in two-dimensional time-frequency representations such as spectrograms. By leveraging this representational advantage, in conjunction with a highly expressive probabilistic model and a multiscale generation procedure, we design a model capable of generating high-fidelity audio samples which capture structure at timescales which time-domain models have yet to achieve. We demonstrate that our model captures longer-range dependencies than time-domain models such as WaveNet across a diverse set of unconditional generation tasks, including single-speaker speech generation, multi-speaker speech generation, and music generation.
We introduce an autoregressive generative model for spectrograms and demonstrate applications to speech and music generation

What would be learned by variational autoencoder(VAE) and what influence the disentanglement of VAE? This paper tries to preliminarily address VAE's intrinsic dimension, real factor, disentanglement and indicator issues theoretically in the idealistic situation and implementation issue practically through noise modeling perspective in the realistic case. On intrinsic dimension issue, due to information conservation, the idealistic VAE learns and only learns intrinsic factor dimension. Besides, suggested by mutual information separation property, the constraint induced by Gaussian prior to the VAE objective encourages the information sparsity in dimension. On disentanglement issue, subsequently, inspired by information conservation theorem the clarification on disentanglement in this paper is made. On real factor issue, due to factor equivalence, the idealistic VAE possibly learns any factor set in the equivalence class. On indicator issue, the behavior of current disentanglement metric is discussed, and several performance indicators regarding the disentanglement and generating influence are subsequently raised to evaluate the performance of VAE model and to supervise the used factors. On implementation issue, the experiments under noise modeling and constraints empirically testify the theoretical analysis and also show their own characteristic in pursuing disentanglement.
This paper tries to preliminarily address the disentanglement theoretically in the idealistic situation and practically through noise modelling perspective in the realistic case.