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: 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.

Output: We introduce an autoregressive generative model for spectrograms and demonstrate applications to speech and music generation

Input: Consider Input: The Expectation-Maximization (EM) algorithm is a fundamental tool in unsupervised machine learning. It is often used as an efficient way to solve Maximum Likelihood (ML) and Maximum A Posteriori estimation problems, especially for models with latent variables. It is also the algorithm of choice to fit mixture models: generative models that represent unlabelled points originating from $k$ different processes, as samples from $k$ multivariate distributions. In this work we define and use a quantum version of EM to fit a Gaussian Mixture Model. Given quantum access to a dataset of $n$ vectors of dimension $d$, our algorithm has convergence and precision guarantees similar to the classical algorithm, but the runtime is only polylogarithmic in the number of elements in the training set, and is polynomial in other parameters - as the dimension of the feature space, and the number of components in the mixture. We generalize further the algorithm by fitting any mixture model of base distributions in the exponential family. We discuss the performance of the algorithm on datasets that are expected to be classified successfully by those algorithms, arguing that on those cases we can give strong guarantees on the runtime.

Output: It's the quantum algorithm for Expectation Maximization. It's fast: the runtime depends only polylogarithmically on the number of elements in the dataset.

Input: Consider Input: Variational autoencoders (VAEs) defined over SMILES string and graph-based representations of molecules promise to improve the optimization of molecular properties, thereby revolutionizing the pharmaceuticals and materials industries. However, these VAEs are hindered by the non-unique nature of SMILES strings and the computational cost of graph convolutions. To efficiently pass messages along all paths through the molecular graph, we encode multiple SMILES strings of a single molecule using a set of stacked recurrent neural networks, harmonizing hidden representations of each atom between SMILES representations, and use attentional pooling to build a final fixed-length latent representation. By then decoding to a disjoint set of SMILES strings of the molecule, our All SMILES VAE learns an almost bijective mapping between molecules and latent representations near the high-probability-mass subspace of the prior. Our SMILES-derived but molecule-based latent representations significantly surpass the state-of-the-art in a variety of fully- and semi-supervised property regression and molecular property optimization tasks.
Output: We pool messages amongst multiple SMILES strings of the same molecule to pass information along all paths through the molecular graph, producing latent representations that significantly surpass the state-of-the-art in a variety of tasks.