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.

Example 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.
Example 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. 

Example Input: Convolutional Neural Networks (CNNs) are composed of multiple convolution layers and show elegant performance in vision tasks.
 The design of the regular convolution is based on the Receptive Field (RF) where the information within a specific region is processed.
 In the view of the regular convolution's RF, the outputs of neurons in lower layers with smaller RF are bundled to create neurons in higher layers with larger RF. 
 As a result, the neurons in high layers are able to capture the global context even though the neurons in low layers only see the local information.
 However, in lower layers of the biological brain, the information outside of the RF changes the properties of neurons.
 In this work, we extend the regular convolution and propose spatially shuffled convolution (ss convolution).
 In ss convolution, the regular convolution is able to use the information outside of its RF by spatial shuffling which is a simple and lightweight operation.
 We perform experiments on CIFAR-10 and ImageNet-1k dataset, and show that ss convolution improves the classification performance across various CNNs.
Example Output: We propose spatially shuffled convolution that the regular convolution incorporates the information from outside of its receptive field.

Example Input: The quality of the representations achieved by embeddings is determined by how well the geometry of the embedding space matches the structure of the data.
 Euclidean space has been the workhorse for embeddings; recently hyperbolic and spherical spaces have gained popularity due to their ability to better embed new types of structured data---such as hierarchical data---but most data is not structured so uniformly.
 We address this problem by proposing learning embeddings in a product manifold combining multiple copies of these model spaces (spherical, hyperbolic, Euclidean), providing a space of heterogeneous curvature suitable for a wide variety of structures.
 We introduce a heuristic to estimate the sectional curvature of graph data and directly determine an appropriate signature---the number of component spaces and their dimensions---of the product manifold.
 Empirically, we jointly learn the curvature and the embedding in the product space via Riemannian optimization.
 We discuss how to define and compute intrinsic quantities such as means---a challenging notion for product manifolds---and provably learnable optimization functions.
 On a range of datasets and reconstruction tasks, our product space embeddings outperform single Euclidean or hyperbolic spaces used in previous works, reducing distortion by 32.55% on a Facebook social network dataset. We learn word embeddings and find that a product of hyperbolic spaces in 50 dimensions consistently improves on baseline Euclidean and hyperbolic embeddings, by 2.6
 points in Spearman rank correlation on similarity tasks
 and 3.4 points on analogy accuracy.

Example Output:
Product manifold embedding spaces with heterogenous curvature yield improved representations compared to traditional embedding spaces for a variety of structures.

