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.

Modern neural network architectures use structured linear transformations, such as low-rank matrices, sparse matrices, permutations, and the Fourier transform, to improve inference speed and reduce memory usage compared to general linear maps. However, choosing which of the myriad structured transformations to use (and its associated parameterization) is a laborious task that requires trading off speed, space, and accuracy. We consider a different approach: we introduce a family of matrices called kaleidoscope matrices (K-matrices) that provably capture any structured matrix with near-optimal space (parameter) and time (arithmetic operation) complexity. We empirically validate that K-matrices can be automatically learned within end-to-end pipelines to replace hand-crafted procedures, in order to improve model quality. For example, replacing channel shuffles in ShuffleNet improves classification accuracy on ImageNet by up to 5%. Learnable K-matrices can also simplify hand-engineered pipelines---we replace filter bank feature computation in speech data preprocessing with a kaleidoscope layer, resulting in only 0.4% loss in accuracy on the TIMIT speech recognition task. K-matrices can also capture latent structure in models: for a challenging permuted image classification task, adding a K-matrix to a standard convolutional architecture can enable learning the latent permutation and improve accuracy by over 8 points. We provide a practically efficient implementation of our approach, and use K-matrices in a Transformer network to attain 36% faster end-to-end inference speed on a language translation task.
We propose a differentiable family of "kaleidoscope matrices," prove that all structured matrices can be represented in this form, and use them to replace hand-crafted linear maps in deep learning models.

Learning representations of data is an important issue in machine learning. Though GAN has led to significant improvements in the data representations, it still has several problems such as unstable training, hidden manifold of data, and huge computational overhead. GAN tends to produce the data simply without any information about the manifold of the data, which hinders from controlling desired features to generate. Moreover, most of GAN's have a large size of manifold, resulting in poor scalability. In this paper, we propose a novel GAN to control the latent semantic representation, called LSC-GAN, which allows us to produce desired data to generate and learns a representation of the data efficiently. Unlike the conventional GAN models with hidden distribution of latent space, we define the distributions explicitly in advance that are trained to generate the data based on the corresponding features by inputting the latent variables that follow the distribution. As the larger scale of latent space caused by deploying various distributions in one latent space makes training unstable while maintaining the dimension of latent space, we need to separate the process of defining the distributions explicitly and operation of generation. We prove that a VAE is proper for the former and modify a loss function of VAE to map the data into the pre-defined latent space so as to locate the reconstructed data as close to the input data according to its characteristics. Moreover, we add the KL divergence to the loss function of LSC-GAN to include this process. The decoder of VAE, which generates the data with the corresponding features from the pre-defined latent space, is used as the generator of the LSC-GAN. Several experiments on the CelebA dataset are conducted to verify the usefulness of the proposed method to generate desired data stably and efficiently, achieving a high compression ratio that can hold about 24 pixels of information in each dimension of latent space. Besides, our model learns the reverse of features such as not laughing (rather frowning) only with data of ordinary and smiling facial expression.
We propose a generative model that not only produces data with desired features from the pre-defined latent space but also fully understands the features of the data to create characteristics that are not in the dataset.

We introduce a new procedural dynamic system that can generate a variety of shapes that often appear as curves, but technically, the figures are plots of many points. We name them spiroplots and show how this new system relates to other procedures or processes that generate figures. Spiroplots are an extremely simple process but with a surprising visual variety. We prove some fundamental properties and analyze some instances to see how the geometry or topology of the input determines the generated figures. We show that some spiroplots have a finite cycle and return to the initial situation, whereas others will produce new points infinitely often. This paper is accompanied by a JavaScript app that allows anyone to generate spiroplots.
A new, very simple dynamic system is introduced that generates pretty patterns; properties are proved and possibilities are explored