580 research outputs found
Classification of Data Generated by Gaussian Mixture Models Using Deep ReLU Networks
This paper studies the binary classification of unbounded data from generated under Gaussian Mixture Models (GMMs) using deep ReLU neural
networks. We obtain \unicode{x2013} for the first time \unicode{x2013}
non-asymptotic upper bounds and convergence rates of the excess risk (excess
misclassification error) for the classification without restrictions on model
parameters. The convergence rates we derive do not depend on dimension ,
demonstrating that deep ReLU networks can overcome the curse of dimensionality
in classification. While the majority of existing generalization analysis of
classification algorithms relies on a bounded domain, we consider an unbounded
domain by leveraging the analyticity and fast decay of Gaussian distributions.
To facilitate our analysis, we give a novel approximation error bound for
general analytic functions using ReLU networks, which may be of independent
interest. Gaussian distributions can be adopted nicely to model data arising in
applications, e.g., speeches, images, and texts; our results provide a
theoretical verification of the observed efficiency of deep neural networks in
practical classification problems
Learning Ability of Interpolating Deep Convolutional Neural Networks
It is frequently observed that overparameterized neural networks generalize
well. Regarding such phenomena, existing theoretical work mainly devotes to
linear settings or fully-connected neural networks. This paper studies the
learning ability of an important family of deep neural networks, deep
convolutional neural networks (DCNNs), under both underparameterized and
overparameterized settings. We establish the first learning rates of
underparameterized DCNNs without parameter or function variable structure
restrictions presented in the literature. We also show that by adding
well-defined layers to a non-interpolating DCNN, we can obtain some
interpolating DCNNs that maintain the good learning rates of the
non-interpolating DCNN. This result is achieved by a novel network deepening
scheme designed for DCNNs. Our work provides theoretical verification of how
overfitted DCNNs generalize well
QAOA with fewer qubits: a coupling framework to solve larger-scale Max-Cut problem
Maximum cut (Max-Cut) problem is one of the most important combinatorial
optimization problems because of its various applications in real life, and
recently Quantum Approximate Optimization Algorithm (QAOA) has been widely
employed to solve it. However, as the size of the problem increases, the number
of qubits required will become larger. With the aim of saving qubits, we
propose a coupling framework for designing QAOA circuits to solve larger-scale
Max-Cut problem. This framework relies on a classical algorithm that
approximately solves a certain variant of Max-Cut, and we derive an
approximation guarantee theoretically, assuming the approximation ratio of the
classical algorithm and QAOA. Furthermore we design a heuristic approach that
fits in our framework and perform sufficient numerical experiments, where we
solve Max-Cut on various -vertex Erd\H{o}s-R\'enyi graphs. Our framework
only consumes qubits and achieves approximation ratio on average,
which outperforms the previous methods showing (quantum algorithm
using the same number of qubits) and (classical algorithm). The
experimental results indicate our well-designed quantum-classical coupling
framework gives satisfactory approximation ratio while reduces the qubit cost,
which sheds light on more potential computing power of NISQ devices
The Transfiguration of the Woman’s Body: A Study of Holy Bible and The Woman’s Bible
This article employs the method of critical discourse analysis to study the changing portrayal of the woman’s body. Our analysis shows the ways in which the woman’s body is constructed as silent, instrumentalized, sinful, and unclean in Holy Bible under the dominance of male discourses. Then we examined how the woman’s body is reconstructed as an independent and glorified entity in The Woman’s Bible, along with the subversion of male discourses by feminist renditions thereof. The study has implications for women who are fighting for their bodily rights
1,3-Dioxo-2,3-dihydro-1H-isoindol-2-yl 2,3,4-tri-O-acetyl-β-d-xyloside
The title compound, C19H19NO10, was obtained from the reaction of α-d-1-bromo-2,3,4-tri-O-acetylxylose with N-hydroxyphthalimide in the presence of potassium carbonate. The asymmetric unit contains two independent molecules, in which the O—CH—O—N torsion angles are 73.0 (4) and 65.0 (4)°. The hexapyranosyl rings adopt chair conformations and the substituent groups are in equatorial positions. In the crystal, molecules are linked by nonclassical C—H⋯O hydrogen bonds
- …