We study many-body localization (MBL) for interacting one-dimensional lattice fermions in random (Anderson) and quasiperiodic (Aubry-Andre) models, focusing on the role of interaction range. We obtain the MBL quantum phase diagrams by calculating the
experimentally relevant inverse participation ratio (IPR) at half-filling using exact diagonalization methods and extrapolating to {the infinite system size}. For short-range interactions, our results produce in the phase diagram a qualitative symmetry between weak and strong interaction limits. For long-range interactions, no such symmetry exists as the strongly interacting system is always many-body localized, independent of the effective disorder strength, and the system is analogous to a pinned Wigner crystal. We obtain various scaling exponents for the IPR, suggesting conditions for different MBL regimes arising from interaction effects.
Data auditing is a process to verify whether certain data have been removed from a trained model. A recently proposed method (Liu et al. 20) uses Kolmogorov-Smirnov (KS) distance for such data auditing. However, it fails under certain practical condi
tions. In this paper, we propose a new method called Ensembled Membership Auditing (EMA) for auditing data removal to overcome these limitations. We compare both methods using benchmark datasets (MNIST and SVHN) and Chest X-ray datasets with multi-layer perceptrons (MLP) and convolutional neural networks (CNN). Our experiments show that EMA is robust under various conditions, including the failure cases of the previously proposed method. Our code is available at: https://github.com/Hazelsuko07/EMA.
We study the boundedness and compactness of the generalized Volterra integral operator on weighted Bergman spaces with doubling weights on the unit disk. A generalized Toeplitz operator is defined and the boundedness, compactness and Schatten class o
f this operator are investigated on the Hilbert weighted Bergman space. As an application, Schatten class membership of generalized Volterra integral operators are also characterized. Finally, we also get the characterizations of Schatten class membership of generalized Toeplitz operator and generalized Volterra integral operators on the Hardy space $H^2$.
Efficient numerical methods are promising tools for delivering unique insights into the fascinating properties of physics, such as the highly frustrated quantum many-body systems. However, the computational complexity of obtaining the wave functions
for accurately describing the quantum states increases exponentially with respect to particle number. Here we present a novel convolutional neural network (CNN) for simulating the two-dimensional highly frustrated spin-$1/2$ $J_1-J_2$ Heisenberg model, meanwhile the simulation is performed at an extreme scale system with low cost and high scalability. By ingenious employment of transfer learning and CNNs translational invariance, we successfully investigate the quantum system with the lattice size up to $24times24$, within 30 million cores of the new generation of Sunway supercomputer. The final achievement demonstrates the effectiveness of CNN-based representation of quantum-state and brings the state-of-the-art record up to a brand-new level from both aspects of remarkable accuracy and unprecedented scales.
Macroscopic cat states have been widely studied to illustrate fundamental principles of quantum physics as well as their application in quantum information processing. In this paper, we propose a quantum speedup method for adiabatic creation of cat s
tates in a Kerr nonlinear resonator via gradient-descent optimal adiabatic control. By simultaneously adiabatic tuning the the cavity detuning and driving field strength, the width of minimum energy gap between the target trajectory and non-adiabatic trajectory can be widen, which allows us to speed up the evolution along the adiabatic path. Compared with the previous proposal of preparing the cat state by only controlling two-photon pumping strength in a Kerr nonlinear resonator, our method can prepare the target state with much shorter time, as well as a high fidelity and a large non-classical volume. It is worth noting that the cat state prepared by our method is also robust against single-photon loss very well. Moreover, when our proposal has a large initial detuning, it will creates a large-size cat state successfully. This proposal of preparing cat states can be implemented in superconducting quantum circuits, which provides a quantum state resource for quantum information encoding and fault-tolerant quantum computing.
Disentangled representation learning has been proposed as an approach to learning general representations. This can be done in the absence of, or with limited, annotations. A good general representation can be readily fine-tuned for new target tasks
using modest amounts of data, or even be used directly in unseen domains achieving remarkable performance in the corresponding task. This alleviation of the data and annotation requirements offers tantalising prospects for tractable and affordable applications in computer vision and healthcare. Finally, disentangled representations can offer model explainability and can help us understand the underlying causal relations of the factors of variation, increasing their suitability for real-world deployment. In this tutorial paper, we will offer an overview of the disentangled representation learning, its building blocks and criteria, and discuss applications in computer vision and medical imaging. We conclude our tutorial by presenting the identified opportunities for the integration of recent machine learning advances into disentanglement, as well as the remaining challenges.
Unsupervised disentanglement learning is a crucial issue for understanding and exploiting deep generative models. Recently, SeFa tries to find latent disentangled directions by performing SVD on the first projection of a pre-trained GAN. However, it
is only applied to the first layer and works in a post-processing way. Hessian Penalty minimizes the off-diagonal entries of the outputs Hessian matrix to facilitate disentanglement, and can be applied to multi-layers.However, it constrains each entry of output independently, making it not sufficient in disentangling the latent directions (e.g., shape, size, rotation, etc.) of spatially correlated variations. In this paper, we propose a simple Orthogonal Jacobian Regularization (OroJaR) to encourage deep generative model to learn disentangled representations. It simply encourages the variation of output caused by perturbations on different latent dimensions to be orthogonal, and the Jacobian with respect to the input is calculated to represent this variation. We show that our OroJaR also encourages the outputs Hessian matrix to be diagonal in an indirect manner. In contrast to the Hessian Penalty, our OroJaR constrains the output in a holistic way, making it very effective in disentangling latent dimensions corresponding to spatially correlated variations. Quantitative and qualitative experimental results show that our method is effective in disentangled and controllable image generation, and performs favorably against the state-of-the-art methods. Our code is available at https://github.com/csyxwei/OroJaR
Ruppeiner geometry has been found to be a novel promising approach to uncover the microstructure of fluid systems and black holes. In this work, combining with the micro model of the Van der Waals fluid, we shall propose a first microscopic interpret
ation for the empirical observation of Ruppeiner geometry. Then employing the microscopic interpretation, we disclose the potential microstructure for the anti-de Sitter black hole systems. Of particular interest, we obtain the microscopic interaction potentials for the underlying black hole molecules. This significantly strengthens the study towards to the black hole nature from the viewpoint of the thermodynamics.
Chatterjee (2021)s ingenious approach to estimating a measure of dependence first proposed by Dette et al. (2013) based on simple rank statistics has quickly caught attention. This measure of dependence has the unusual property of being between 0 and
1, and being 0 or 1 if and only if the corresponding pair of random variables is independent or one is a measurable function of the other almost surely. However, more recent studies (Cao and Bickel, 2020; Shi et al., 2021b) showed that independence tests based on Chatterjees rank correlation are unfortunately rate-inefficient against various local alternatives and they call for variants. We answer this call by proposing revised Chatterjees rank correlations that still consistently estimate the same dependence measure but provably achieve near-parametric efficiency in testing against Gaussian rotation alternatives. This is possible via incorporating many right nearest neighbors in constructing the correlation coefficients. We thus overcome the only one disadvantage of Chatterjees rank correlation (Chatterjee, 2021, Section 7).
Industrial automation is one of the key application scenarios of the fifth (5G) wireless communication network. The high requirements of industrial communication systems for latency and reliability lead to the need for industrial channel models to su
pport massive multiple-input multipleoutput (MIMO) and millimeter wave communication. In addition, due to the complex environment, huge communication equipment, and numerous metal scatterers, industrial channels have special rich dense multipath components (DMCs). Considering these characteristics, a novel three dimensional (3D) non-stationary geometry-based stochastic model (GBSM) for industrial automation wireless channel is proposed in this paper. Channel characteristics including the transfer function, time-varying space-time-frequency correlation function (STFCF), and root mean square (RMS) delay spread, model parameters including delay scaling factor and power decay factor are studied and analyzed. Besides, according to the indoor factory scenario classification of the 3rd Generation Partnership Project (3GPP) TR 38.901, two sub-scenarios considering the clutter density are simulated. Simulated cumulative distribution functions (CDFs) of RMS delay spread show a good consistency with the measurement data.
