Entanglement-guided architectures of machine learning by quantum tensor network

It is a fundamental, but still elusive question whether the schemes based on quantum mechanics, in particular on quantum entanglement, can be used for classical information processing and machine learning. Even partial answer to this question would bring important insights to both fields of machine learning and quantum mechanics. In this work, we implement simple numerical experiments, related to pattern/images classification, in which we represent the classifiers by many-qubit quantum states written in the matrix product states (MPS). Classical machine learning algorithm is applied to these quantum states to learn the classical data. We explicitly show how quantum entanglement (i.e., single-site and bipartite entanglement) can emerge in such represented images. Entanglement characterizes here the importance of data, and such information are practically used to guide the architecture of MPS, and improve the efficiency. The number of needed qubits can be reduced to less than 1/10 of the original number, which is within the access of the state-of-the-art quantum computers. We expect such numerical experiments could open new paths in charactering classical machine learning algorithms, and at the same time shed lights on the generic quantum simulations/computations of machine learning tasks.Comment: 10 pages, 5 figure

The Analysis of the Causes of Willy’s Death in Arthur Miller’s Death of a Salesman

Death of a Salesman is a classic tragic work in contemporary America.  It discusses some social factors in Willy Loman’s death, such as the influence of the American Dream and the Great Depression. It also makes a detailed study on the flaws in the character of Willy Loman, some of which contribute to his own death, such as his misguided social values and his twisted relationship with his family. The paper aims at a further study on Willy Loman’s death and to put forward the author’s view on various causes of his death. Then it concludes that Willy’s death is the result of American society and his own character defect

Mira Variable Stars From LAMOST DR4 Data: Emission Features, Temperature Types, and Candidate Selection

Based on an extensive spectral study of a photometrically confirmed sample of Mira variables, we find a relationship between relative Balmer emission-line strength and spectral temperature of O-rich Mira stars. The $F_{\rm H\delta}/F_{\rm H\gamma}$ flux ratio increases from less than unity to five as stars cool down from M0 to M10, which is likely driven by increasing TiO absorption above the deepest shock-emitting regions. We also discuss the relationship between the equivalent widths of the Balmer emission lines and the photometric luminosity phase of our Mira sample stars. Using our 291 Mira spectra as templates for reference, 191 Mira candidates are newly identified from the LAMOST DR4 catalog. We summarize the criteria adopted to select Mira candidates based on emission-line indices and molecular absorption bands. This enlarged spectral sample of Mira variables has the potential to contribute significantly to our knowledge of the optical properties of Mira stars and will facilitate further studies of these late-type, long-period variables.Comment: 21 pages; ApJS, in pres

Discrete Distribution Estimation under User-level Local Differential Privacy

We study discrete distribution estimation under user-level local differential privacy (LDP). In user-level $\varepsilon$-LDP, each user has $m\ge1$ samples and the privacy of all $m$ samples must be preserved simultaneously. We resolve the following dilemma: While on the one hand having more samples per user should provide more information about the underlying distribution, on the other hand, guaranteeing the privacy of all $m$ samples should make the estimation task more difficult. We obtain tight bounds for this problem under almost all parameter regimes. Perhaps surprisingly, we show that in suitable parameter regimes, having $m$ samples per user is equivalent to having $m$ times more users, each with only one sample. Our results demonstrate interesting phase transitions for $m$ and the privacy parameter $\varepsilon$ in the estimation risk. Finally, connecting with recent results on shuffled DP, we show that combined with random shuffling, our algorithm leads to optimal error guarantees (up to logarithmic factors) under the central model of user-level DP in certain parameter regimes. We provide several simulations to verify our theoretical findings.Comment: 26 pages, 4 figure

Learning For Predictive Control: A Dual Gaussian Process Approach

An important issue in model-based control design is that an accurate dynamic model of the system is generally nonlinear, complex, and costly to obtain. This limits achievable control performance in practice. Gaussian process (GP) based estimation of system models is an effective tool to learn unknown dynamics directly from input/output data. However, conventional GP-based control methods often ignore the computational cost associated with accumulating data during the operation of the system and how to handle forgetting in continuous adaption. In this paper, we present a novel Dual Gaussian Process (DGP) based model predictive control (MPC) strategy that enables efficient use of online learning based predictive control without the danger of catastrophic forgetting. The bio-inspired DGP structure is a combination of a long-term GP and a short-term GP, where the long-term GP is used to keep the learned knowledge in memory and the short-term GP is employed to rapidly compensate unknown dynamics during online operation. Furthermore, a novel recursive online update strategy for the short-term GP is proposed to successively improve the learnt model during online operation. Effectiveness of the proposed strategy is demonstrated via numerical simulations.Comment: arXiv admin note: substantial text overlap with arXiv:2112.1166

Learning For Predictive Control:A Dual Gaussian Process Approach

An important issue in model-based control design is that an accurate dynamic model of the system is generally nonlinear, complex, and costly to obtain. This limits achievable control performance in practice. Gaussian process (GP) based estimation of system models is an effective tool to learn unknown dynamics directly from input/output data. However, conventional GP-based control methods often ignore the computational cost associated with accumulating data during the operation of the system and how to handle forgetting in continuous adaption. In this paper, we present a novel Dual Gaussian Process (DGP) based model predictive control (MPC) strategy that enables efficient use of online learning based predictive control without the danger of catastrophic forgetting. The bio-inspired DGP structure is a combination of a long-term GP and a short-term GP, where the long-term GP is used to keep the learned knowledge in memory and the short-term GP is employed to rapidly compensate unknown dynamics during online operation. Furthermore, a novel recursive online update strategy for the short-term GP is proposed to successively improve the learnt model during online operation. Effectiveness of the proposed strategy is demonstrated via numerical simulations