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Quantum adversarial machine learning is an emerging field that studies the vulnerability of quantum learning systems against adversarial perturbations and develops possible defense strategies. Quantum universal adversarial perturbations are small perturbations, which can make different input samples into adversarial examples that may deceive a given quantum classifier. This is a field that was rarely looked into but worthwhile investigating because universal perturbations might simplify malicious attacks to a large extent, causing unexpected devastation to quantum machine learning models. In this paper, we take a step forward and explore the quantum universal perturbations in the context of heterogeneous classification tasks. In particular, we find that quantum classifiers that achieve almost state-of-the-art accuracy on two different classification tasks can be both conclusively deceived by one carefully-crafted universal perturbation. This result is explicitly demonstrated with well-designed quantum continual learning models with elastic weight consolidation method to avoid catastrophic forgetting, as well as real-life heterogeneous datasets from hand-written digits and medical MRI images. Our results provide a simple and efficient way to generate universal perturbations on heterogeneous classification tasks and thus would provide valuable guidance for future quantum learning technologies.

Feature attribution is a fundamental task in both machine learning and data analysis, which involves determining the contribution of individual features or variables to a model's output. This process helps identify the most important features for predicting an outcome. The history of feature attribution methods can be traced back to General Additive Models (GAMs), which extend linear regression models by incorporating non-linear relationships between dependent and independent variables. In recent years, gradient-based methods and surrogate models have been applied to unravel complex Artificial Intelligence (AI) systems, but these methods have limitations. GAMs tend to achieve lower accuracy, gradient-based methods can be difficult to interpret, and surrogate models often suffer from stability and fidelity issues. Furthermore, most existing methods do not consider users' contexts, which can significantly influence their preferences. To address these limitations and advance the current state-of-the-art, we define a novel feature attribution framework called Context-Aware Feature Attribution Through Argumentation (CA-FATA). Our framework harnesses the power of argumentation by treating each feature as an argument that can either support, attack or neutralize a prediction. Additionally, CA-FATA formulates feature attribution as an argumentation procedure, and each computation has explicit semantics, which makes it inherently interpretable. CA-FATA also easily integrates side information, such as users' contexts, resulting in more accurate predictions.

Bagging is a commonly used ensemble technique in statistics and machine learning to improve the performance of prediction procedures. In this paper, we study the prediction risk of variants of bagged predictors under the proportional asymptotics regime, in which the ratio of the number of features to the number of observations converges to a constant. Specifically, we propose a general strategy to analyze the prediction risk under squared error loss of bagged predictors using classical results on simple random sampling. Specializing the strategy, we derive the exact asymptotic risk of the bagged ridge and ridgeless predictors with an arbitrary number of bags under a well-specified linear model with arbitrary feature covariance matrices and signal vectors. Furthermore, we prescribe a generic cross-validation procedure to select the optimal subsample size for bagging and discuss its utility to eliminate the non-monotonic behavior of the limiting risk in the sample size (i.e., double or multiple descents). In demonstrating the proposed procedure for bagged ridge and ridgeless predictors, we thoroughly investigate the oracle properties of the optimal subsample size and provide an in-depth comparison between different bagging variants.

Quantum computing promises transformational gains for solving some problems, but little to none for others. For anyone hoping to use quantum computers now or in the future, it is important to know which problems will benefit. In this paper, we introduce a framework for answering this question both intuitively and quantitatively. The underlying structure of the framework is a race between quantum and classical computers, where their relative strengths determine when each wins. While classical computers operate faster, quantum computers can sometimes run more efficient algorithms. Whether the speed advantage or the algorithmic advantage dominates determines whether a problem will benefit from quantum computing or not. Our analysis reveals that many problems, particularly those of small to moderate size that can be important for typical businesses, will not benefit from quantum computing. Conversely, larger problems or those with particularly big algorithmic gains will benefit from near-term quantum computing. Since very large algorithmic gains are rare in practice and theorized to be rare even in principle, our analysis suggests that the benefits from quantum computing will flow either to users of these rare cases, or practitioners processing very large data.

We present a machine-learning strategy for finite element analysis of solid mechanics wherein we replace complex portions of a computational domain with a data-driven surrogate. In the proposed strategy, we decompose a computational domain into an "outer" coarse-scale domain that we resolve using a finite element method (FEM) and an "inner" fine-scale domain. We then develop a machine-learned (ML) model for the impact of the inner domain on the outer domain. In essence, for solid mechanics, our machine-learned surrogate performs static condensation of the inner domain degrees of freedom. This is achieved by learning the map from (virtual) displacements on the inner-outer domain interface boundary to forces contributed by the inner domain to the outer domain on the same interface boundary. We consider two such mappings, one that directly maps from displacements to forces without constraints, and one that maps from displacements to forces by virtue of learning a symmetric positive semi-definite (SPSD) stiffness matrix. We demonstrate, in a simplified setting, that learning an SPSD stiffness matrix results in a coarse-scale problem that is well-posed with a unique solution. We present numerical experiments on several exemplars, ranging from finite deformations of a cube to finite deformations with contact of a fastener-bushing geometry. We demonstrate that enforcing an SPSD stiffness matrix is critical for accurate FEM-ML coupled simulations, and that the resulting methods can accurately characterize out-of-sample loading configurations with significant speedups over the standard FEM simulations.

Reinforcement learning (RL) has helped improve decision-making in several applications. However, applying traditional RL is challenging in some applications, such as rehabilitation of people with a spinal cord injury (SCI). Among other factors, using RL in this domain is difficult because there are many possible treatments (i.e., large action space) and few patients (i.e., limited training data). Treatments for SCIs have natural groupings, so we propose two approaches to grouping treatments so that an RL agent can learn effectively from limited data. One relies on domain knowledge of SCI rehabilitation and the other learns similarities among treatments using an embedding technique. We then use Fitted Q Iteration to train an agent that learns optimal treatments. Through a simulation study designed to reflect the properties of SCI rehabilitation, we find that both methods can help improve the treatment decisions of physiotherapists, but the approach based on domain knowledge offers better performance. Our findings provide a "proof of concept" that RL can be used to help improve the treatment of those with an SCI and indicates that continued efforts to gather data and apply RL to this domain are worthwhile.

Sparse Bayesian learning (SBL) has been extensively utilized in data-driven modeling to combat the issue of overfitting. While SBL excels in linear-in-parameter models, its direct applicability is limited in models where observations possess nonlinear relationships with unknown parameters. Recently, a semi-analytical Bayesian framework known as nonlinear sparse Bayesian learning (NSBL) was introduced by the authors to induce sparsity among model parameters during the Bayesian inversion of nonlinear-in-parameter models. NSBL relies on optimally selecting the hyperparameters of sparsity-inducing Gaussian priors. It is inherently an approximate method since the uncertainty in the hyperparameter posterior is disregarded as we instead seek the maximum a posteriori (MAP) estimate of the hyperparameters (type-II MAP estimate). This paper aims to investigate the hierarchical structure that forms the basis of NSBL and validate its accuracy through a comparison with a one-level hierarchical Bayesian inference as a benchmark in the context of three numerical experiments: (i) a benchmark linear regression example with Gaussian prior and Gaussian likelihood, (ii) the same regression problem with a highly non-Gaussian prior, and (iii) an example of a dynamical system with a non-Gaussian prior and a highly non-Gaussian likelihood function, to explore the performance of the algorithm in these new settings. Through these numerical examples, it can be shown that NSBL is well-suited for physics-based models as it can be readily applied to models with non-Gaussian prior distributions and non-Gaussian likelihood functions. Moreover, we illustrate the accuracy of the NSBL algorithm as an approximation to the one-level hierarchical Bayesian inference and its ability to reduce the computational cost while adequately exploring the parameter posteriors.

Measurement-based quantum computation (MBQC) offers a fundamentally unique paradigm to design quantum algorithms. Indeed, due to the inherent randomness of quantum measurements, the natural operations in MBQC are not deterministic and unitary, but are rather augmented with probabilistic byproducts. Yet, the main algorithmic use of MBQC so far has been to completely counteract this probabilistic nature in order to simulate unitary computations expressed in the circuit model. In this work, we propose designing MBQC algorithms that embrace this inherent randomness and treat the random byproducts in MBQC as a resource for computation. As a natural application where randomness can be beneficial, we consider generative modeling, a task in machine learning centered around generating complex probability distributions. To address this task, we propose a variational MBQC algorithm equipped with control parameters that allow to directly adjust the degree of randomness to be admitted in the computation. Our numerical findings indicate that this additional randomness can lead to significant gains in learning performance in certain generative modeling tasks. These results highlight the potential advantages in exploiting the inherent randomness of MBQC and motivate further research into MBQC-based algorithms.

A numerical method is proposed for simulation of composite open quantum systems. It is based on Lindblad master equations and adiabatic elimination. Each subsystem is assumed to converge exponentially towards a stationary subspace, slightly impacted by some decoherence channels and weakly coupled to the other subsystems. This numerical method is based on a perturbation analysis with an asymptotic expansion. It exploits the formulation of the slow dynamics with reduced dimension. It relies on the invariant operators of the local and nominal dissipative dynamics attached to each subsystem. Second-order expansion can be computed only with local numerical calculations. It avoids computations on the tensor-product Hilbert space attached to the full system. This numerical method is particularly well suited for autonomous quantum error correction schemes. Simulations of such reduced models agree with complete full model simulations for typical gates acting on one and two cat-qubits (Z, ZZ and CNOT) when the mean photon number of each cat-qubit is less than 8. For larger mean photon numbers and gates with three cat-qubits (ZZZ and CCNOT), full model simulations are almost impossible whereas reduced model simulations remain accessible. In particular, they capture both the dominant phase-flip error-rate and the very small bit-flip error-rate with its exponential suppression versus the mean photon number.

Most state-of-the-art machine learning techniques revolve around the optimisation of loss functions. Defining appropriate loss functions is therefore critical to successfully solving problems in this field. We present a survey of the most commonly used loss functions for a wide range of different applications, divided into classification, regression, ranking, sample generation and energy based modelling. Overall, we introduce 33 different loss functions and we organise them into an intuitive taxonomy. Each loss function is given a theoretical backing and we describe where it is best used. This survey aims to provide a reference of the most essential loss functions for both beginner and advanced machine learning practitioners.