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This study proposes a unified theory and statistical learning approach for traffic conflict detection, addressing the long-existing call for a consistent and comprehensive methodology to evaluate the collision risk emerged in road user interactions. The proposed theory assumes a context-dependent probabilistic collision risk and frames conflict detection as estimating the risk by statistical learning from observed proximities and contextual variables. Three primary tasks are integrated: representing interaction context from selected observables, inferring proximity distributions in different contexts, and applying extreme value theory to relate conflict intensity with conflict probability. As a result, this methodology is adaptable to various road users and interaction scenarios, enhancing its applicability without the need for pre-labelled conflict data. Demonstration experiments are executed using real-world trajectory data, with the unified metric trained on lane-changing interactions on German highways and applied to near-crash events from the 100-Car Naturalistic Driving Study in the U.S. The experiments demonstrate the methodology's ability to provide effective collision warnings, generalise across different datasets and traffic environments, cover a broad range of conflicts, and deliver a long-tailed distribution of conflict intensity. This study contributes to traffic safety by offering a consistent and explainable methodology for conflict detection applicable across various scenarios. Its societal implications include enhanced safety evaluations of traffic infrastructures, more effective collision warning systems for autonomous and driving assistance systems, and a deeper understanding of road user behaviour in different traffic conditions, contributing to a potential reduction in accident rates and improving overall traffic safety.

The efficacy of interpolating via Variably Scaled Kernels (VSKs) is known to be dependent on the definition of a proper scaling function, but no numerical recipes to construct it are available. Previous works suggest that such a function should mimic the target one, but no theoretical evidence is provided. This paper fills both the gaps: it proves that a scaling function reflecting the target one may lead to enhanced approximation accuracy, and it provides a user-independent tool for learning the scaling function by means of Discontinuous Neural Networks ({\delta}NN), i.e., NNs able to deal with possible discontinuities. Numerical evidence supports our claims, as it shows that the key features of the target function can be clearly recovered in the learned scaling function.

To overcome the imbalanced multimodal learning problem, where models prefer the training of specific modalities, existing methods propose to control the training of uni-modal encoders from different perspectives, taking the inter-modal performance discrepancy as the basis. However, the intrinsic limitation of modality capacity is ignored. The scarcely informative modalities can be recognized as ``worse-learnt'' ones, which could force the model to memorize more noise, counterproductively affecting the multimodal model ability. Moreover, the current modality modulation methods narrowly concentrate on selected worse-learnt modalities, even suppressing the training of others. Hence, it is essential to consider the intrinsic limitation of modality capacity and take all modalities into account during balancing. To this end, we propose the Diagnosing \& Re-learning method. The learning state of each modality is firstly estimated based on the separability of its uni-modal representation space, and then used to softly re-initialize the corresponding uni-modal encoder. In this way, the over-emphasizing of scarcely informative modalities is avoided. In addition, encoders of worse-learnt modalities are enhanced, simultaneously avoiding the over-training of other modalities. Accordingly, multimodal learning is effectively balanced and enhanced. Experiments covering multiple types of modalities and multimodal frameworks demonstrate the superior performance of our simple-yet-effective method for balanced multimodal learning. The source code and dataset are available at \url{//github.com/GeWu-Lab/Diagnosing_Relearning_ECCV2024}.

Geometric deep learning models, which incorporate the relevant molecular symmetries within the neural network architecture, have considerably improved the accuracy and data efficiency of predictions of molecular properties. Building on this success, we introduce 3DReact, a geometric deep learning model to predict reaction properties from three-dimensional structures of reactants and products. We demonstrate that the invariant version of the model is sufficient for existing reaction datasets. We illustrate its competitive performance on the prediction of activation barriers on the GDB7-22-TS, Cyclo-23-TS and Proparg-21-TS datasets in different atom-mapping regimes. We show that, compared to existing models for reaction property prediction, 3DReact offers a flexible framework that exploits atom-mapping information, if available, as well as geometries of reactants and products (in an invariant or equivariant fashion). Accordingly, it performs systematically well across different datasets, atom-mapping regimes, as well as both interpolation and extrapolation tasks.

The rapid pace of development in quantum computing technology has sparked a proliferation of benchmarks for assessing the performance of quantum computing hardware and software. Good benchmarks empower scientists, engineers, programmers, and users to understand a computing system's power, but bad benchmarks can misdirect research and inhibit progress. In this Perspective, we survey the science of quantum computer benchmarking. We discuss the role of benchmarks and benchmarking, and how good benchmarks can drive and measure progress towards the long-term goal of useful quantum computations, i.e., "quantum utility". We explain how different kinds of benchmark quantify the performance of different parts of a quantum computer, we survey existing benchmarks, critically discuss recent trends in benchmarking, and highlight important open research questions in this field.

We consider the statistical linear inverse problem of making inference on an unknown source function in an elliptic partial differential equation from noisy observations of its solution. We employ nonparametric Bayesian procedures based on Gaussian priors, leading to convenient conjugate formulae for posterior inference. We review recent results providing theoretical guarantees on the quality of the resulting posterior-based estimation and uncertainty quantification, and we discuss the application of the theory to the important classes of Gaussian series priors defined on the Dirichlet-Laplacian eigenbasis and Mat\'ern process priors. We provide an implementation of posterior inference for both classes of priors, and investigate its performance in a numerical simulation study.

Sufficient dimension reduction has received much interest over the past 30 years. Most existing approaches focus on statistical models linking the response to the covariate through a regression equation, and as such are not adapted to binary classification problems. We address the question of dimension reduction for binary classification by fitting a localized nearest-neighbor logistic model with $\ell_1$-penalty in order to estimate the gradient of the conditional probability of interest. Our theoretical analysis shows that the pointwise convergence rate of the gradient estimator is optimal under very mild conditions. The dimension reduction subspace is estimated using an outer product of such gradient estimates at several points in the covariate space. Our implementation uses cross-validation on the misclassification rate to estimate the dimension of this subspace. We find that the proposed approach outperforms existing competitors in synthetic and real data applications.

Language models achieve impressive results in tasks involving complex multistep reasoning, but scaling these capabilities further traditionally requires expensive collection of more annotated data. In this work, we explore the potential of improving the capabilities of language models without new data, merely using automated feedback to the validity of their predictions in arithmetic reasoning (self-training). We find that models can substantially improve in both single-round (offline) and online self-training. In the offline setting, supervised methods are able to deliver gains comparable to preference optimization, but in online self-training, preference optimization shows to largely outperform supervised training thanks to superior stability and robustness on unseen types of problems.

A common method for estimating the Hessian operator from random samples on a low-dimensional manifold involves locally fitting a quadratic polynomial. Although widely used, it is unclear if this estimator introduces bias, especially in complex manifolds with boundaries and nonuniform sampling. Rigorous theoretical guarantees of its asymptotic behavior have been lacking. We show that, under mild conditions, this estimator asymptotically converges to the Hessian operator, with nonuniform sampling and curvature effects proving negligible, even near boundaries. Our analysis framework simplifies the intensive computations required for direct analysis.

The remarkable practical success of deep learning has revealed some major surprises from a theoretical perspective. In particular, simple gradient methods easily find near-optimal solutions to non-convex optimization problems, and despite giving a near-perfect fit to training data without any explicit effort to control model complexity, these methods exhibit excellent predictive accuracy. We conjecture that specific principles underlie these phenomena: that overparametrization allows gradient methods to find interpolating solutions, that these methods implicitly impose regularization, and that overparametrization leads to benign overfitting. We survey recent theoretical progress that provides examples illustrating these principles in simpler settings. We first review classical uniform convergence results and why they fall short of explaining aspects of the behavior of deep learning methods. We give examples of implicit regularization in simple settings, where gradient methods lead to minimal norm functions that perfectly fit the training data. Then we review prediction methods that exhibit benign overfitting, focusing on regression problems with quadratic loss. For these methods, we can decompose the prediction rule into a simple component that is useful for prediction and a spiky component that is useful for overfitting but, in a favorable setting, does not harm prediction accuracy. We focus specifically on the linear regime for neural networks, where the network can be approximated by a linear model. In this regime, we demonstrate the success of gradient flow, and we consider benign overfitting with two-layer networks, giving an exact asymptotic analysis that precisely demonstrates the impact of overparametrization. We conclude by highlighting the key challenges that arise in extending these insights to realistic deep learning settings.