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Generative models have demonstrated impressive results in vision, language, and speech. However, even with massive datasets, they struggle with precision, generating physically invalid or factually incorrect data. This is particularly problematic when the generated data must satisfy constraints, for example, to meet product specifications in engineering design or to adhere to the laws of physics in a natural scene. To improve precision while preserving diversity and fidelity, we propose a novel training mechanism that leverages datasets of constraint-violating data points, which we consider invalid. Our approach minimizes the divergence between the generative distribution and the valid prior while maximizing the divergence with the invalid distribution. We demonstrate how generative models like GANs and DDPMs that we augment to train with invalid data vastly outperform their standard counterparts which solely train on valid data points. For example, our training procedure generates up to 98 % fewer invalid samples on 2D densities, improves connectivity and stability four-fold on a stacking block problem, and improves constraint satisfaction by 15 % on a structural topology optimization benchmark in engineering design. We also analyze how the quality of the invalid data affects the learning procedure and the generalization properties of models. Finally, we demonstrate significant improvements in sample efficiency, showing that a tenfold increase in valid samples leads to a negligible difference in constraint satisfaction, while less than 10 % invalid samples lead to a tenfold improvement. Our proposed mechanism offers a promising solution for improving precision in generative models while preserving diversity and fidelity, particularly in domains where constraint satisfaction is critical and data is limited, such as engineering design, robotics, and medicine.

Autonomous racing control is a challenging research problem as vehicles are pushed to their limits of handling to achieve an optimal lap time; therefore, vehicles exhibit highly nonlinear and complex dynamics. Difficult-to-model effects, such as drifting, aerodynamics, chassis weight transfer, and suspension can lead to infeasible and suboptimal trajectories. While offline planning allows optimizing a full reference trajectory for the minimum lap time objective, such modeling discrepancies are particularly detrimental when using offline planning, as planning model errors compound with controller modeling errors. Gaussian Process Regression (GPR) can compensate for modeling errors. However, previous works primarily focus on modeling error in real-time control without consideration for how the model used in offline planning can affect the overall performance. In this work, we propose a double-GPR error compensation algorithm to reduce model uncertainties; specifically, we compensate both the planner's model and controller's model with two respective GPR-based error compensation functions. Furthermore, we design an iterative framework to re-collect error-rich data using the racing control system. We test our method in the high-fidelity racing simulator Gran Turismo Sport (GTS); we find that our iterative, double-GPR compensation functions improve racing performance and iteration stability in comparison to a single compensation function applied merely for real-time control.

Evolutionary algorithms provide gradient-free optimisation which is beneficial for models that have difficulty in obtaining gradients; for instance, geoscientific landscape evolution models. However, such models are at times computationally expensive and even distributed swarm-based optimisation with parallel computing struggles. We can incorporate efficient strategies such as surrogate-assisted optimisation to address the challenges; however, implementing inter-process communication for surrogate-based model training is difficult. In this paper, we implement surrogate-based estimation of fitness evaluation in distributed swarm optimisation over a parallel computing architecture. We first test the framework on a set of benchmark optimisation problems and then apply it to a geoscientific model that features a landscape evolution model. Our results demonstrate very promising results for benchmark functions and the Badlands landscape evolution model. We obtain a reduction in computational time while retaining optimisation solution accuracy through the use of surrogates in a parallel computing environment. The major contribution of the paper is in the application of surrogate-based optimisation for geoscientific models which can in the future help in a better understanding of paleoclimate and geomorphology.

In this work, we present Fairness Aware Counterfactuals for Subgroups (FACTS), a framework for auditing subgroup fairness through counterfactual explanations. We start with revisiting (and generalizing) existing notions and introducing new, more refined notions of subgroup fairness. We aim to (a) formulate different aspects of the difficulty of individuals in certain subgroups to achieve recourse, i.e. receive the desired outcome, either at the micro level, considering members of the subgroup individually, or at the macro level, considering the subgroup as a whole, and (b) introduce notions of subgroup fairness that are robust, if not totally oblivious, to the cost of achieving recourse. We accompany these notions with an efficient, model-agnostic, highly parameterizable, and explainable framework for evaluating subgroup fairness. We demonstrate the advantages, the wide applicability, and the efficiency of our approach through a thorough experimental evaluation of different benchmark datasets.

Autonomous vehicles require motion forecasting of their surrounding multi-agents (pedestrians and vehicles) to make optimal decisions for navigation. The existing methods focus on techniques to utilize the positions and velocities of these agents and fail to capture semantic information from the scene. Moreover, to mitigate the increase in computational complexity associated with the number of agents in the scene, some works leverage Euclidean distance to prune far-away agents. However, distance-based metric alone is insufficient to select relevant agents and accurately perform their predictions. To resolve these issues, we propose Semantics-aware Interactive Motion Forecasting (SIMF) method to capture semantics along with spatial information, and optimally select relevant agents for motion prediction. Specifically, we achieve this by implementing a semantic-aware selection of relevant agents from the scene and passing them through an attention mechanism to extract global encodings. These encodings along with agents' local information are passed through an encoder to obtain time-dependent latent variables for a motion policy predicting the future trajectories. Our results show that the proposed approach outperforms state-of-the-art baselines and provides more accurate predictions in a scene-consistent manner.

By an analogy to the duality between the recurrence time and the longest match length, we introduce a quantity dual to the maximal repetition length, which we call the repetition time. Using the generalized Kac lemma for successive recurrence times by Chen Moy, we sandwich the repetition time in terms of min-entropies with no or relatively short conditioning. The sole assumption is stationarity and ergodicity. The proof is surprisingly short and the claim is fully general in contrast to earlier approaches by Szpankowski and by D\k{e}bowski. We discuss the analogy of this result with the Wyner-Ziv/Ornstein-Weiss theorem, which sandwiches the recurrence time in terms of Shannon entropies. We formulate the respective sandwich bounds in a way that applies also to the case of stretched exponential growth observed empirically for natural language.

Optimal design is a critical yet challenging task within many applications. This challenge arises from the need for extensive trial and error, often done through simulations or running field experiments. Fortunately, sequential optimal design, also referred to as Bayesian optimization when using surrogates with a Bayesian flavor, has played a key role in accelerating the design process through efficient sequential sampling strategies. However, a key opportunity exists nowadays. The increased connectivity of edge devices sets forth a new collaborative paradigm for Bayesian optimization. A paradigm whereby different clients collaboratively borrow strength from each other by effectively distributing their experimentation efforts to improve and fast-track their optimal design process. To this end, we bring the notion of consensus to Bayesian optimization, where clients agree (i.e., reach a consensus) on their next-to-sample designs. Our approach provides a generic and flexible framework that can incorporate different collaboration mechanisms. In lieu of this, we propose transitional collaborative mechanisms where clients initially rely more on each other to maneuver through the early stages with scant data, then, at the late stages, focus on their own objectives to get client-specific solutions. Theoretically, we show the sub-linear growth in regret for our proposed framework. Empirically, through simulated datasets and a real-world collaborative material discovery experiment, we show that our framework can effectively accelerate and improve the optimal design process and benefit all participants.

In this paper, we use Prior-data Fitted Networks (PFNs) as a flexible surrogate for Bayesian Optimization (BO). PFNs are neural processes that are trained to approximate the posterior predictive distribution (PPD) through in-context learning on any prior distribution that can be efficiently sampled from. We describe how this flexibility can be exploited for surrogate modeling in BO. We use PFNs to mimic a naive Gaussian process (GP), an advanced GP, and a Bayesian Neural Network (BNN). In addition, we show how to incorporate further information into the prior, such as allowing hints about the position of optima (user priors), ignoring irrelevant dimensions, and performing non-myopic BO by learning the acquisition function. The flexibility underlying these extensions opens up vast possibilities for using PFNs for BO. We demonstrate the usefulness of PFNs for BO in a large-scale evaluation on artificial GP samples and three different hyperparameter optimization testbeds: HPO-B, Bayesmark, and PD1. We publish code alongside trained models at //github.com/automl/PFNs4BO.

In this work we consider a model problem of deep neural learning, namely the learning of a given function when it is assumed that we have access to its point values on a finite set of points. The deep neural network interpolant is the the resulting approximation of f, which is obtained by a typical machine learning algorithm involving a given DNN architecture and an optimisation step, which is assumed to be solved exactly. These are among the simplest regression algorithms based on neural networks. In this work we introduce a new approach to the estimation of the (generalisation) error and to convergence. Our results include (i) estimates of the error without any structural assumption on the neural networks and under mild regularity assumptions on the learning function f (ii) convergence of the approximations to the target function f by only requiring that the neural network spaces have appropriate approximation capability.

In this study, we focus on learning Hamiltonian systems, which involves predicting the coordinate (q) and momentum (p) variables generated by a symplectic mapping. Based on Chen & Tao (2021), the symplectic mapping is represented by a generating function. To extend the prediction time period, we develop a new learning scheme by splitting the time series (q_i, p_i) into several partitions. We then train a large-step neural network (LSNN) to approximate the generating function between the first partition (i.e. the initial condition) and each one of the remaining partitions. This partition approach makes our LSNN effectively suppress the accumulative error when predicting the system evolution. Then we train the LSNN to learn the motions of the 2:3 resonant Kuiper belt objects for a long time period of 25000 yr. The results show that there are two significant improvements over the neural network constructed in our previous work (Li et al. 2022): (1) the conservation of the Jacobi integral, and (2) the highly accurate predictions of the orbital evolution. Overall, we propose that the designed LSNN has the potential to considerably improve predictions of the long-term evolution of more general Hamiltonian systems.