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Heuristics are crucial in SAT solvers, while no heuristic rules are suitable for all problem instances. Therefore, it typically requires to refine specific solvers for specific problem instances. In this context, we present AutoSAT, a novel framework for automatically optimizing heuristics in SAT solvers. AutoSAT is based on Large Large Models (LLMs) which is able to autonomously generate code, conduct evaluation, then utilize the feedback to further optimize heuristics, thereby reducing human intervention and enhancing solver capabilities. AutoSAT operates on a plug-and-play basis, eliminating the need for extensive preliminary setup and model training, and fosters a Chain of Thought collaborative process with fault-tolerance, ensuring robust heuristic optimization. Extensive experiments on a Conflict-Driven Clause Learning (CDCL) solver demonstrates the overall superior performance of AutoSAT, especially in solving some specific SAT problem instances.

Abstraction ability is crucial in human intelligence, which can also benefit various tasks in NLP study. Existing work shows that LLMs are deficient in abstract ability, and how to improve it remains unexplored. In this work, we design the framework AbsInstruct to enhance LLMs' abstraction ability through instruction tuning. The framework builds instructions with in-depth explanations to assist LLMs in capturing the underlying rationale of abstraction. Meanwhile, we introduce a plausibility estimator to select instructions that are more consistent with the abstraction knowledge of LLMs to be aligned. Then, our framework combines abstraction instructions with general-purpose ones to build a hybrid dataset. Extensive experiments and analyses demonstrate that our framework can considerably enhance LLMs' abstraction ability with strong generalization performance while maintaining their general instruction-following abilities.

Understanding treatment heterogeneity is crucial for reliable decision-making in treatment evaluation and selection. While the conditional average treatment effect (CATE) is commonly used to capture treatment heterogeneity induced by covariates and design individualized treatment policies, it remains an averaging metric within subpopulations. This limitation prevents it from unveiling individual-level risks, potentially leading to misleading results. This article addresses this gap by examining individual risk for binary outcomes, specifically focusing on the fraction negatively affected (FNA) conditional on covariates -- a metric assessing the percentage of individuals experiencing worse outcomes with treatment compared to control. Under the strong ignorability assumption, FNA is unidentifiable, and we find that previous bounds are wide and practically unattainable except in certain degenerate cases. By introducing a plausible positive correlation assumption for the potential outcomes, we obtain significantly improved bounds compared to previous studies. We show that even with a positive and statistically significant CATE, the lower bound on FNA can be positive, i.e., in the best-case scenario many units will be harmed if receiving treatment. We establish a nonparametric sensitivity analysis framework for FNA using the Pearson correlation coefficient as the sensitivity parameter, thereby exploring the relationships among the correlation coefficient, FNA, and CATE. We also present a practical and tractable method for selecting the range of correlation coefficients. Furthermore, we propose flexible estimators for refined FNA bounds and prove their consistency and asymptotic normality.

Adversarial Attacks on Face Recognition (FR) encompass two types: impersonation attacks and evasion attacks. We observe that achieving a successful impersonation attack on FR does not necessarily ensure a successful dodging attack on FR in the black-box setting. Introducing a novel attack method named Pre-training Pruning Restoration Attack (PPR), we aim to enhance the performance of dodging attacks whilst avoiding the degradation of impersonation attacks. Our method employs adversarial example pruning, enabling a portion of adversarial perturbations to be set to zero, while tending to maintain the attack performance. By utilizing adversarial example pruning, we can prune the pre-trained adversarial examples and selectively free up certain adversarial perturbations. Thereafter, we embed adversarial perturbations in the pruned area, which enhances the dodging performance of the adversarial face examples. The effectiveness of our proposed attack method is demonstrated through our experimental results, showcasing its superior performance.

Image attribution algorithms aim to identify important regions that are highly relevant to model decisions. Although existing attribution solutions can effectively assign importance to target elements, they still face the following challenges: 1) existing attribution methods generate inaccurate small regions thus misleading the direction of correct attribution, and 2) the model cannot produce good attribution results for samples with wrong predictions. To address the above challenges, this paper re-models the above image attribution problem as a submodular subset selection problem, aiming to enhance model interpretability using fewer regions. To address the lack of attention to local regions, we construct a novel submodular function to discover more accurate fine-grained interpretation regions. To enhance the attribution effect for all samples, we also impose four different constraints on the selection of sub-regions, i.e., confidence, effectiveness, consistency, and collaboration scores, to assess the importance of various subsets. Moreover, our theoretical analysis substantiates that the proposed function is in fact submodular. Extensive experiments show that the proposed method outperforms SOTA methods on two face datasets (Celeb-A and VGG-Face2) and one fine-grained dataset (CUB-200-2011). For correctly predicted samples, the proposed method improves the Deletion and Insertion scores with an average of 4.9% and 2.5% gain relative to HSIC-Attribution. For incorrectly predicted samples, our method achieves gains of 81.0% and 18.4% compared to the HSIC-Attribution algorithm in the average highest confidence and Insertion score respectively. The code is released at //github.com/RuoyuChen10/SMDL-Attribution.

When is heterogeneity in the composition of an autonomous robotic team beneficial and when is it detrimental? We investigate and answer this question in the context of a minimally viable model that examines the role of heterogeneous speeds in perimeter defense problems, where defenders share a total allocated speed budget. We consider two distinct problem settings and develop strategies based on dynamic programming and on local interaction rules. We present a theoretical analysis of both approaches and our results are extensively validated using simulations. Interestingly, our results demonstrate that the viability of heterogeneous teams depends on the amount of information available to the defenders. Moreover, our results suggest a universality property: across a wide range of problem parameters the optimal ratio of the speeds of the defenders remains nearly constant.

Recently, Mutual Information (MI) has attracted attention in bounding the generalization error of Deep Neural Networks (DNNs). However, it is intractable to accurately estimate the MI in DNNs, thus most previous works have to relax the MI bound, which in turn weakens the information theoretic explanation for generalization. To address the limitation, this paper introduces a probabilistic representation of DNNs for accurately estimating the MI. Leveraging the proposed MI estimator, we validate the information theoretic explanation for generalization, and derive a tighter generalization bound than the state-of-the-art relaxations.

We consider the problem of explaining the predictions of graph neural networks (GNNs), which otherwise are considered as black boxes. Existing methods invariably focus on explaining the importance of graph nodes or edges but ignore the substructures of graphs, which are more intuitive and human-intelligible. In this work, we propose a novel method, known as SubgraphX, to explain GNNs by identifying important subgraphs. Given a trained GNN model and an input graph, our SubgraphX explains its predictions by efficiently exploring different subgraphs with Monte Carlo tree search. To make the tree search more effective, we propose to use Shapley values as a measure of subgraph importance, which can also capture the interactions among different subgraphs. To expedite computations, we propose efficient approximation schemes to compute Shapley values for graph data. Our work represents the first attempt to explain GNNs via identifying subgraphs explicitly and directly. Experimental results show that our SubgraphX achieves significantly improved explanations, while keeping computations at a reasonable level.

Graph Neural Networks (GNNs) have been studied from the lens of expressive power and generalization. However, their optimization properties are less well understood. We take the first step towards analyzing GNN training by studying the gradient dynamics of GNNs. First, we analyze linearized GNNs and prove that despite the non-convexity of training, convergence to a global minimum at a linear rate is guaranteed under mild assumptions that we validate on real-world graphs. Second, we study what may affect the GNNs' training speed. Our results show that the training of GNNs is implicitly accelerated by skip connections, more depth, and/or a good label distribution. Empirical results confirm that our theoretical results for linearized GNNs align with the training behavior of nonlinear GNNs. Our results provide the first theoretical support for the success of GNNs with skip connections in terms of optimization, and suggest that deep GNNs with skip connections would be promising in practice.