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Venn Prediction (VP) is a new machine learning framework for producing well-calibrated probabilistic predictions. In particular it provides well-calibrated lower and upper bounds for the conditional probability of an example belonging to each possible class of the problem at hand. This paper proposes five VP methods based on Neural Networks (NNs), which is one of the most widely used machine learning techniques. The proposed methods are evaluated experimentally on four benchmark datasets and the obtained results demonstrate the empirical well-calibratedness of their outputs and their superiority over the outputs of the traditional NN classifier.

Machine-Learned Likelihoods (MLL) combines machine-learning classification techniques with likelihood-based inference tests to estimate the experimental sensitivity of high-dimensional data sets. We extend the MLL method by including Kernel Density Estimators (KDE) to avoid binning the classifier output to extract the resulting one-dimensional signal and background probability density functions. We first test our method on toy models generated with multivariate Gaussian distributions, where the true probability distribution functions are known. Later, we apply the method to two cases of interest at the LHC: a search for exotic Higgs bosons, and a $Z'$ boson decaying into lepton pairs. In contrast to physical-based quantities, the typical fluctuations of the ML outputs give non-smooth probability distributions for pure-signal and pure-background samples. The non-smoothness is propagated into the density estimation due to the good performance and flexibility of the KDE method. We study its impact on the final significance computation, and we compare the results using the average of several independent ML output realizations, which allows us to obtain smoother distributions. We conclude that the significance estimation turns out to be not sensible to this issue.

Spectral Graph Neural Networks (GNNs) have achieved tremendous success in graph machine learning, with polynomial filters applied for graph convolutions, where all nodes share the identical filter weights to mine their local contexts. Despite the success, existing spectral GNNs usually fail to deal with complex networks (e.g., WWW) due to such homogeneous spectral filtering setting that ignores the regional heterogeneity as typically seen in real-world networks. To tackle this issue, we propose a novel diverse spectral filtering (DSF) framework, which automatically learns node-specific filter weights to exploit the varying local structure properly. Particularly, the diverse filter weights consist of two components -- A global one shared among all nodes, and a local one that varies along network edges to reflect node difference arising from distinct graph parts -- to balance between local and global information. As such, not only can the global graph characteristics be captured, but also the diverse local patterns can be mined with awareness of different node positions. Interestingly, we formulate a novel optimization problem to assist in learning diverse filters, which also enables us to enhance any spectral GNNs with our DSF framework. We showcase the proposed framework on three state-of-the-arts including GPR-GNN, BernNet, and JacobiConv. Extensive experiments over 10 benchmark datasets demonstrate that our framework can consistently boost model performance by up to 4.92% in node classification tasks, producing diverse filters with enhanced interpretability. Code is available at \url{//github.com/jingweio/DSF}.

Large Language Models (LLMs) have shown remarkable performance in various basic natural language tasks. For completing the complex task, we still need a plan for the task to guide LLMs to generate the specific solutions step by step. LLMs can directly generate task plans, but these plans may still contain factual errors or are incomplete. A high-quality task plan contains correct step-by-step solutions for solving all situations and behavioral instructions for avoiding mistakes. To obtain it, we propose the Learning to Plan method, which involves two phases: (1) In the first learning task plan phase, it iteratively updates the task plan with new step-by-step solutions and behavioral instructions, which are obtained by prompting LLMs to derive from training error feedback. (2) In the subsequent test phase, the LLM uses the learned task plan to guide the inference of LLM on the test set. We demonstrate the effectiveness of our method on the five different reasoning type tasks (8 datasets). Further, our analysis experiment shows that the task plan learned by one LLM can directly guide another LLM to improve its performance, which reveals a new transfer learning paradigm. We release the code at \url{//github.com/Eureka6174/LearnNLPlan}

Prompt learning has emerged as an effective and data-efficient technique in large Vision-Language Models (VLMs). However, when adapting VLMs to specialized domains such as remote sensing and medical imaging, domain prompt learning remains underexplored. While large-scale domain-specific foundation models can help tackle this challenge, their concentration on a single vision level makes it challenging to prompt both vision and language modalities. To overcome this, we propose to leverage domain-specific knowledge from domain-specific foundation models to transfer the robust recognition ability of VLMs from generalized to specialized domains, using quaternion networks. Specifically, the proposed method involves using domain-specific vision features from domain-specific foundation models to guide the transformation of generalized contextual embeddings from the language branch into a specialized space within the quaternion networks. Moreover, we present a hierarchical approach that generates vision prompt features by analyzing intermodal relationships between hierarchical language prompt features and domain-specific vision features. In this way, quaternion networks can effectively mine the intermodal relationships in the specific domain, facilitating domain-specific vision-language contrastive learning. Extensive experiments on domain-specific datasets show that our proposed method achieves new state-of-the-art results in prompt learning.

Graph Neural Networks (GNNs) have shown promising results on a broad spectrum of applications. Most empirical studies of GNNs directly take the observed graph as input, assuming the observed structure perfectly depicts the accurate and complete relations between nodes. However, graphs in the real world are inevitably noisy or incomplete, which could even exacerbate the quality of graph representations. In this work, we propose a novel Variational Information Bottleneck guided Graph Structure Learning framework, namely VIB-GSL, in the perspective of information theory. VIB-GSL advances the Information Bottleneck (IB) principle for graph structure learning, providing a more elegant and universal framework for mining underlying task-relevant relations. VIB-GSL learns an informative and compressive graph structure to distill the actionable information for specific downstream tasks. VIB-GSL deduces a variational approximation for irregular graph data to form a tractable IB objective function, which facilitates training stability. Extensive experimental results demonstrate that the superior effectiveness and robustness of VIB-GSL.

The time and effort involved in hand-designing deep neural networks is immense. This has prompted the development of Neural Architecture Search (NAS) techniques to automate this design. However, NAS algorithms tend to be slow and expensive; they need to train vast numbers of candidate networks to inform the search process. This could be alleviated if we could partially predict a network's trained accuracy from its initial state. In this work, we examine the overlap of activations between datapoints in untrained networks and motivate how this can give a measure which is usefully indicative of a network's trained performance. We incorporate this measure into a simple algorithm that allows us to search for powerful networks without any training in a matter of seconds on a single GPU, and verify its effectiveness on NAS-Bench-101, NAS-Bench-201, NATS-Bench, and Network Design Spaces. Our approach can be readily combined with more expensive search methods; we examine a simple adaptation of regularised evolutionary search. Code for reproducing our experiments is available at //github.com/BayesWatch/nas-without-training.

Recently, contrastive learning (CL) has emerged as a successful method for unsupervised graph representation learning. Most graph CL methods first perform stochastic augmentation on the input graph to obtain two graph views and maximize the agreement of representations in the two views. Despite the prosperous development of graph CL methods, the design of graph augmentation schemes -- a crucial component in CL -- remains rarely explored. We argue that the data augmentation schemes should preserve intrinsic structures and attributes of graphs, which will force the model to learn representations that are insensitive to perturbation on unimportant nodes and edges. However, most existing methods adopt uniform data augmentation schemes, like uniformly dropping edges and uniformly shuffling features, leading to suboptimal performance. In this paper, we propose a novel graph contrastive representation learning method with adaptive augmentation that incorporates various priors for topological and semantic aspects of the graph. Specifically, on the topology level, we design augmentation schemes based on node centrality measures to highlight important connective structures. On the node attribute level, we corrupt node features by adding more noise to unimportant node features, to enforce the model to recognize underlying semantic information. We perform extensive experiments of node classification on a variety of real-world datasets. Experimental results demonstrate that our proposed method consistently outperforms existing state-of-the-art baselines and even surpasses some supervised counterparts, which validates the effectiveness of the proposed contrastive framework with adaptive augmentation.

Graph Neural Networks (GNNs) have proven to be useful for many different practical applications. However, many existing GNN models have implicitly assumed homophily among the nodes connected in the graph, and therefore have largely overlooked the important setting of heterophily, where most connected nodes are from different classes. In this work, we propose a novel framework called CPGNN that generalizes GNNs for graphs with either homophily or heterophily. The proposed framework incorporates an interpretable compatibility matrix for modeling the heterophily or homophily level in the graph, which can be learned in an end-to-end fashion, enabling it to go beyond the assumption of strong homophily. Theoretically, we show that replacing the compatibility matrix in our framework with the identity (which represents pure homophily) reduces to GCN. Our extensive experiments demonstrate the effectiveness of our approach in more realistic and challenging experimental settings with significantly less training data compared to previous works: CPGNN variants achieve state-of-the-art results in heterophily settings with or without contextual node features, while maintaining comparable performance in homophily settings.

Graph Neural Networks (GNNs) have received considerable attention on graph-structured data learning for a wide variety of tasks. The well-designed propagation mechanism which has been demonstrated effective is the most fundamental part of GNNs. Although most of GNNs basically follow a message passing manner, litter effort has been made to discover and analyze their essential relations. In this paper, we establish a surprising connection between different propagation mechanisms with a unified optimization problem, showing that despite the proliferation of various GNNs, in fact, their proposed propagation mechanisms are the optimal solution optimizing a feature fitting function over a wide class of graph kernels with a graph regularization term. Our proposed unified optimization framework, summarizing the commonalities between several of the most representative GNNs, not only provides a macroscopic view on surveying the relations between different GNNs, but also further opens up new opportunities for flexibly designing new GNNs. With the proposed framework, we discover that existing works usually utilize naive graph convolutional kernels for feature fitting function, and we further develop two novel objective functions considering adjustable graph kernels showing low-pass or high-pass filtering capabilities respectively. Moreover, we provide the convergence proofs and expressive power comparisons for the proposed models. Extensive experiments on benchmark datasets clearly show that the proposed GNNs not only outperform the state-of-the-art methods but also have good ability to alleviate over-smoothing, and further verify the feasibility for designing GNNs with our unified optimization framework.