亚洲男人的天堂2018av,欧美草比,久久久久久免费视频精选,国色天香在线看免费,久久久久亚洲av成人片仓井空

Transferability estimation aims to provide heuristics for quantifying how suitable a pre-trained model is for a specific downstream task, without fine-tuning them all. Prior studies have revealed that well-trained models exhibit the phenomenon of Neural Collapse. Based on a widely used neural collapse metric in existing literature, we observe a strong correlation between the neural collapse of pre-trained models and their corresponding fine-tuned models. Inspired by this observation, we propose a novel method termed Fair Collapse (FaCe) for transferability estimation by comprehensively measuring the degree of neural collapse in the pre-trained model. Typically, FaCe comprises two different terms: the variance collapse term, which assesses the class separation and within-class compactness, and the class fairness term, which quantifies the fairness of the pre-trained model towards each class. We investigate FaCe on a variety of pre-trained classification models across different network architectures, source datasets, and training loss functions. Results show that FaCe yields state-of-the-art performance on different tasks including image classification, semantic segmentation, and text classification, which demonstrate the effectiveness and generalization of our method.

The diagonal entries of pseudoinverse of the Laplacian matrix of a graph appear in many important practical applications, since they contain much information of the graph and many relevant quantities can be expressed in terms of them, such as Kirchhoff index and current flow centrality. However, a na\"{\i}ve approach for computing the diagonal of a matrix inverse has cubic computational complexity in terms of the matrix dimension, which is not acceptable for large graphs with millions of nodes. Thus, rigorous solutions to the diagonal of the Laplacian matrices for general graphs, even for particluar graphs are much less. In this paper, we propose a theoretically guaranteed estimation algorithm, which approximates all diagonal entries of the pseudoinverse of a graph Laplacian in nearly linear time with respect to the number of edges in the graph. We execute extensive experiments on real-life networks, which indicate that our algorithm is both efficient and accurate. Also, we determine exact expressions for the diagonal elements of pseudoinverse of the Laplacian matrices for Koch networks and uniform recursive trees, and compare them with those obtained by our approximation algorithm. Finally, we use our algorithm to evaluate the Kirchhoff index of three deterministic model networks, for which the Kirchhoff index can be rigorously determined. These results further show the effectiveness and efficiency of our algorithm.

Neural collapse provides an elegant mathematical characterization of learned last layer representations (a.k.a. features) and classifier weights in deep classification models. Such results not only provide insights but also motivate new techniques for improving practical deep models. However, most of the existing empirical and theoretical studies in neural collapse focus on the case that the number of classes is small relative to the dimension of the feature space. This paper extends neural collapse to cases where the number of classes are much larger than the dimension of feature space, which broadly occur for language models, retrieval systems, and face recognition applications. We show that the features and classifier exhibit a generalized neural collapse phenomenon, where the minimum one-vs-rest margins is maximized.We provide empirical study to verify the occurrence of generalized neural collapse in practical deep neural networks. Moreover, we provide theoretical study to show that the generalized neural collapse provably occurs under unconstrained feature model with spherical constraint, under certain technical conditions on feature dimension and number of classes.

We study a general online combinatorial auction problem in algorithmic mechanism design. A provider allocates multiple types of capacity-limited resources to customers that arrive in a sequential and arbitrary manner. Each customer has a private valuation function on bundles of resources that she can purchase (e.g., a combination of different resources such as CPU and RAM in cloud computing). The provider charges payment from customers who purchase a bundle of resources and incurs an increasing supply cost with respect to the totality of resources allocated. The goal is to maximize the social welfare, namely, the total valuation of customers for their purchased bundles, minus the total supply cost of the provider for all the resources that have been allocated. We adopt the competitive analysis framework and provide posted-price mechanisms with optimal competitive ratios. Our pricing mechanism is optimal in the sense that no other online algorithms can achieve a better competitive ratio. We validate the theoretic results via empirical studies of online resource allocation in cloud computing. Our numerical results demonstrate that the proposed pricing mechanism is competitive and robust against system uncertainties and outperforms existing benchmarks.

We take a random matrix theory approach to random sketching and show an asymptotic first-order equivalence of the regularized sketched pseudoinverse of a positive semidefinite matrix to a certain evaluation of the resolvent of the same matrix. We focus on real-valued regularization and extend previous results on an asymptotic equivalence of random matrices to the real setting, providing a precise characterization of the equivalence even under negative regularization, including a precise characterization of the smallest nonzero eigenvalue of the sketched matrix, which may be of independent interest. We then further characterize the second-order equivalence of the sketched pseudoinverse. We also apply our results to the analysis of the sketch-and-project method and to sketched ridge regression. Lastly, we prove that these results generalize to asymptotically free sketching matrices, obtaining the resulting equivalence for orthogonal sketching matrices and comparing our results to several common sketches used in practice.

In knowledge distillation research, feature-based methods have dominated due to their ability to effectively tap into extensive teacher models. In contrast, logit-based approaches are considered to be less adept at extracting hidden 'dark knowledge' from teachers. To bridge this gap, we present LumiNet, a novel knowledge-transfer algorithm designed to enhance logit-based distillation. We introduce a perception matrix that aims to recalibrate logits through adjustments based on the model's representation capability. By meticulously analyzing intra-class dynamics, LumiNet reconstructs more granular inter-class relationships, enabling the student model to learn a richer breadth of knowledge. Both teacher and student models are mapped onto this refined matrix, with the student's goal being to minimize representational discrepancies. Rigorous testing on benchmark datasets (CIFAR-100, ImageNet, and MSCOCO) attests to LumiNet's efficacy, revealing its competitive edge over leading feature-based methods. Moreover, in exploring the realm of transfer learning, we assess how effectively the student model, trained using our method, adapts to downstream tasks. Notably, when applied to Tiny ImageNet, the transferred features exhibit remarkable performance, further underscoring LumiNet's versatility and robustness in diverse settings. With LumiNet, we hope to steer the research discourse towards a renewed interest in the latent capabilities of logit-based knowledge distillation.

We present an acceleration method for sequences of large-scale linear systems, such as the ones arising from the numerical solution of time-dependent partial differential equations coupled with algebraic constraints. We discuss different approaches to leverage the subspace containing the history of solutions computed at previous time steps in order to generate a good initial guess for the iterative solver. In particular, we propose a novel combination of reduced-order projection with randomized linear algebra techniques, which drastically reduces the number of iterations needed for convergence. We analyze the accuracy of the initial guess produced by the reduced-order projection when the coefficients of the linear system depend analytically on time. Extending extrapolation results by Demanet and Townsend to a vector-valued setting, we show that the accuracy improves rapidly as the size of the history increases, a theoretical result confirmed by our numerical observations. In particular, we apply the developed method to the simulation of plasma turbulence in the boundary of a fusion device, showing that the time needed for solving the linear systems is significantly reduced.

Mathematical reasoning is a fundamental aspect of human intelligence and is applicable in various fields, including science, engineering, finance, and everyday life. The development of artificial intelligence (AI) systems capable of solving math problems and proving theorems has garnered significant interest in the fields of machine learning and natural language processing. For example, mathematics serves as a testbed for aspects of reasoning that are challenging for powerful deep learning models, driving new algorithmic and modeling advances. On the other hand, recent advances in large-scale neural language models have opened up new benchmarks and opportunities to use deep learning for mathematical reasoning. In this survey paper, we review the key tasks, datasets, and methods at the intersection of mathematical reasoning and deep learning over the past decade. We also evaluate existing benchmarks and methods, and discuss future research directions in this domain.

We introduce a multi-task setup of identifying and classifying entities, relations, and coreference clusters in scientific articles. We create SciERC, a dataset that includes annotations for all three tasks and develop a unified framework called Scientific Information Extractor (SciIE) for with shared span representations. The multi-task setup reduces cascading errors between tasks and leverages cross-sentence relations through coreference links. Experiments show that our multi-task model outperforms previous models in scientific information extraction without using any domain-specific features. We further show that the framework supports construction of a scientific knowledge graph, which we use to analyze information in scientific literature.

We propose a novel attention gate (AG) model for medical imaging that automatically learns to focus on target structures of varying shapes and sizes. Models trained with AGs implicitly learn to suppress irrelevant regions in an input image while highlighting salient features useful for a specific task. This enables us to eliminate the necessity of using explicit external tissue/organ localisation modules of cascaded convolutional neural networks (CNNs). AGs can be easily integrated into standard CNN architectures such as the U-Net model with minimal computational overhead while increasing the model sensitivity and prediction accuracy. The proposed Attention U-Net architecture is evaluated on two large CT abdominal datasets for multi-class image segmentation. Experimental results show that AGs consistently improve the prediction performance of U-Net across different datasets and training sizes while preserving computational efficiency. The code for the proposed architecture is publicly available.