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For ultra-reliable, low-latency communications (URLLC) applications such as mission-critical industrial control and extended reality (XR), it is important to ensure the communication quality of individual packets. Prior studies have considered Probabilistic Per-packet Real-time Communications (PPRC) guarantees for single-cell, single-channel networks, but they have not considered real-world complexities such as inter-cell interference in large-scale networks with multiple communication channels and heterogeneous real-time requirements. To fill the gap, we propose a real-time scheduling algorithm based on \emph{local-deadline-partition (LDP)}, and the LDP algorithm ensures PPRC guarantee for large-scale, multi-channel networks with heterogeneous real-time constraints. We also address the associated challenge of schedulability test. In particular, we propose the concept of \emph{feasible set}, identify a closed-form sufficient condition for the schedulability of PPRC traffic, and then propose an efficient distributed algorithm for the schedulability test. We numerically study the properties of the LDP algorithm and observe that it significantly improves the network capacity of URLLC, for instance, by a factor of 5-20 as compared with a typical method. Furthermore, the PPRC traffic supportable by the LDP algorithm is significantly higher than that of state-of-the-art comparison schemes. This demonstrates the potential of fine-grained scheduling algorithms for URLLC wireless systems regarding interference scenarios.

The problem Power Dominating Set (PDS) is motivated by the placement of phasor measurement units to monitor electrical networks. It asks for a minimum set of vertices in a graph that observes all remaining vertices by exhaustively applying two observation rules. Our contribution is twofold. First, we determine the parameterized complexity of PDS by proving it is $W[P]$-complete when parameterized with respect to the solution size. We note that it was only known to be $W[2]$-hard before. Our second and main contribution is a new algorithm for PDS that efficiently solves practical instances. Our algorithm consists of two complementary parts. The first is a set of reduction rules for PDS that can also be used in conjunction with previously existing algorithms. The second is an algorithm for solving the remaining kernel based on the implicit hitting set approach. Our evaluation on a set of power grid instances from the literature shows that our solver outperforms previous state-of-the-art solvers for PDS by more than one order of magnitude on average. Furthermore, our algorithm can solve previously unsolved instances of continental scale within a few minutes.

As the saying goes, "seeing is believing". However, with the development of digital face editing tools, we can no longer trust what we can see. Although face forgery detection has made promising progress, most current methods are designed manually by human experts, which is labor-consuming. In this paper, we develop an end-to-end framework based on neural architecture search (NAS) for deepfake detection, which can automatically design network architectures without human intervention. First, a forgery-oriented search space is created to choose appropriate operations for this task. Second, we propose a novel performance estimation metric, which guides the search process to select more general models. The cross-dataset search is also considered to develop more general architectures. Eventually, we connect the cells in a cascaded pyramid way for final forgery classification. Compared with state-of-the-art networks artificially designed, our method achieves competitive performance in both in-dataset and cross-dataset scenarios.

We present an analysis of large-scale load balancing systems, where the processing time distribution of tasks depends on both the task and server types. Our study focuses on the asymptotic regime, where the number of servers and task types tend to infinity in proportion. In heterogeneous environments, commonly used load balancing policies such as Join Fastest Idle Queue and Join Fastest Shortest Queue exhibit poor performance and even shrink the stability region. Interestingly, prior to this work, finding a scalable policy with a provable performance guarantee in this setup remained an open question. To address this gap, we propose and analyze two asymptotically delay-optimal dynamic load balancing policies. The first policy efficiently reserves the processing capacity of each server for ``good" tasks and routes tasks using the vanilla Join Idle Queue policy. The second policy, called the speed-priority policy, significantly increases the likelihood of assigning tasks to the respective ``good" servers capable of processing them at high speeds. By leveraging a framework inspired by the graphon literature and employing the mean-field method and stochastic coupling arguments, we demonstrate that both policies achieve asymptotic zero queuing. Specifically, as the system scales, the probability of a typical task being assigned to an idle server approaches 1.

Diffusion models, which convert noise into new data instances by learning to reverse a Markov diffusion process, have become a cornerstone in contemporary generative modeling. While their practical power has now been widely recognized, the theoretical underpinnings remain far from mature. In this work, we develop a suite of non-asymptotic theory towards understanding the data generation process of diffusion models in discrete time, assuming access to reliable estimates of the (Stein) score functions. For a popular deterministic sampler (based on the probability flow ODE), we establish a convergence rate proportional to $1/T$ (with $T$ the total number of steps), improving upon past results; for another mainstream stochastic sampler (i.e., a type of the denoising diffusion probabilistic model (DDPM)), we derive a convergence rate proportional to $1/\sqrt{T}$, matching the state-of-the-art theory. Our theory imposes only minimal assumptions on the target data distribution (e.g., no smoothness assumption is imposed), and is developed based on an elementary yet versatile non-asymptotic approach without resorting to toolboxes for SDEs and ODEs. Further, we design two accelerated variants, improving the convergence to $1/T^2$ for the ODE-based sampler and $1/T$ for the DDPM-type sampler, which might be of independent theoretical and empirical interest.

In many applications, the labeled data at the learner's disposal is subject to privacy constraints and is relatively limited. To derive a more accurate predictor for the target domain, it is often beneficial to leverage publicly available labeled data from an alternative domain, somewhat close to the target domain. This is the modern problem of supervised domain adaptation from a public source to a private target domain. We present two $(\epsilon, \delta)$-differentially private adaptation algorithms for supervised adaptation, for which we make use of a general optimization problem, recently shown to benefit from favorable theoretical learning guarantees. Our first algorithm is designed for regression with linear predictors and shown to solve a convex optimization problem. Our second algorithm is a more general solution for loss functions that may be non-convex but Lipschitz and smooth. While our main objective is a theoretical analysis, we also report the results of several experiments first demonstrating that the non-private versions of our algorithms outperform adaptation baselines and next showing that, for larger values of the target sample size or $\epsilon$, the performance of our private algorithms remains close to that of the non-private formulation.

We study the Electrical Impedance Tomography Bayesian inverse problem for recovering the conductivity given noisy measurements of the voltage on some boundary surface electrodes. The uncertain conductivity depends linearly on a countable number of uniformly distributed random parameters in a compact interval, with the coefficient functions in the linear expansion decaying at an algebraic rate. We analyze the surrogate Markov Chain Monte Carlo (MCMC) approach for sampling the posterior probability measure, where the multivariate sparse adaptive interpolation, with interpolating points chosen according to a lower index set, is used for approximating the forward map. The forward equation is approximated once before running the MCMC for all the realizations, using interpolation on the finite element (FE) approximation at the parametric interpolating points. When evaluation of the solution is needed for a realization, we only need to compute a polynomial, thus cutting drastically the computation time. We contribute a rigorous error estimate for the MCMC convergence. In particular, we show that there is a nested sequence of interpolating lower index sets for which we can derive an interpolation error estimate in terms of the cardinality of these sets, uniformly for all the parameter realizations. An explicit convergence rate for the MCMC sampling of the posterior expectation of the conductivity is rigorously derived, in terms of the interpolating point number, the accuracy of the FE approximation of the forward equation, and the MCMC sample number. We perform numerical experiments using an adaptive greedy approach to construct the sets of interpolation points. We show the benefits of this approach over the simple MCMC where the forward equation is repeatedly solved for all the samples and the non-adaptive surrogate MCMC with an isotropic index set treating all the random parameters equally.

Sampling methods (e.g., node-wise, layer-wise, or subgraph) has become an indispensable strategy to speed up training large-scale Graph Neural Networks (GNNs). However, existing sampling methods are mostly based on the graph structural information and ignore the dynamicity of optimization, which leads to high variance in estimating the stochastic gradients. The high variance issue can be very pronounced in extremely large graphs, where it results in slow convergence and poor generalization. In this paper, we theoretically analyze the variance of sampling methods and show that, due to the composite structure of empirical risk, the variance of any sampling method can be decomposed into \textit{embedding approximation variance} in the forward stage and \textit{stochastic gradient variance} in the backward stage that necessities mitigating both types of variance to obtain faster convergence rate. We propose a decoupled variance reduction strategy that employs (approximate) gradient information to adaptively sample nodes with minimal variance, and explicitly reduces the variance introduced by embedding approximation. We show theoretically and empirically that the proposed method, even with smaller mini-batch sizes, enjoys a faster convergence rate and entails a better generalization compared to the existing methods.

Graph convolution networks (GCN) are increasingly popular in many applications, yet remain notoriously hard to train over large graph datasets. They need to compute node representations recursively from their neighbors. Current GCN training algorithms suffer from either high computational costs that grow exponentially with the number of layers, or high memory usage for loading the entire graph and node embeddings. In this paper, we propose a novel efficient layer-wise training framework for GCN (L-GCN), that disentangles feature aggregation and feature transformation during training, hence greatly reducing time and memory complexities. We present theoretical analysis for L-GCN under the graph isomorphism framework, that L-GCN leads to as powerful GCNs as the more costly conventional training algorithm does, under mild conditions. We further propose L^2-GCN, which learns a controller for each layer that can automatically adjust the training epochs per layer in L-GCN. Experiments show that L-GCN is faster than state-of-the-arts by at least an order of magnitude, with a consistent of memory usage not dependent on dataset size, while maintaining comparable prediction performance. With the learned controller, L^2-GCN can further cut the training time in half. Our codes are available at //github.com/Shen-Lab/L2-GCN.

Over the past few years, we have seen fundamental breakthroughs in core problems in machine learning, largely driven by advances in deep neural networks. At the same time, the amount of data collected in a wide array of scientific domains is dramatically increasing in both size and complexity. Taken together, this suggests many exciting opportunities for deep learning applications in scientific settings. But a significant challenge to this is simply knowing where to start. The sheer breadth and diversity of different deep learning techniques makes it difficult to determine what scientific problems might be most amenable to these methods, or which specific combination of methods might offer the most promising first approach. In this survey, we focus on addressing this central issue, providing an overview of many widely used deep learning models, spanning visual, sequential and graph structured data, associated tasks and different training methods, along with techniques to use deep learning with less data and better interpret these complex models --- two central considerations for many scientific use cases. We also include overviews of the full design process, implementation tips, and links to a plethora of tutorials, research summaries and open-sourced deep learning pipelines and pretrained models, developed by the community. We hope that this survey will help accelerate the use of deep learning across different scientific domains.