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In this paper we propose a multiscale method for the acoustic wave equation in highly oscillatory media. We use a higher-order extension of the localized orthogonal decomposition method combined with a higher-order time stepping scheme and present rigorous a-priori error estimates in the energy-induced norm. We find that in the very general setting without additional assumptions on the coefficient beyond boundedness, arbitrary orders of convergence cannot be expected but that increasing the polynomial degree may still considerably reduce the size of the error. Under additional regularity assumptions, higher orders can be obtained as well. Numerical examples are presented that confirm the theoretical results.

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iOS 8 提供的應用間和應用跟系統的功能交互特性。
  • Today (iOS and OS X): widgets for the Today view of Notification Center
  • Share (iOS and OS X): post content to web services or share content with others
  • Actions (iOS and OS X): app extensions to view or manipulate inside another app
  • Photo Editing (iOS): edit a photo or video in Apple's Photos app with extensions from a third-party apps
  • Finder Sync (OS X): remote file storage in the Finder with support for Finder content annotation
  • Storage Provider (iOS): an interface between files inside an app and other apps on a user's device
  • Custom Keyboard (iOS): system-wide alternative keyboards

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This paper tackles the problem of motion deblurring of dynamic scenes. Although end-to-end fully convolutional designs have recently advanced the state-of-the-art in non-uniform motion deblurring, their performance-complexity trade-off is still sub-optimal. Most existing approaches achieve a large receptive field by increasing the number of generic convolution layers and kernel size. In this work, we propose a pixel adaptive and feature attentive design for handling large blur variations across different spatial locations and process each test image adaptively. We design a content-aware global-local filtering module that significantly improves performance by considering not only global dependencies but also by dynamically exploiting neighboring pixel information. We further introduce a pixel-adaptive non-uniform sampling strategy that implicitly discovers the difficult-to-restore regions present in the image and, in turn, performs fine-grained refinement in a progressive manner. Extensive qualitative and quantitative comparisons with prior art on deblurring benchmarks demonstrate that our approach performs favorably against the state-of-the-art deblurring algorithms.

Fourier analysis has been an instrumental tool in the development of signal processing. This leads us to wonder whether this framework could similarly benefit generative modelling. In this paper, we explore this question through the scope of time series diffusion models. More specifically, we analyze whether representing time series in the frequency domain is a useful inductive bias for score-based diffusion models. By starting from the canonical SDE formulation of diffusion in the time domain, we show that a dual diffusion process occurs in the frequency domain with an important nuance: Brownian motions are replaced by what we call mirrored Brownian motions, characterized by mirror symmetries among their components. Building on this insight, we show how to adapt the denoising score matching approach to implement diffusion models in the frequency domain. This results in frequency diffusion models, which we compare to canonical time diffusion models. Our empirical evaluation on real-world datasets, covering various domains like healthcare and finance, shows that frequency diffusion models better capture the training distribution than time diffusion models. We explain this observation by showing that time series from these datasets tend to be more localized in the frequency domain than in the time domain, which makes them easier to model in the former case. All our observations point towards impactful synergies between Fourier analysis and diffusion models.

In this paper, we show that a simple self-supervised pre-trained audio model can achieve comparable inference efficiency to more complicated pre-trained models with speech transformer encoders. These speech transformers rely on mixing convolutional modules with self-attention modules. They achieve state-of-the-art performance on ASR with top efficiency. We first show that employing these speech transformers as an encoder significantly improves the efficiency of pre-trained audio models as well. However, our study shows that we can achieve comparable efficiency with advanced self-attention solely. We demonstrate that this simpler approach is particularly beneficial with a low-bit weight quantization technique of a neural network to improve efficiency. We hypothesize that it prevents propagating the errors between different quantized modules compared to recent speech transformers mixing quantized convolution and the quantized self-attention modules.

In this paper, we first present the character texture generation system \textit{Minecraft-ify}, specified to Minecraft video game toward in-game application. Ours can generate face-focused image for texture mapping tailored to 3D virtual character having cube manifold. While existing projects or works only generate texture, proposed system can inverse the user-provided real image, or generate average/random appearance from learned distribution. Moreover, it can be manipulated with text-guidance using StyleGAN and StyleCLIP. These features provide a more extended user experience with enlarged freedom as a user-friendly AI-tool. Project page can be found at //gh-bumsookim.github.io/Minecraft-ify/

In this paper, we present a distribution-dependent PAC-Chernoff bound that is perfectly tight for interpolators even under overparametrized model classes. This bound relies on basic principles of Large Deviation Theory and naturally provides a characterization of the smoothness of a model described as a simple real-valued function. Based on this distribution-dependent bound and the novel definition of smoothness, we propose an unifying theoretical explanation of why some interpolators generalize remarkably well while others not. And why a wide range of modern learning techniques (i.e., $\ell_2$-norm, distance-from-initialization, input-gradient and variance regularization together with data augmentation, invariant architectures, and overparameterization) are able to find them. The emergent conclusion is that all these methods provide complimentary procedures that bias the optimizer to smoother interpolators, which, according to this theoretical analysis, are the ones with better generalization error. One of the main insights of this study is that distribution-dependent bounds serve as a powerful tool better understand the complex dynamics behind the generalization capabilities of highly-overparameterized interpolators.

In this paper, we introduce a new flow-based method for global optimization of Lipschitz functions, called Stein Boltzmann Sampling (SBS). Our method samples from the Boltzmann distribution that becomes asymptotically uniform over the set of the minimizers of the function to be optimized. Candidate solutions are sampled via the \emph{Stein Variational Gradient Descent} algorithm. We prove the asymptotic convergence of our method, introduce two SBS variants, and provide a detailed comparison with several state-of-the-art global optimization algorithms on various benchmark functions. The design of our method, the theoretical results, and our experiments, suggest that SBS is particularly well-suited to be used as a continuation of efficient global optimization methods as it can produce better solutions while making a good use of the budget.

In this paper, we prove the first Bayesian regret bounds for Thompson Sampling in reinforcement learning in a multitude of settings. We simplify the learning problem using a discrete set of surrogate environments, and present a refined analysis of the information ratio using posterior consistency. This leads to an upper bound of order $\widetilde{O}(H\sqrt{d_{l_1}T})$ in the time inhomogeneous reinforcement learning problem where $H$ is the episode length and $d_{l_1}$ is the Kolmogorov $l_1-$dimension of the space of environments. We then find concrete bounds of $d_{l_1}$ in a variety of settings, such as tabular, linear and finite mixtures, and discuss how how our results are either the first of their kind or improve the state-of-the-art.

In this paper, we introduce a two-level attention schema, Poolingformer, for long document modeling. Its first level uses a smaller sliding window pattern to aggregate information from neighbors. Its second level employs a larger window to increase receptive fields with pooling attention to reduce both computational cost and memory consumption. We first evaluate Poolingformer on two long sequence QA tasks: the monolingual NQ and the multilingual TyDi QA. Experimental results show that Poolingformer sits atop three official leaderboards measured by F1, outperforming previous state-of-the-art models by 1.9 points (79.8 vs. 77.9) on NQ long answer, 1.9 points (79.5 vs. 77.6) on TyDi QA passage answer, and 1.6 points (67.6 vs. 66.0) on TyDi QA minimal answer. We further evaluate Poolingformer on a long sequence summarization task. Experimental results on the arXiv benchmark continue to demonstrate its superior performance.

In this paper, we propose a novel Feature Decomposition and Reconstruction Learning (FDRL) method for effective facial expression recognition. We view the expression information as the combination of the shared information (expression similarities) across different expressions and the unique information (expression-specific variations) for each expression. More specifically, FDRL mainly consists of two crucial networks: a Feature Decomposition Network (FDN) and a Feature Reconstruction Network (FRN). In particular, FDN first decomposes the basic features extracted from a backbone network into a set of facial action-aware latent features to model expression similarities. Then, FRN captures the intra-feature and inter-feature relationships for latent features to characterize expression-specific variations, and reconstructs the expression feature. To this end, two modules including an intra-feature relation modeling module and an inter-feature relation modeling module are developed in FRN. Experimental results on both the in-the-lab databases (including CK+, MMI, and Oulu-CASIA) and the in-the-wild databases (including RAF-DB and SFEW) show that the proposed FDRL method consistently achieves higher recognition accuracy than several state-of-the-art methods. This clearly highlights the benefit of feature decomposition and reconstruction for classifying expressions.

In this paper, we proposed to apply meta learning approach for low-resource automatic speech recognition (ASR). We formulated ASR for different languages as different tasks, and meta-learned the initialization parameters from many pretraining languages to achieve fast adaptation on unseen target language, via recently proposed model-agnostic meta learning algorithm (MAML). We evaluated the proposed approach using six languages as pretraining tasks and four languages as target tasks. Preliminary results showed that the proposed method, MetaASR, significantly outperforms the state-of-the-art multitask pretraining approach on all target languages with different combinations of pretraining languages. In addition, since MAML's model-agnostic property, this paper also opens new research direction of applying meta learning to more speech-related applications.

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