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In this work, we propose fully nonconforming, locally exactly divergence-free discretizations based on lowest order Crouziex-Raviart finite element and piecewise constant spaces to study the optimal control of stationary double diffusion model presented in [B\"urger, M\'endez, Ruiz-Baier, SINUM (2019), 57:1318-1343]. The well-posedness of the discrete uncontrolled state and adjoint equations are discussed using discrete lifting and fixed point arguments, and convergence results are derived rigorously under minimal regularity. Building upon our recent work [Tushar, Khan, Mohan arXiv (2023)], we prove the local optimality of a reference control using second-order sufficient optimality condition for the control problem, and use it along with an optimize-then-discretize approach to prove optimal order a priori error estimates for the control, state and adjoint variables upto the regularity of the solution. The optimal control is computed using a primal-dual active set strategy as a semi-smooth Newton method and computational tests validate the predicted error decay rates and illustrate the proposed scheme's applicability to optimal control of thermohaline circulation problems.

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Decision-making, a complicated task requiring various types of abilities, presents an excellent framework for assessing Large Language Models (LLMs). Our research investigates LLMs' decision-making capabilities through the lens of a well-established field, Game Theory. We focus specifically on games that support the participation of more than two agents simultaneously. Subsequently, we introduce our framework, GAMA-Bench, including eight classical multi-agent games. We design a scoring scheme to assess a model's performance in these games quantitatively. Through GAMA-Bench, we investigate LLMs' robustness, generalizability, and enhancement strategies. Results reveal that while GPT-3.5 shows satisfying robustness, its generalizability is relatively limited. However, its performance can be improved through approaches such as Chain-of-Thought. Additionally, we conduct evaluations across various LLMs and find that GPT-4 outperforms other models on GAMA-Bench, achieving a score of 60.5. Moreover, Gemini-1.0-Pro and GPT-3.5 (0613, 1106, 0125) demonstrate similar intelligence on GAMA-Bench. The code and experimental results are made publicly available via //github.com/CUHK-ARISE/GAMABench.

Multi-modal foundation models such as CLIP have showcased impressive zero-shot capabilities. However, their applicability in resource-constrained environments is limited due to their large number of parameters and high inference time. While existing approaches have scaled down the entire CLIP architecture, we focus on training smaller variants of the image encoder, which suffices for efficient zero-shot classification. The use of synthetic data has shown promise in distilling representations from larger teachers, resulting in strong few-shot and linear probe performance. However, we find that this approach surprisingly fails in true zero-shot settings when using contrastive losses. We identify the exploitation of spurious features as being responsible for poor generalization between synthetic and real data. However, by using the image feature-based L2 distillation loss, we mitigate these problems and train students that achieve zero-shot performance which on four domain-specific datasets is on-par with a ViT-B/32 teacher model trained on DataCompXL, while featuring up to 92% fewer parameters.

Procedural noise is a fundamental component of computer graphics pipelines, offering a flexible way to generate textures that exhibit "natural" random variation. Many different types of noise exist, each produced by a separate algorithm. In this paper, we present a single generative model which can learn to generate multiple types of noise as well as blend between them. In addition, it is capable of producing spatially-varying noise blends despite not having access to such data for training. These features are enabled by training a denoising diffusion model using a novel combination of data augmentation and network conditioning techniques. Like procedural noise generators, the model's behavior is controllable via interpretable parameters and a source of randomness. We use our model to produce a variety of visually compelling noise textures. We also present an application of our model to improving inverse procedural material design; using our model in place of fixed-type noise nodes in a procedural material graph results in higher-fidelity material reconstructions without needing to know the type of noise in advance.

FPGAs are rarely mentioned when discussing the implementation of large machine learning applications, such as Large Language Models (LLMs), in the data center. There has been much evidence showing that single FPGAs can be competitive with GPUs in performance for some computations, especially for low latency, and often much more efficient when power is considered. This suggests that there is merit to exploring the use of multiple FPGAs for large machine learning applications. The challenge with using multiple FPGAs is that there is no commonly-accepted flow for developing and deploying multi-FPGA applications, i.e., there are no tools to describe a large application, map it to multiple FPGAs and then deploy the application on a multi-FPGA platform. In this paper, we explore the feasibility of implementing large transformers using multiple FPGAs by developing a scalable multi-FPGA platform and some tools to map large applications to the platform. We validate our approach by designing an efficient multi-FPGA version of the I-BERT transformer and implement one encoder using six FPGAs as a working proof-of-concept to show that our platform and tools work. Based on our proof-of-concept prototype and the estimations of performance using the latest FPGAs compared to GPUs, we conclude that there can be a place for FPGAs in the world of large machine learning applications. We demonstrate a promising first step that shows that with the right infrastructure and tools it is reasonable to continue to explore the possible benefits of using FPGAs for applications such as LLMs.

The rapidly evolving multimodal Large Language Models (LLMs) urgently require new benchmarks to uniformly evaluate their performance on understanding and textually describing music. However, due to semantic gaps between Music Information Retrieval (MIR) algorithms and human understanding, discrepancies between professionals and the public, and low precision of annotations, existing music description datasets cannot serve as benchmarks. To this end, we present MuChin, the first open-source music description benchmark in Chinese colloquial language, designed to evaluate the performance of multimodal LLMs in understanding and describing music. We established the Caichong Music Annotation Platform (CaiMAP) that employs an innovative multi-person, multi-stage assurance method, and recruited both amateurs and professionals to ensure the precision of annotations and alignment with popular semantics. Utilizing this method, we built a dataset with multi-dimensional, high-precision music annotations, the Caichong Music Dataset (CaiMD), and carefully selected 1,000 high-quality entries to serve as the test set for MuChin. Based on MuChin, we analyzed the discrepancies between professionals and amateurs in terms of music description, and empirically demonstrated the effectiveness of annotated data for fine-tuning LLMs. Ultimately, we employed MuChin to evaluate existing music understanding models on their ability to provide colloquial descriptions of music. All data related to the benchmark, along with the scoring code and detailed appendices, have been open-sourced (//github.com/CarlWangChina/MuChin/).

Our study provides evidence that CNNs struggle to effectively extract orientation features. We show that the use of Complex Structure Tensor, which contains compact orientation features with certainties, as input to CNNs consistently improves identification accuracy compared to using grayscale inputs alone. Experiments also demonstrated that our inputs, which were provided by mini complex conv-nets, combined with reduced CNN sizes, outperformed full-fledged, prevailing CNN architectures. This suggests that the upfront use of orientation features in CNNs, a strategy seen in mammalian vision, not only mitigates their limitations but also enhances their explainability and relevance to thin-clients. Experiments were done on publicly available data sets comprising periocular images for biometric identification and verification (Close and Open World) using 6 State of the Art CNN architectures. We reduced SOA Equal Error Rate (EER) on the PolyU dataset by 5-26% depending on data and scenario.

In this paper, we establish the second-order randomized identification capacity (RID capacity) of the Additive White Gaussian Noise Channel (AWGNC). On the one hand, we obtain a refined version of Hayashi's theorem to prove the achievability part. On the other, we investigate the relationship between identification and channel resolvability, then we propose a finer quantization method to prove the converse part. Consequently, the second-order RID capacity of the AWGNC has the same form as the second-order transmission capacity. The only difference is that the maximum number of messages in RID scales double exponentially in the blocklength.

Large Language Models (LLMs) have rapidly become important tools in Biomedical and Health Informatics (BHI), enabling new ways to analyze data, treat patients, and conduct research. This bibliometric review aims to provide a panoramic view of how LLMs have been used in BHI by examining research articles and collaboration networks from 2022 to 2023. It further explores how LLMs can improve Natural Language Processing (NLP) applications in various BHI areas like medical diagnosis, patient engagement, electronic health record management, and personalized medicine. To do this, our bibliometric review identifies key trends, maps out research networks, and highlights major developments in this fast-moving field. Lastly, it discusses the ethical concerns and practical challenges of using LLMs in BHI, such as data privacy and reliable medical recommendations. Looking ahead, we consider how LLMs could further transform biomedical research as well as healthcare delivery and patient outcomes. This bibliometric review serves as a resource for stakeholders in healthcare, including researchers, clinicians, and policymakers, to understand the current state and future potential of LLMs in BHI.

Graph Neural Networks (GNNs) have gained momentum in graph representation learning and boosted the state of the art in a variety of areas, such as data mining (\emph{e.g.,} social network analysis and recommender systems), computer vision (\emph{e.g.,} object detection and point cloud learning), and natural language processing (\emph{e.g.,} relation extraction and sequence learning), to name a few. With the emergence of Transformers in natural language processing and computer vision, graph Transformers embed a graph structure into the Transformer architecture to overcome the limitations of local neighborhood aggregation while avoiding strict structural inductive biases. In this paper, we present a comprehensive review of GNNs and graph Transformers in computer vision from a task-oriented perspective. Specifically, we divide their applications in computer vision into five categories according to the modality of input data, \emph{i.e.,} 2D natural images, videos, 3D data, vision + language, and medical images. In each category, we further divide the applications according to a set of vision tasks. Such a task-oriented taxonomy allows us to examine how each task is tackled by different GNN-based approaches and how well these approaches perform. Based on the necessary preliminaries, we provide the definitions and challenges of the tasks, in-depth coverage of the representative approaches, as well as discussions regarding insights, limitations, and future directions.

Machine learning techniques have deeply rooted in our everyday life. However, since it is knowledge- and labor-intensive to pursue good learning performance, human experts are heavily involved in every aspect of machine learning. In order to make machine learning techniques easier to apply and reduce the demand for experienced human experts, automated machine learning (AutoML) has emerged as a hot topic with both industrial and academic interest. In this paper, we provide an up to date survey on AutoML. First, we introduce and define the AutoML problem, with inspiration from both realms of automation and machine learning. Then, we propose a general AutoML framework that not only covers most existing approaches to date but also can guide the design for new methods. Subsequently, we categorize and review the existing works from two aspects, i.e., the problem setup and the employed techniques. Finally, we provide a detailed analysis of AutoML approaches and explain the reasons underneath their successful applications. We hope this survey can serve as not only an insightful guideline for AutoML beginners but also an inspiration for future research.

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