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We introduce a Robust version of the Variational Physics-Informed Neural Networks method (RVPINNs). As in VPINNs, we define the quadratic loss functional in terms of a Petrov-Galerkin-type variational formulation of the PDE problem: the trial space is a (Deep) Neural Network (DNN) manifold, while the test space is a finite-dimensional vector space. Whereas the VPINN's loss depends upon the selected basis functions of a given test space, herein, we minimize a loss based on the discrete dual norm of the residual. The main advantage of such a loss definition is that it provides a reliable and efficient estimator of the true error in the energy norm under the assumption of the existence of a local Fortin operator. We test the performance and robustness of our algorithm in several advection-diffusion problems. These numerical results perfectly align with our theoretical findings, showing that our estimates are sharp.

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The rise of Large Language Models (LLMs) has affected various disciplines that got beyond mere text generation. Going beyond their textual nature, this project proposal aims to investigate the interaction between LLMs and non-verbal communication, specifically focusing on gestures. The proposal sets out a plan to examine the proficiency of LLMs in deciphering both explicit and implicit non-verbal cues within textual prompts and their ability to associate these gestures with various contextual factors. The research proposes to test established psycholinguistic study designs to construct a comprehensive dataset that pairs textual prompts with detailed gesture descriptions, encompassing diverse regional variations, and semantic labels. To assess LLMs' comprehension of gestures, experiments are planned, evaluating their ability to simulate human behaviour in order to replicate psycholinguistic experiments. These experiments consider cultural dimensions and measure the agreement between LLM-identified gestures and the dataset, shedding light on the models' contextual interpretation of non-verbal cues (e.g. gestures).

Face Recognition (FR) systems can suffer from physical (i.e., print photo) and digital (i.e., DeepFake) attacks. However, previous related work rarely considers both situations at the same time. This implies the deployment of multiple models and thus more computational burden. The main reasons for this lack of an integrated model are caused by two factors: (1) The lack of a dataset including both physical and digital attacks with ID consistency which means the same ID covers the real face and all attack types; (2) Given the large intra-class variance between these two attacks, it is difficult to learn a compact feature space to detect both attacks simultaneously. To address these issues, we collect a Unified physical-digital Attack dataset, called UniAttackData. The dataset consists of $1,800$ participations of 2 and 12 physical and digital attacks, respectively, resulting in a total of 29,706 videos. Then, we propose a Unified Attack Detection framework based on Vision-Language Models (VLMs), namely UniAttackDetection, which includes three main modules: the Teacher-Student Prompts (TSP) module, focused on acquiring unified and specific knowledge respectively; the Unified Knowledge Mining (UKM) module, designed to capture a comprehensive feature space; and the Sample-Level Prompt Interaction (SLPI) module, aimed at grasping sample-level semantics. These three modules seamlessly form a robust unified attack detection framework. Extensive experiments on UniAttackData and three other datasets demonstrate the superiority of our approach for unified face attack detection.

This paper presents new solutions for Private Information Retrieval (PIR) with side information. This problem is motivated by PIR settings in which a client has side information about the data held by the servers and would like to leverage this information in order to improve the download rate. The problem of PIR with side information has been the subject of several recent studies that presented achievability schemes as well as converses for both multi-server and single-server settings. However, the solutions for the multi-server settings adapted from the solutions for the single-server setting in a rather straightforward manner, relying on the concept of super-messages. Such solutions require an exponential degree of sub-packetization (in terms of the number of messages). This paper makes the following contributions. First, we revisit the PIR problem with side information and present a new approach to leverage side information in the context of PIR. The key idea of our approach is a randomized algorithm to determine the linear combinations of the sub-packets that need to be recovered from each server. In addition, our approach takes advantage of the fact that the identity of the side information messages does not need to be kept private, and, as a result, the information retrieval scheme does not need to be symmetric. Second, we present schemes for PIR with side information that achieve a higher rate than previously proposed solutions and require a significantly lower degree of sub-packetization (linear in the number of servers). Our scheme not only achieves the highest known download rate for the problem at hand but also invalidates a previously claimed converse bound on the maximum achievable download rate.

We propose a novel technique to enhance Knowledge Graph Reasoning by combining Graph Convolution Neural Network (GCN) with the Attention Mechanism. This approach utilizes the Attention Mechanism to examine the relationships between entities and their neighboring nodes, which helps to develop detailed feature vectors for each entity. The GCN uses shared parameters to effectively represent the characteristics of adjacent entities. We first learn the similarity of entities for node representation learning. By integrating the attributes of the entities and their interactions, this method generates extensive implicit feature vectors for each entity, improving performance in tasks including entity classification and link prediction, outperforming traditional neural network models. To conclude, this work provides crucial methodological support for a range of applications, such as search engines, question-answering systems, recommendation systems, and data integration tasks.

Modern SAT or QBF solvers are expected to produce correctness certificates. However, certificates have worst-case exponential size (unless $\textsf{NP}=\textsf{coNP}$), and at recent SAT competitions the largest certificates of unsatisfiability are starting to reach terabyte size. Recently, Couillard, Czerner, Esparza, and Majumdar have suggested to replace certificates with interactive proof systems based on the $\textsf{IP}=\textsf{PSPACE}$ theorem. They have presented an interactive protocol between a prover and a verifier for an extension of QBF. The overall running time of the protocol is linear in the time needed by a standard BDD-based algorithm, and the time invested by the verifier is polynomial in the size of the formula. (So, in particular, the verifier never has to read or process exponentially long certificates). We call such an interactive protocol competitive with the BDD algorithm for solving QBF. While BDD-algorithms are state-of-the-art for certain classes of QBF instances, no modern (UN)SAT solver is based on BDDs. For this reason, we initiate the study of interactive certification for more practical SAT algorithms. In particular, we address the question whether interactive protocols can be competitive with some variant of resolution. We present two contributions. First, we prove a theorem that reduces the problem of finding competitive interactive protocols to finding an arithmetisation of formulas satisfying certain commutativity properties. (Arithmetisation is the fundamental technique underlying the $\textsf{IP}=\textsf{PSPACE}$ theorem.) Then, we apply the theorem to give the first interactive protocol for the Davis-Putnam resolution procedure.

This paper presents the Holistic and Multi-Granular Surgical Scene Understanding of Prostatectomies (GraSP) dataset, a curated benchmark that models surgical scene understanding as a hierarchy of complementary tasks with varying levels of granularity. Our approach enables a multi-level comprehension of surgical activities, encompassing long-term tasks such as surgical phases and steps recognition and short-term tasks including surgical instrument segmentation and atomic visual actions detection. To exploit our proposed benchmark, we introduce the Transformers for Actions, Phases, Steps, and Instrument Segmentation (TAPIS) model, a general architecture that combines a global video feature extractor with localized region proposals from an instrument segmentation model to tackle the multi-granularity of our benchmark. Through extensive experimentation, we demonstrate the impact of including segmentation annotations in short-term recognition tasks, highlight the varying granularity requirements of each task, and establish TAPIS's superiority over previously proposed baselines and conventional CNN-based models. Additionally, we validate the robustness of our method across multiple public benchmarks, confirming the reliability and applicability of our dataset. This work represents a significant step forward in Endoscopic Vision, offering a novel and comprehensive framework for future research towards a holistic understanding of surgical procedures.

Understanding the decision-making process of Graph Neural Networks (GNNs) is crucial to their interpretability. Most existing methods for explaining GNNs typically rely on training auxiliary models, resulting in the explanations remain black-boxed. This paper introduces Graph Output Attribution (GOAt), a novel method to attribute graph outputs to input graph features, creating GNN explanations that are faithful, discriminative, as well as stable across similar samples. By expanding the GNN as a sum of scalar products involving node features, edge features and activation patterns, we propose an efficient analytical method to compute contribution of each node or edge feature to each scalar product and aggregate the contributions from all scalar products in the expansion form to derive the importance of each node and edge. Through extensive experiments on synthetic and real-world data, we show that our method not only outperforms various state-ofthe-art GNN explainers in terms of the commonly used fidelity metric, but also exhibits stronger discriminability, and stability by a remarkable margin.

With the bomb ignited by ChatGPT, Transformer-based Large Language Models (LLMs) have paved a revolutionary path toward Artificial General Intelligence (AGI) and have been applied in diverse areas as knowledge bases, human interfaces, and dynamic agents. However, a prevailing limitation exists: many current LLMs, constrained by resources, are primarily pre-trained on shorter texts, rendering them less effective for longer-context prompts, commonly encountered in real-world settings. In this paper, we present a comprehensive survey focusing on the advancement of model architecture in Transformer-based LLMs to optimize long-context capabilities across all stages from pre-training to inference. We firstly delineate and analyze the problems of handling long-context input and output with the current Transformer-based models. Then, we mainly offer a holistic taxonomy to navigate the landscape of Transformer upgrades on architecture to solve these problems. Afterward, we provide the investigation on wildly used evaluation necessities tailored for long-context LLMs, including datasets, metrics, and baseline models, as well as some amazing optimization toolkits like libraries, systems, and compilers to augment LLMs' efficiency and efficacy across different stages. Finally, we further discuss the predominant challenges and potential avenues for future research in this domain. Additionally, we have established a repository where we curate relevant literature with real-time updates at //github.com/Strivin0311/long-llms-learning.

Despite the recent progress in Graph Neural Networks (GNNs), it remains challenging to explain the predictions made by GNNs. Existing explanation methods mainly focus on post-hoc explanations where another explanatory model is employed to provide explanations for a trained GNN. The fact that post-hoc methods fail to reveal the original reasoning process of GNNs raises the need of building GNNs with built-in interpretability. In this work, we propose Prototype Graph Neural Network (ProtGNN), which combines prototype learning with GNNs and provides a new perspective on the explanations of GNNs. In ProtGNN, the explanations are naturally derived from the case-based reasoning process and are actually used during classification. The prediction of ProtGNN is obtained by comparing the inputs to a few learned prototypes in the latent space. Furthermore, for better interpretability and higher efficiency, a novel conditional subgraph sampling module is incorporated to indicate which part of the input graph is most similar to each prototype in ProtGNN+. Finally, we evaluate our method on a wide range of datasets and perform concrete case studies. Extensive results show that ProtGNN and ProtGNN+ can provide inherent interpretability while achieving accuracy on par with the non-interpretable counterparts.

We propose a novel single shot object detection network named Detection with Enriched Semantics (DES). Our motivation is to enrich the semantics of object detection features within a typical deep detector, by a semantic segmentation branch and a global activation module. The segmentation branch is supervised by weak segmentation ground-truth, i.e., no extra annotation is required. In conjunction with that, we employ a global activation module which learns relationship between channels and object classes in a self-supervised manner. Comprehensive experimental results on both PASCAL VOC and MS COCO detection datasets demonstrate the effectiveness of the proposed method. In particular, with a VGG16 based DES, we achieve an mAP of 81.7 on VOC2007 test and an mAP of 32.8 on COCO test-dev with an inference speed of 31.5 milliseconds per image on a Titan Xp GPU. With a lower resolution version, we achieve an mAP of 79.7 on VOC2007 with an inference speed of 13.0 milliseconds per image.

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