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Core computations in Graph Neural Network (GNN) training and inference are often mapped to sparse matrix operations such as sparse-dense matrix multiplication (SpMM). These sparse operations are harder to optimize by manual tuning because their performance depends significantly on the sparsity of input graphs, GNN models, and computing platforms. To address this challenge, we present iSpLib, a PyTorch-based C++ library equipped with auto-tuned sparse operations. iSpLib expedites GNN training with a cache-enabled backpropagation that stores intermediate matrices in local caches. The library offers a user-friendly Python plug-in that allows users to take advantage of our optimized PyTorch operations out-of-the-box for any existing linear algebra-based PyTorch implementation of popular GNNs (Graph Convolution Network, GraphSAGE, Graph Inference Network, etc.) with only two lines of additional code. We demonstrate that iSpLib obtains up to 27x overall training speedup compared to the equivalent PyTorch 2.1.0 and PyTorch Geometric 2.4.0 implementations on the CPU. Our library is publicly available at //github.com/HipGraph/iSpLib (//doi.org/10.5281/zenodo.10806511).

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Large pre-trained models have had a significant impact on computer vision by enabling multi-modal learning, where the CLIP model has achieved impressive results in image classification, object detection, and semantic segmentation. However, the model's performance on 3D point cloud processing tasks is limited due to the domain gap between depth maps from 3D projection and training images of CLIP. This paper proposes DiffCLIP, a new pre-training framework that incorporates stable diffusion with ControlNet to minimize the domain gap in the visual branch. Additionally, a style-prompt generation module is introduced for few-shot tasks in the textual branch. Extensive experiments on the ModelNet10, ModelNet40, and ScanObjectNN datasets show that DiffCLIP has strong abilities for 3D understanding. By using stable diffusion and style-prompt generation, DiffCLIP achieves an accuracy of 43.2\% for zero-shot classification on OBJ\_BG of ScanObjectNN, which is state-of-the-art performance, and an accuracy of 80.6\% for zero-shot classification on ModelNet10, which is comparable to state-of-the-art performance.

Graph Transformers (GTs) have significantly advanced the field of graph representation learning by overcoming the limitations of message-passing graph neural networks (GNNs) and demonstrating promising performance and expressive power. However, the quadratic complexity of self-attention mechanism in GTs has limited their scalability, and previous approaches to address this issue often suffer from expressiveness degradation or lack of versatility. To address this issue, we propose AnchorGT, a novel attention architecture for GTs with global receptive field and almost linear complexity, which serves as a flexible building block to improve the scalability of a wide range of GT models. Inspired by anchor-based GNNs, we employ structurally important $k$-dominating node set as anchors and design an attention mechanism that focuses on the relationship between individual nodes and anchors, while retaining the global receptive field for all nodes. With its intuitive design, AnchorGT can easily replace the attention module in various GT models with different network architectures and structural encodings, resulting in reduced computational overhead without sacrificing performance. In addition, we theoretically prove that AnchorGT attention can be strictly more expressive than Weisfeiler-Lehman test, showing its superiority in representing graph structures. Our experiments on three state-of-the-art GT models demonstrate that their AnchorGT variants can achieve better results while being faster and significantly more memory efficient.

Traditional recommender systems such as matrix factorization methods rely on learning a shared dense embedding space to represent both items and user preferences. Sequence models such as RNN, GRUs, and, recently, Transformers have also excelled in the task of sequential recommendation. This task requires understanding the sequential structure present in users' historical interactions to predict the next item they may like. Building upon the success of Large Language Models (LLMs) in a variety of tasks, researchers have recently explored using LLMs that are pretrained on vast corpora of text for sequential recommendation. To use LLMs in sequential recommendations, both the history of user interactions and the model's prediction of the next item are expressed in text form. We propose CALRec, a two-stage LLM finetuning framework that finetunes a pretrained LLM in a two-tower fashion using a mixture of two contrastive losses and a language modeling loss: the LLM is first finetuned on a data mixture from multiple domains followed by another round of target domain finetuning. Our model significantly outperforms many state-of-the-art baselines (+37% in Recall@1 and +24% in NDCG@10) and systematic ablation studies reveal that (i) both stages of finetuning are crucial, and, when combined, we achieve improved performance, and (ii) contrastive alignment is effective among the target domains explored in our experiments.

Deterministic and nondeterministic finite automata (DFAs and NFAs) are abstract models of computation commonly taught in introductory computing theory courses. These models have important applications (such as fast regular expression matching), and are used to introduce formal language theory. Undergraduate students often struggle with understanding these models at first, due to the level of abstraction. As a result, various pedagogical tools have been developed to allow students to practice with these models. We introduce the FSM Builder, a new pedagogical tool enabling students to practice constructing DFAs and NFAs with a graphical editor, giving personalized feedback and partial credit. The algorithms used for generating these are heavily inspired by previous works. The key advantages to its competitors are greater flexibility and scalability. This is because the FSM Builder is implemented using efficient algorithms from an open source package, allowing for easy extension and question creation. We discuss the implementation of the tool, how it stands out from previous tools, and takeaways from experiences of using the tool in multiple large courses. Survey results indicate the interface and feedback provided by the tool were useful to students.

Rate split multiple access (RSMA) has been proven as an effective communication scheme for 5G and beyond, especially in vehicular scenarios. However, RSMA requires complicated iterative algorithms for proper resource allocation, which cannot fulfill the stringent latency requirement in resource constrained vehicles. Although data driven approaches can alleviate this issue, they suffer from poor generalizability and scarce training data. In this paper, we propose a fractional programming (FP) based deep unfolding (DU) approach to address resource allocation problem for a weighted sum rate optimization in RSMA. By carefully designing the penalty function, we couple the variable update with projected gradient descent algorithm (PGD). Following the structure of PGD, we embed few learnable parameters in each layer of the DU network. Through extensive simulation, we have shown that the proposed model-based neural networks has similar performance as optimal results given by traditional algorithm but with much lower computational complexity, less training data, and higher resilience to test set data and out-of-distribution (OOD) data.

We introduce the Rigged Dynamic Mode Decomposition (Rigged DMD) algorithm, which computes generalized eigenfunction decompositions of Koopman operators. By considering the evolution of observables, Koopman operators transform complex nonlinear dynamics into a linear framework suitable for spectral analysis. While powerful, traditional Dynamic Mode Decomposition (DMD) techniques often struggle with continuous spectra. Rigged DMD addresses these challenges with a data-driven methodology that approximates the Koopman operator's resolvent and its generalized eigenfunctions using snapshot data from the system's evolution. At its core, Rigged DMD builds wave-packet approximations for generalized Koopman eigenfunctions and modes by integrating Measure-Preserving Extended Dynamic Mode Decomposition with high-order kernels for smoothing. This provides a robust decomposition encompassing both discrete and continuous spectral elements. We derive explicit high-order convergence theorems for generalized eigenfunctions and spectral measures. Additionally, we propose a novel framework for constructing rigged Hilbert spaces using time-delay embedding, significantly extending the algorithm's applicability. We provide examples, including systems with a Lebesgue spectrum, integrable Hamiltonian systems, the Lorenz system, and a high-Reynolds number lid-driven flow in a two-dimensional square cavity, demonstrating Rigged DMD's convergence, efficiency, and versatility. This work paves the way for future research and applications of decompositions with continuous spectra.

Pre-trained Language Models (PLMs) which are trained on large text corpus via self-supervised learning method, have yielded promising performance on various tasks in Natural Language Processing (NLP). However, though PLMs with huge parameters can effectively possess rich knowledge learned from massive training text and benefit downstream tasks at the fine-tuning stage, they still have some limitations such as poor reasoning ability due to the lack of external knowledge. Research has been dedicated to incorporating knowledge into PLMs to tackle these issues. In this paper, we present a comprehensive review of Knowledge-Enhanced Pre-trained Language Models (KE-PLMs) to provide a clear insight into this thriving field. We introduce appropriate taxonomies respectively for Natural Language Understanding (NLU) and Natural Language Generation (NLG) to highlight these two main tasks of NLP. For NLU, we divide the types of knowledge into four categories: linguistic knowledge, text knowledge, knowledge graph (KG), and rule knowledge. The KE-PLMs for NLG are categorized into KG-based and retrieval-based methods. Finally, we point out some promising future directions of KE-PLMs.

Causal Machine Learning (CausalML) is an umbrella term for machine learning methods that formalize the data-generation process as a structural causal model (SCM). This allows one to reason about the effects of changes to this process (i.e., interventions) and what would have happened in hindsight (i.e., counterfactuals). We categorize work in \causalml into five groups according to the problems they tackle: (1) causal supervised learning, (2) causal generative modeling, (3) causal explanations, (4) causal fairness, (5) causal reinforcement learning. For each category, we systematically compare its methods and point out open problems. Further, we review modality-specific applications in computer vision, natural language processing, and graph representation learning. Finally, we provide an overview of causal benchmarks and a critical discussion of the state of this nascent field, including recommendations for future work.

The existence of representative datasets is a prerequisite of many successful artificial intelligence and machine learning models. However, the subsequent application of these models often involves scenarios that are inadequately represented in the data used for training. The reasons for this are manifold and range from time and cost constraints to ethical considerations. As a consequence, the reliable use of these models, especially in safety-critical applications, is a huge challenge. Leveraging additional, already existing sources of knowledge is key to overcome the limitations of purely data-driven approaches, and eventually to increase the generalization capability of these models. Furthermore, predictions that conform with knowledge are crucial for making trustworthy and safe decisions even in underrepresented scenarios. This work provides an overview of existing techniques and methods in the literature that combine data-based models with existing knowledge. The identified approaches are structured according to the categories integration, extraction and conformity. Special attention is given to applications in the field of autonomous driving.

Spectral clustering is a leading and popular technique in unsupervised data analysis. Two of its major limitations are scalability and generalization of the spectral embedding (i.e., out-of-sample-extension). In this paper we introduce a deep learning approach to spectral clustering that overcomes the above shortcomings. Our network, which we call SpectralNet, learns a map that embeds input data points into the eigenspace of their associated graph Laplacian matrix and subsequently clusters them. We train SpectralNet using a procedure that involves constrained stochastic optimization. Stochastic optimization allows it to scale to large datasets, while the constraints, which are implemented using a special-purpose output layer, allow us to keep the network output orthogonal. Moreover, the map learned by SpectralNet naturally generalizes the spectral embedding to unseen data points. To further improve the quality of the clustering, we replace the standard pairwise Gaussian affinities with affinities leaned from unlabeled data using a Siamese network. Additional improvement can be achieved by applying the network to code representations produced, e.g., by standard autoencoders. Our end-to-end learning procedure is fully unsupervised. In addition, we apply VC dimension theory to derive a lower bound on the size of SpectralNet. State-of-the-art clustering results are reported on the Reuters dataset. Our implementation is publicly available at //github.com/kstant0725/SpectralNet .

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