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Correlation Clustering is a classic clustering objective arising in numerous machine learning and data mining applications. Given a graph $G=(V,E)$, the goal is to partition the vertex set into clusters so as to minimize the number of edges between clusters plus the number of edges missing within clusters. The problem is APX-hard and the best known polynomial time approximation factor is 1.73 by Cohen-Addad, Lee, Li, and Newman [FOCS'23]. They use an LP with $|V|^{1/\epsilon^{\Theta(1)}}$ variables for some small $\epsilon$. However, due to the practical relevance of correlation clustering, there has also been great interest in getting more efficient sequential and parallel algorithms. The classic combinatorial \emph{pivot} algorithm of Ailon, Charikar and Newman [JACM'08] provides a 3-approximation in linear time. Like most other algorithms discussed here, this uses randomization. Recently, Behnezhad, Charikar, Ma and Tan [FOCS'22] presented a $3+\epsilon$-approximate solution for solving problem in a constant number of rounds in the Massively Parallel Computation (MPC) setting. Very recently, Cao, Huang, Su [SODA'24] provided a 2.4-approximation in a polylogarithmic number of rounds in the MPC model and in $\tilde{O} (|E|^{1.5})$ time in the classic sequential setting. They asked whether it is possible to get a better than 3-approximation in near-linear time? We resolve this problem with an efficient combinatorial algorithm providing a drastically better approximation factor. It achieves a $\sim 2-2/13 < 1.847$-approximation in sub-linear ($\tilde O(|V|)$) sequential time or in sub-linear ($\tilde O(|V|)$) space in the streaming setting. In the MPC model, we give an algorithm using only a constant number of rounds that achieves a $\sim 2-1/8 < 1.876$-approximation.

Operator learning has become a powerful tool in machine learning for modeling complex physical systems. Although Deep Operator Networks (DeepONet) show promise, they require extensive data acquisition. Physics-informed DeepONets (PI-DeepONet) mitigate data scarcity but suffer from inefficient training processes. We introduce Separable Operator Networks (SepONet), a novel framework that significantly enhances the efficiency of physics-informed operator learning. SepONet uses independent trunk networks to learn basis functions separately for different coordinate axes, enabling faster and more memory-efficient training via forward-mode automatic differentiation. We provide theoretical guarantees for SepONet using the universal approximation theorem and validate its performance through comprehensive benchmarking against PI-DeepONet. Our results demonstrate that for the 1D time-dependent advection equation, when targeting a mean relative $\ell_{2}$ error of less than 6% on 100 unseen variable coefficients, SepONet provides up to $112 \times$ training speed-up and $82 \times$ GPU memory usage reduction compared to PI-DeepONet. Similar computational advantages are observed across various partial differential equations, with SepONet's efficiency gains scaling favorably as problem complexity increases. This work paves the way for extreme-scale learning of continuous mappings between infinite-dimensional function spaces.

Offline reinforcement learning (RL) is a promising direction that allows RL agents to pre-train on large datasets, avoiding the recurrence of expensive data collection. To advance the field, it is crucial to generate large-scale datasets. Compositional RL is particularly appealing for generating such large datasets, since 1)~it permits creating many tasks from few components, 2)~the task structure may enable trained agents to solve new tasks by combining relevant learned components, and 3)~the compositional dimensions provide a notion of task relatedness. This paper provides four offline RL datasets for simulated robotic manipulation created using the $256$ tasks from CompoSuite [Mendez at al., 2022a]. Each dataset is collected from an agent with a different degree of performance, and consists of $256$ million transitions. We provide training and evaluation settings for assessing an agent's ability to learn compositional task policies. Our benchmarking experiments show that current offline RL methods can learn the training tasks to some extent and that compositional methods outperform non-compositional methods. Yet current methods are unable to extract the compositional structure to generalize to unseen tasks, highlighting a need for future research in offline compositional RL.

Scaling up neural models has yielded significant advancements in a wide array of tasks, particularly in language generation. Previous studies have found that the performance of neural models frequently adheres to predictable scaling laws, correlated with factors such as training set size and model size. This insight is invaluable, especially as large-scale experiments grow increasingly resource-intensive. Yet, such scaling law has not been fully explored in dense retrieval due to the discrete nature of retrieval metrics and complex relationships between training data and model sizes in retrieval tasks. In this study, we investigate whether the performance of dense retrieval models follows the scaling law as other neural models. We propose to use contrastive log-likelihood as the evaluation metric and conduct extensive experiments with dense retrieval models implemented with different numbers of parameters and trained with different amounts of annotated data. Results indicate that, under our settings, the performance of dense retrieval models follows a precise power-law scaling related to the model size and the number of annotations. Additionally, we examine scaling with prevalent data augmentation methods to assess the impact of annotation quality, and apply the scaling law to find the best resource allocation strategy under a budget constraint. We believe that these insights will significantly contribute to understanding the scaling effect of dense retrieval models and offer meaningful guidance for future research endeavors.

Graph Neural Networks (GNN) is an emerging field for learning on non-Euclidean data. Recently, there has been increased interest in designing GNN that scales to large graphs. Most existing methods use "graph sampling" or "layer-wise sampling" techniques to reduce training time. However, these methods still suffer from degrading performance and scalability problems when applying to graphs with billions of edges. This paper presents GBP, a scalable GNN that utilizes a localized bidirectional propagation process from both the feature vectors and the training/testing nodes. Theoretical analysis shows that GBP is the first method that achieves sub-linear time complexity for both the precomputation and the training phases. An extensive empirical study demonstrates that GBP achieves state-of-the-art performance with significantly less training/testing time. Most notably, GBP can deliver superior performance on a graph with over 60 million nodes and 1.8 billion edges in less than half an hour on a single machine.

The aim of this work is to develop a fully-distributed algorithmic framework for training graph convolutional networks (GCNs). The proposed method is able to exploit the meaningful relational structure of the input data, which are collected by a set of agents that communicate over a sparse network topology. After formulating the centralized GCN training problem, we first show how to make inference in a distributed scenario where the underlying data graph is split among different agents. Then, we propose a distributed gradient descent procedure to solve the GCN training problem. The resulting model distributes computation along three lines: during inference, during back-propagation, and during optimization. Convergence to stationary solutions of the GCN training problem is also established under mild conditions. Finally, we propose an optimization criterion to design the communication topology between agents in order to match with the graph describing data relationships. A wide set of numerical results validate our proposal. To the best of our knowledge, this is the first work combining graph convolutional neural networks with distributed optimization.

We introduce an approach for deep reinforcement learning (RL) that improves upon the efficiency, generalization capacity, and interpretability of conventional approaches through structured perception and relational reasoning. It uses self-attention to iteratively reason about the relations between entities in a scene and to guide a model-free policy. Our results show that in a novel navigation and planning task called Box-World, our agent finds interpretable solutions that improve upon baselines in terms of sample complexity, ability to generalize to more complex scenes than experienced during training, and overall performance. In the StarCraft II Learning Environment, our agent achieves state-of-the-art performance on six mini-games -- surpassing human grandmaster performance on four. By considering architectural inductive biases, our work opens new directions for overcoming important, but stubborn, challenges in deep RL.

Attention networks in multimodal learning provide an efficient way to utilize given visual information selectively. However, the computational cost to learn attention distributions for every pair of multimodal input channels is prohibitively expensive. To solve this problem, co-attention builds two separate attention distributions for each modality neglecting the interaction between multimodal inputs. In this paper, we propose bilinear attention networks (BAN) that find bilinear attention distributions to utilize given vision-language information seamlessly. BAN considers bilinear interactions among two groups of input channels, while low-rank bilinear pooling extracts the joint representations for each pair of channels. Furthermore, we propose a variant of multimodal residual networks to exploit eight-attention maps of the BAN efficiently. We quantitatively and qualitatively evaluate our model on visual question answering (VQA 2.0) and Flickr30k Entities datasets, showing that BAN significantly outperforms previous methods and achieves new state-of-the-arts on both datasets.

We investigate a lattice-structured LSTM model for Chinese NER, which encodes a sequence of input characters as well as all potential words that match a lexicon. Compared with character-based methods, our model explicitly leverages word and word sequence information. Compared with word-based methods, lattice LSTM does not suffer from segmentation errors. Gated recurrent cells allow our model to choose the most relevant characters and words from a sentence for better NER results. Experiments on various datasets show that lattice LSTM outperforms both word-based and character-based LSTM baselines, achieving the best results.