网络嵌入旨在学习网络中节点的低维度潜在表示,所学习到的特征表示可以用作基于图的各种任务的特征,例如分类,聚类,链路预测和可视化。

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网络嵌入在社交推荐和网络分析中得到了广泛的应用,如推荐系统、图异常检测等。然而,以前的大多数方法不能有效地处理大型图,这是由于(i)图上的计算通常是昂贵的,(ii)图的大小或向量的中间结果可能是非常大的,导致要在一台机器上处理。本文利用Apache Spark提出了一种高效的大型图上网络嵌入的分布式算法,该算法将一个图递归地划分为若干个小的子图来捕获节点的内部和外部结构信息,然后并行计算每个子图的网络嵌入。最后,通过聚合所有子图上的输出,以线性代价得到节点的嵌入。在那之后,我们在各种实验中证明了我们提出的方法能够在几个小时内处理拥有数十亿条边的图,并且比最先进的方法至少快4倍。在链路预测和节点分类任务方面分别提高了4.25%和4.27%。最后,我们将所提出的算法应用于腾讯的两款网络游戏中,分别应用好友推荐和项目推荐,在运行时间上提高了竞争者高达91.11%,在相应的评价指标上提高了12.80%。

https://arxiv.org/abs/2106.10620

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Recent advances show that neural networks embedded with physics-informed priors significantly outperform vanilla neural networks in learning and predicting the long term dynamics of complex physical systems from noisy data. Despite this success, there has only been a limited study on how to optimally combine physics priors to improve predictive performance. To tackle this problem we unpack and generalize recent innovations into individual inductive bias segments. As such, we are able to systematically investigate all possible combinations of inductive biases of which existing methods are a natural subset. Using this framework we introduce Variational Integrator Graph Networks - a novel method that unifies the strengths of existing approaches by combining an energy constraint, high-order symplectic variational integrators, and graph neural networks. We demonstrate, across an extensive ablation, that the proposed unifying framework outperforms existing methods, for data-efficient learning and in predictive accuracy, across both single and many-body problems studied in recent literature. We empirically show that the improvements arise because high order variational integrators combined with a potential energy constraint induce coupled learning of generalized position and momentum updates which can be formalized via the Partitioned Runge-Kutta method.

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