The skip-gram model for learning word embeddings (Mikolov et al. 2013) has
been widely popular, and DeepWalk (Perozzi et al. 2014), among other methods,
has extended the model to learning node representations from networks. Recent
work of Qiu et al. (2018) provides a closed-form expression for the DeepWalk
objective, obviating the need for sampling for small datasets and improving
accuracy. In these methods, the "window size" T within which words or nodes are
considered to co-occur is a key hyperparameter. We study the objective in the
limit as T goes to infinity, which allows us to simplify the expression of Qiu
et al. We prove that this limiting objective corresponds to factoring a simple
transformation of the pseudoinverse of the graph Laplacian, linking DeepWalk to
extensive prior work in spectral graph embeddings. Further, we show that by a
applying a simple nonlinear entrywise transformation to this pseudoinverse, we
recover a good approximation of the finite-T objective and embeddings that are
competitive with those from DeepWalk and other skip-gram methods in multi-label
classification. Surprisingly, we find that even simple binary thresholding of
the Laplacian pseudoinverse is often competitive, suggesting that the core
advancement of recent methods is a nonlinearity on top of the classical
spectral embedding approach.

本研究通过对窗口大小 T 趋近于无限大的情形下，对 Qiu 等人的目标函数进行简化，证明了其将 DeepWalk 与谱图嵌入联系在一起的结论，并表明非线性性质是现有方法的核心进展。

InfiniteWalk：带有非线性的拉普拉斯嵌入的深度网络嵌入

InfiniteWalk: Deep Network Embeddings as Laplacian Embeddings with a  Nonlinearity

Just as semantic hashing can accelerate information retrieval, binary valued
embeddings can significantly reduce latency in the retrieval of graphical data.
We introduce a simple but effective model for learning such binary vectors for
nodes in a graph. By imagining the embeddings as independent coin flips of
varying bias, continuous optimization techniques can be applied to the
approximate expected loss. Embeddings optimized in this fashion consistently
outperform the quantization of both spectral graph embeddings and various
learned real-valued embeddings, on both ranking and pre-ranking tasks for a
variety of datasets.

通过将图表数据的嵌入视为不同偏置下的独立硬币翻转，应用持续优化技术来获得二元向量的简单且有效模型，得出了优于谱图嵌入和各种学习实值嵌入的量化结果，可以显著降低图表数据检索的延迟。