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Network data are ubiquitous in modern machine learning, with tasks ofinterest including node classification, node clustering and link prediction. Afrequent approach begins by learning an Euclidean embedding of the network, towhich algorithms developed for vector-valued data are applied. For largenetworks, embeddings are learned using stochastic gradient methods where thesub-sampling scheme can be freely chosen. Despite the strong empiricalperformance of such methods, they are not well understood theoretically. Ourwork encapsulates representation methods using a subsampling approach, such asnode2vec, into a single unifying framework. We prove, under the assumption thatthe graph is exchangeable, that the distribution of the learned embeddingvectors asymptotically decouples. Moreover, we characterize the asymptoticdistribution and provided rates of convergence, in terms of the latentparameters, which includes the choice of loss function and the embeddingdimension. This provides a theoretical foundation to understand what theembedding vectors represent and how well these methods perform on downstreamtasks. Notably, we observe that typically used loss functions may lead toshortcomings, such as a lack of Fisher consistency.

Asymptotics of Network Embeddings Learned via Subsampling