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Contrastive learning has recently achieved remarkable success in many domainsincluding graphs. However contrastive loss, especially for graphs, requires alarge number of negative samples which is unscalable and computationallyprohibitive with a quadratic time complexity. Sub-sampling is not optimal andincorrect negative sampling leads to sampling bias. In this work, we propose ameta-node based approximation technique that can (a) proxy all negativecombinations (b) in quadratic cluster size time complexity, (c) at graph level,not node level, and (d) exploit graph sparsity. By replacing node-pairs withadditive cluster-pairs, we compute the negatives in cluster-time at graphlevel. The resulting Proxy approximated meta-node Contrastive (PamC) loss,based on simple optimized GPU operations, captures the full set of negatives,yet is efficient with a linear time complexity. By avoiding sampling, weeffectively eliminate sample bias. We meet the criterion for larger number ofsamples, thus achieving block-contrastiveness, which is proven to outperformpair-wise losses. We use learnt soft cluster assignments for the meta-nodeconstriction, and avoid possible heterophily and noise added during edgecreation. Theoretically, we show that real world graphs easily satisfyconditions necessary for our approximation. Empirically, we show promisingaccuracy gains over state-of-the-art graph clustering on 6 benchmarks.Importantly, we gain substantially in efficiency; up to 3x in training time,1.8x in inference time and over 5x in GPU memory reduction.

Efficient block contrastive learning via parameter-free meta-node approximation