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Context: To overcome this challenge, we propose GMPool, a general pooling framework that does not require an universal number of clusters as a user hyperparameter. Figure 1 depicts the overall framework of GMPool. The core intuition is that the product of a pooling matrix with itself forms a grouping matrix, where each (i,j)-th entry indicates the pairwise clustering similarity: whether the nodes i and j are pooled to the same clusters. For each graph, GMPool parameterizes the clustering similarities in its grouping matrix via a classification layer. Finally, we perform SVD on the grouping matrix to obtain the pooling matrix such that the overall rank represents the suitable number of clusters. We also test a single-pooling variant NGMPool that does not perform any decomposition, but rather uses the grouping matrix as is. In real-world molecular property prediction tasks, we show that our approach outperforms previous baselines, while successfully learning suitable clusters. The main contributions of this paper are as follows:•We design a grouping matrix-based pooling operator that does not require users to specify the number of clusters a priori.•We propose GMPool and NGMPool. GMPool performs SVD on the grouping matrix to obtain the pooling matrix, whereas NGMPool utilizes the grouping matrix as is.•We demonstrate the power of our methods both quantitatively and qualitatively on a wide range of real molecular property prediction tasks.

Question: How does NGMPool work exactly? How is it different from GMPool?
NGMPool is a single-pooling variant of GMPool that does not perform SVD on the grouping matrix, but rather uses the grouping matrix as is.