Recent work in graph neural networks (GNNs) has led to improvements in molecular activity and property prediction tasks. Unfortunately, GNNs often fail to capture the relative importance of interactions between molecular substructures, in part due to the absence of efficient intermediate pooling steps. To address these issues, we propose LaPool (Laplacian Pooling), a novel, data-driven, and interpretable hierarchical graph pooling method that takes into account both node features and graph structure to improve molecular understanding. We benchmark LaPool and show that it not only outperforms recent GNNs on molecular graph understanding and prediction tasks but also remains highly competitive on other graph types. We then demonstrate the improved interpretability achieved with LaPool using both qualitative and quantitative assessments, highlighting its potential applications in drug discovery.
This paper proposes a graph down-sampling component named LaPool. It uses the graph signal to dynamically select some "important" centroids and learn a sparse assignment matrix for clustering the remaining nodes.
This paper should be rejected due to the following reasons.
1. Strange new results compared with its previous version
The paper has a previous arxiv version. While the method does not change, the performance in this current submission has dramatic change compared with previous version: the proposed model seems much improved, while some important baselines (that outperform the proposed model) only have 50% of it previous performance in this submission.
For example, for Table 1 in the current version, the proposed model reached almost perfect scores in both F1 and AUC. However in previous version for the same setting and experiment (in Table 2 and 3 of its arxiv version), the performance are much lower especially the Structural alert prediction results.  Their previous results, which show the model does not perform better than DiffPool .
For the structural alert prediction results on DiffPool, below I copied and pasted the results from the arxiv version
                                  
Table 3: Structural alert prediction results 
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                                             Tox21                   |               ChEMBL
                       F1-macro F1-micro ROC-AUC F1-macro F1-micro ROC-AUC
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GIN                     78.9        68.3             72.6           93.6         76.7          59.2
DiffPool              79.2        68.0             75.6           94.5        83.3          59.3
Graph U-net      71.1        47.6             67.9           92.9        68.1          59.3
LaPooldistance 80.6        74.2             73.5           95.2        81.3          59.5
LaPoolunreg     81.3        72.8             74.1           94.1        75.8          58.9
LaPool3hop       79.1        71.6             74.8           93.8        75.0          59.1
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One example: 
(1) in the ICLR version, The F1 score for DiffPool is only 48.638 ± 9.916 on ChEMBL data (about 50% of its previous level) but F1 for the proposed method is improved. Why is that? 
(2) same as baseline  Graph U-net , the ICLR version reports F1 37.585 ± 2.978, why is that?
(3) same as GIN, in the ICLR version, F1 is only 31.759 ± 3.728, less than 50% of its previous level in arxiv version.
The author needs to justify this dramatic change.
2. Although LaPool can dynamically select centroids, for a dense graph such as a complete graph, only one centroid will remain there since there is only one node which has larger signal variation than all its neighbors, as shown in Eq. 4. This consequently hurts the model performance on more dense graphs. That may be why in Table 2, on dense data "DD", LaPool performs much worse than baseline DiffPool. Also on another dense data "FRANKENSTEIN", LaPool does not performs significantly better than DiffPool.
 
3, the evaluation of interpretability is not convincing. This paper considers  "interpretability as the degree to which a human (in this context, a medicinal chemist) can understand the cause of the model’s decision". Therefore, the conclusion that this model is more interpretable is based on only one person's subjective judgement.  Even so, from the scores the model does not outperform baseline "GIN" that much.