Graph neural networks (GNNs) have quickly become one of the most important tools in computational chemistry and molecular machine learning. GNNs are a type of deep learning architecture designed for the adaptive extraction of vectorial features directly from graph-shaped input data, such as low-level molecular graphs. The feature-extraction mechanism of most modern GNNs can be decomposed into two phases:

• Message-passing: In this phase the node feature vectors of the graph are iteratively updated following a trainable local neighbourhood-aggregation scheme often referred to as message-passing. Each iteration delivers a set of updated node feature vectors which is then imagined to form a new “layer” on top of all the previous sets of node feature vectors.
• Global graph pooling: After a sufficient number of layers has been computed, the updated node feature vectors are used to generate a single vectorial representation of the entire graph. This step is known as global graph readout or global graph pooling. Usually only the top layer (i.e. the final set of updated node feature vectors) is used for global graph pooling, but variations of this are possible that involve all computed graph layers and even the set of initial node feature vectors. Commonly employed global graph pooling strategies include taking the sum or the average of the node features in the top graph layer.

While a lot of research attention has been focused on designing novel and more powerful message-passing schemes for GNNs, the global graph pooling step has often been treated with relative neglect. As mentioned in my previous post on the issues of GNNs, I believe this to be problematic. Naive global pooling methods (such as simply summing up all final node feature vectors) can potentially form dangerous information bottlenecks within the neural graph learning pipeline. In the worst case, such information bottlenecks pose the risk of largely cancelling out the information signal delivered by the message-passing step, no matter how sophisticated the message-passing scheme.

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