max_num_elements

[erikhuck]

Several aggregation operators have this max_num_elements parameter with a definition of "The maximum number of elements within a single aggregation group". What is an "aggregation group"? A graph? What is an "element" in this context? A node?

[rusty1s]

Since Aggregation can be performed on all kinds of level, e.g., going from edge-level representations to node-level ones, or going from node-level representation to graph-level ones, we framed this rather generally.

Here, max_num_elements means the maximum size of elements aggregated into one group. For example, if you have a feature matrix with 6 elements, and index looks like [0, 0, 1, 1, 1, 2], then max_num_elements would be index.bincount().max() == 3.

[erikhuck]

@rusty1s In your example, there is a graph with 2 nodes, a graph with 3 nodes, and a graph with 1 node. All these graphs have a different number of nodes. My concern is that the AttentionalAggregation will exclude some of the nodes if the number of nodes surpasses this max_num_elements value. But it sounds like, in the case of the AttentionalAggregation, the max_num_elements does not have to do with the number of nodes in a graph, but the number of graphs?? What happens when max_num_elements is not specified?

[rusty1s]

If you do not specify max_num_elements it will be inferred via bincount().max(), and it will not drop any nodes. It will only drop nodes if you explicitly specify max_num_elements to be smaller than the maximum nodes in one of your graphs.

In general, you don't need to worry about setting this argument at all. The reason we introduced this argument in the first-place is due to compilation and to avoid a device sync between CPU and GPU.

[erikhuck]

@rusty1s Perfect! Related to this, I see this warning in other aggregation operators, e.g. the LSTMAggregation:
"LSTMAggregation is not a permutation-invariant operator." Do I understand correctly that this is said because the LSTM expects a certain number of elements (i.e. graph nodes) and some graphs have different numbers of nodes? In other words, all the graphs need to have the same number of nodes for the LSTMAggregation or nodes will be excluded? Can the AttentionalAggregation handle any number of graph nodes?

[rusty1s]

All aggregations can handle a varying number of nodes. The note refers to that within a group/neighborhood, the aggregation is not permutation-invariant, so you will get different outputs depending on how your neighborhood is sorted. This is due to the sequential nature of LSTMs. The AttentionalAggregation doesn't have this issue.